Mister Exam
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of e^(2-x)
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of (2*x-1)^2
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Derivative of (2x+3)^2
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Identical expressions
- sqrt((one -sin(2x))/(one +sin(2x)))
- square root of ((1 minus sinus of (2x)) divide by (1 plus sinus of (2x)))
- square root of ((one minus sinus of (2x)) divide by (one plus sinus of (2x)))
- √((1-sin(2x))/(1+sin(2x)))
- sqrt1-sin2x/1+sin2x
- sqrt((1-sin(2x)) divide by (1+sin(2x)))
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Similar expressions
- sqrt((1+sin(2x))/(1+sin(2x)))
- sqrt((1-sin(2x))/(1-sin(2x)))
Derivative of sqrt((1-sin(2x))/(1+sin(2x)))
The solution
You have entered
[src]
______________ / 1 - sin(2*x) / ------------ \/ 1 + sin(2*x)
$$\sqrt{\frac{- \sin{\left(2 x \right)} + 1}{\sin{\left(2 x \right)} + 1}}$$
/ ______________\ d | / 1 - sin(2*x) | --| / ------------ | dx\\/ 1 + sin(2*x) /
$$\frac{d}{d x} \sqrt{\frac{- \sin{\left(2 x \right)} + 1}{\sin{\left(2 x \right)} + 1}}$$
Detail solution
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Let .
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Apply the power rule: goes to
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Then, apply the chain rule. Multiply by :
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Apply the quotient rule, which is:
and .
To find :
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Differentiate term by term:
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The derivative of the constant is zero.
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The derivative of a constant times a function is the constant times the derivative of the function.
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Let .
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The derivative of sine is cosine:
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Then, apply the chain rule. Multiply by :
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the power rule: goes to
So, the result is:
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The result of the chain rule is:
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So, the result is:
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The result is:
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To find :
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Differentiate term by term:
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The derivative of the constant is zero.
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Let .
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The derivative of sine is cosine:
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Then, apply the chain rule. Multiply by :
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The derivative of a constant times a function is the constant times the derivative of the function.
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Apply the power rule: goes to
So, the result is:
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The result of the chain rule is:
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The result is:
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Now plug in to the quotient rule:
The result of the chain rule is:
Now simplify:
The answer is:
The first derivative
[src]
______________
/ 1 - sin(2*x) / cos(2*x) (1 - sin(2*x))*cos(2*x)\
/ ------------ *(1 + sin(2*x))*|- ------------ - -----------------------|
\/ 1 + sin(2*x) | 1 + sin(2*x) 2 |
\ (1 + sin(2*x)) /
----------------------------------------------------------------------------
1 - sin(2*x)
$$\frac{\sqrt{\frac{- \sin{\left(2 x \right)} + 1}{\sin{\left(2 x \right)} + 1}} \left(- \frac{\left(- \sin{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{\cos{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \left(\sin{\left(2 x \right)} + 1\right)}{- \sin{\left(2 x \right)} + 1}$$
The second derivative
[src]
/ 2 \
| / -1 + sin(2*x)\ 2 2 / -1 + sin(2*x)\ 2 / -1 + sin(2*x)\ |
___________________ | 2 |-1 + -------------| *cos (2*x) 2*cos (2*x)*|-1 + -------------| 2*cos (2*x)*|-1 + -------------| 2 |
/ -(-1 + sin(2*x)) | 4*cos (2*x) \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ 2*(-1 + sin(2*x))*sin(2*x) \ 1 + sin(2*x)/ 4*cos (2*x)*(-1 + sin(2*x))|
/ ----------------- *|-2*sin(2*x) - ------------ + ------------------------------- - -------------------------------- + -------------------------- + -------------------------------- + ---------------------------|
\/ 1 + sin(2*x) | 1 + sin(2*x) -1 + sin(2*x) 1 + sin(2*x) 1 + sin(2*x) -1 + sin(2*x) 2 |
\ (1 + sin(2*x)) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
-1 + sin(2*x)
$$\frac{\sqrt{- \frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1}} \left(\frac{\left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} - \frac{2 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{4 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - 2 \sin{\left(2 x \right)} - \frac{4 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1}$$
The third derivative
[src]
/ / 2 2 \ / 2 2 \ / 2 2 \ \
| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 3 2 / -1 + sin(2*x)\ | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 |
| 8*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 8*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| / -1 + sin(2*x)\ 2 2 / -1 + sin(2*x)\ / -1 + sin(2*x)\ 2 6*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| / -1 + sin(2*x)\ / -1 + sin(2*x)\ / -1 + sin(2*x)\ 2 2 / -1 + sin(2*x)\|
___________________ | | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 | 2 |-1 + -------------| *cos (2*x) 2 8*cos (2*x)*|-1 + -------------| 6*|-1 + -------------| *cos (2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | 4*|-1 + -------------|*sin(2*x) 4*|-1 + -------------|*sin(2*x) 6*|-1 + -------------| *cos (2*x) 8*cos (2*x)*|-1 + -------------||
/ -(-1 + sin(2*x)) | \ (1 + sin(2*x)) / 4*(-1 + sin(2*x)) \ (1 + sin(2*x)) / 24*sin(2*x) 24*cos (2*x) \ 1 + sin(2*x)/ 24*cos (2*x)*(-1 + sin(2*x)) 24*(-1 + sin(2*x))*sin(2*x) \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/|
/ ----------------- *|-4 - ------------------------------------------------------------------------------------- + ----------------- + ------------------------------------------------------------------------------------- + ------------ + --------------- - ------------------------------- - ---------------------------- - --------------------------- - -------------------------------- - --------------------------------- - ---------------------------------------------------------------------------------------------------------- - ------------------------------- + ------------------------------- + --------------------------------- + --------------------------------|*cos(2*x)
\/ 1 + sin(2*x) | -1 + sin(2*x) 1 + sin(2*x) 1 + sin(2*x) 1 + sin(2*x) 2 2 3 2 2 2 -1 + sin(2*x) -1 + sin(2*x) 1 + sin(2*x) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) |
\ (1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
-1 + sin(2*x)
$$\frac{\sqrt{- \frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1}} \left(- \frac{\left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{6 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{6 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{4 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1} - \frac{4 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} + \frac{8 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{8 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{4 \left(\sin{\left(2 x \right)} - 1\right)}{\sin{\left(2 x \right)} + 1} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 4 + \frac{8 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} + 1} + \frac{24 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{24 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{8 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1}\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1}$$
5-th derivative
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/ 2 2 2 \
| / 2 2 \ / 2 2 \ / 2 2 4 4 2 2 2 2 \ / 2 2 \ / 2 2 4 4 2 2 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 4 4 2 2 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ 2 / 2 2 \ / 2 2 \ / 2 2 \ 3 / 2 2 \ 2 / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ 2 / 2 2 \ / 2 2 \ / 2 2 \|
| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| | 8*cos (2*x) 6*sin (2*x) 24*cos (2*x) (-1 + sin(2*x))*sin(2*x) 24*cos (2*x)*(-1 + sin(2*x)) 6*sin (2*x)*(-1 + sin(2*x)) 8*cos (2*x)*(-1 + sin(2*x)) 36*cos (2*x)*sin(2*x) 36*cos (2*x)*(-1 + sin(2*x))*sin(2*x)| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| | 8*cos (2*x) 6*sin (2*x) 24*cos (2*x) (-1 + sin(2*x))*sin(2*x) 24*cos (2*x)*(-1 + sin(2*x)) 6*sin (2*x)*(-1 + sin(2*x)) 8*cos (2*x)*(-1 + sin(2*x)) 36*cos (2*x)*sin(2*x) 36*cos (2*x)*(-1 + sin(2*x))*sin(2*x)| 5 2 2 | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 3 | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| / -1 + sin(2*x)\ 4 2 / -1 + sin(2*x)\ | 8*cos (2*x) 6*sin (2*x) 24*cos (2*x) (-1 + sin(2*x))*sin(2*x) 24*cos (2*x)*(-1 + sin(2*x)) 6*sin (2*x)*(-1 + sin(2*x)) 8*cos (2*x)*(-1 + sin(2*x)) 36*cos (2*x)*sin(2*x) 36*cos (2*x)*(-1 + sin(2*x))*sin(2*x)| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| 2 / -1 + sin(2*x)\ | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 / -1 + sin(2*x)\ 2 | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| / -1 + sin(2*x)\ | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| 2 3 2 3 / -1 + sin(2*x)\ 2 | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 4 / -1 + sin(2*x)\ 2 | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| 3 2 / -1 + sin(2*x)\ | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 2 / -1 + sin(2*x)\ | -1 + sin(2*x) 6*sin(2*x) 6*cos (2*x) 6*cos (2*x)*(-1 + sin(2*x)) 6*(-1 + sin(2*x))*sin(2*x)| 2 / -1 + sin(2*x)\ | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 3 / -1 + sin(2*x)\ 2 | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| / -1 + sin(2*x)\ | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))| 2 2 / -1 + sin(2*x)\ | 2*cos (2*x) (-1 + sin(2*x))*sin(2*x) 2*cos (2*x)*(-1 + sin(2*x))||
| 160*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 64*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 64*|-sin(2*x) - ------------ + ------------ + --------------- + ------------------------ - ---------------------------- - --------------------------- + --------------------------- + --------------------- - -------------------------------------| 64*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 64*|-sin(2*x) - ------------ + ------------ + --------------- + ------------------------ - ---------------------------- - --------------------------- + --------------------------- + --------------------- - -------------------------------------| / -1 + sin(2*x)\ 4 / -1 + sin(2*x)\ 4 4 / -1 + sin(2*x)\ 384*cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 384*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x) / -1 + sin(2*x)\ 4 96*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|*sin(2*x) 2 / -1 + sin(2*x)\ 60*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| *|-1 + -------------| / -1 + sin(2*x)\ 4 / -1 + sin(2*x)\ / -1 + sin(2*x)\ / -1 + sin(2*x)\ 2 40*|-1 + -------------|*|-sin(2*x) - ------------ + ------------ + --------------- + ------------------------ - ---------------------------- - --------------------------- + --------------------------- + --------------------- - -------------------------------------| 80*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------| 96*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------|*sin(2*x) 2 / -1 + sin(2*x)\ 160*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 192*cos (2*x)*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------| 2 / -1 + sin(2*x)\ 560*cos (2*x)*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| / -1 + sin(2*x)\ 2 200*|-1 + -------------| *cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 200*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x) 192*cos (2*x)*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------| / -1 + sin(2*x)\ 4 2 / -1 + sin(2*x)\ / -1 + sin(2*x)\ 4 / -1 + sin(2*x)\ 2 / -1 + sin(2*x)\ 2 20*|-1 + -------------| *cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| / -1 + sin(2*x)\ 4 40*|-1 + -------------| *cos (2*x)*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------| 2 / -1 + sin(2*x)\ / -1 + sin(2*x)\ 4 200*cos (2*x)*|-1 + -------------|*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------| 384*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x) 4 / -1 + sin(2*x)\ 384*cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| / -1 + sin(2*x)\ 4 200*cos (2*x)*|-1 + -------------|*|-1 + ------------- + ------------ + --------------- - --------------------------- - --------------------------| 160*cos (2*x)*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| / -1 + sin(2*x)\ 2 / -1 + sin(2*x)\ 2 200*|-1 + -------------| *cos (2*x)*|-sin(2*x) - ------------ + ------------------------ + ---------------------------| 200*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------|*sin(2*x) / -1 + sin(2*x)\ 2 2 / -1 + sin(2*x)\ 720*cos (2*x)*|-1 + -------------|*|-sin(2*x) - ------------ + ------------------------ + ---------------------------||
___________________ | 2 | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 3 1 + sin(2*x) 4 2 2 2 3 | | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 3 1 + sin(2*x) 4 2 2 2 3 | 2 4 |-1 + -------------| *cos (2*x) 4 2 400*|-1 + -------------| *cos (2*x) 384*cos (2*x)*|-1 + -------------| | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 | 140*|-1 + -------------| *cos (2*x) | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | 96*sin (2*x)*|-1 + -------------| | 1 + sin(2*x) 1 + sin(2*x) 2 | \ 1 + sin(2*x)/ 20*|-1 + -------------| *cos (2*x) 16*|-1 + -------------|*sin(2*x) 16*|-1 + -------------|*sin(2*x) 40*|-1 + -------------| *cos (2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 3 1 + sin(2*x) 4 2 2 2 3 | | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | 128*cos (2*x)*|-1 + -------------| | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | 2 2 2 576*cos (2*x)*|-1 + -------------|*sin(2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | 320*|-1 + -------------| *cos (2*x)*sin(2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | 160*|-1 + -------------| *cos (2*x) 128*cos (2*x)*|-1 + -------------| 60*|-1 + -------------| *cos (2*x) 40*|-1 + -------------| *cos (2*x) 40*|-1 + -------------| *cos (2*x)*sin(2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | 20*|-1 + -------------| *cos (2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | 96*sin (2*x)*|-1 + -------------| 200*|-1 + -------------| *cos (2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | | 1 + sin(2*x) 1 + sin(2*x) 2 | 384*cos (2*x)*|-1 + -------------| | 1 + sin(2*x) 1 + sin(2*x) 2 | 560*|-1 + -------------| *cos (2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 3 2 | \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | 80*|-1 + -------------| *cos (2*x)*sin(2*x) 40*|-1 + -------------| *cos (2*x)*sin(2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 | 400*|-1 + -------------| *cos (2*x)*sin(2*x) 576*cos (2*x)*|-1 + -------------|*sin(2*x) \ 1 + sin(2*x)/ | 1 + sin(2*x) 1 + sin(2*x) 2 ||
/ -(-1 + sin(2*x)) | 960*cos (2*x) 480*sin(2*x) \ (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / 16*(-1 + sin(2*x)) \ (1 + sin(2*x)) / \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / 1440*sin (2*x) 1920*cos (2*x) \ 1 + sin(2*x)/ 1920*cos (2*x)*(-1 + sin(2*x)) 1440*sin (2*x)*(-1 + sin(2*x)) \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / 480*(-1 + sin(2*x))*sin(2*x) 960*cos (2*x)*(-1 + sin(2*x)) 3840*cos (2*x)*sin(2*x) 3840*cos (2*x)*(-1 + sin(2*x))*sin(2*x) \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) / \ (1 + sin(2*x)) / \ 1 + sin(2*x)/ \ 1 + sin(2*x)/ \ (1 + sin(2*x)) /|
/ ----------------- *|16 - --------------- - ------------ - ---------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------ + -------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------- + --------------- - ------------------------------- - ------------------------------ - ------------------------------ - ----------------------------------- - 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--------------------------------------- - ------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- - -------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------- - ---------------------------------- - ---------------------------------- - ---------------------------------- - ------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- + ---------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------- + ----------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ + ---------------------------------- + ------------------------------------------------------------------------------------------------- + ----------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------- + -------------------------------------------- + ------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------|*cos(2*x)
\/ 1 + sin(2*x) | 2 1 + sin(2*x) 2 1 + sin(2*x) 1 + sin(2*x) 1 + sin(2*x) -1 + sin(2*x) -1 + sin(2*x) 2 4 4 5 3 4 4 3 2 4 1 + sin(2*x) 2 2 4 1 + sin(2*x) -1 + sin(2*x) 2 -1 + sin(2*x) -1 + sin(2*x) -1 + sin(2*x) 2 (1 + sin(2*x))*(-1 + sin(2*x)) 2 2 3 3 4 3 3 3 3 2 (1 + sin(2*x))*(-1 + sin(2*x)) 2 2 (1 + sin(2*x))*(-1 + sin(2*x)) 2 2 (1 + sin(2*x))*(-1 + sin(2*x)) 3 3 3 2 (1 + sin(2*x))*(-1 + sin(2*x)) 3 2 (1 + sin(2*x))*(-1 + sin(2*x)) 3 2 3 (1 + sin(2*x))*(-1 + sin(2*x)) 2 2 2 2 (1 + sin(2*x))*(-1 + sin(2*x)) 2 2 2 |
\ (1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x)) *(-1 + sin(2*x)) (1 + sin(2*x)) *(-1 + sin(2*x)) (-1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x)) *(-1 + sin(2*x)) (1 + sin(2*x)) *(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) (1 + sin(2*x))*(-1 + sin(2*x)) /
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-1 + sin(2*x)
$$\frac{\sqrt{- \frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1}} \left(- \frac{\left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{5} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} + \frac{20 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{4} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{20 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{4} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{60 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{20 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} - \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{140 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{3} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{80 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} + \frac{400 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{160 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} - \frac{320 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} + \frac{560 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{400 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right)^{2} \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} - \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{16 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{40 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{8 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{36 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \sin{\left(2 x \right)} + \frac{6 \sin^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{8 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{36 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{24 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}}\right)}{\sin{\left(2 x \right)} - 1} + \frac{16 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} + \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{128 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{160 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{60 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)^{2}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{200 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{128 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{720 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} + \frac{576 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{560 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} - \frac{576 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}} + \frac{384 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{384 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{4}} - \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{80 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right)}{\sin{\left(2 x \right)} - 1} + \frac{96 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1} - \frac{192 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{192 \left(\frac{\sin{\left(2 x \right)} - 1}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - 1 + \frac{6 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{6 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{16 \left(\sin{\left(2 x \right)} - 1\right)}{\sin{\left(2 x \right)} + 1} + \frac{480 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{1440 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} + \frac{960 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{3840 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \frac{1920 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{5}} + 16 - \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} + 1} - \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{8 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{36 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \sin{\left(2 x \right)} + \frac{6 \sin^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{8 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{36 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{24 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}}\right)}{\sin{\left(2 x \right)} + 1} - \frac{480 \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{1440 \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{960 \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{3840 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} + \frac{1920 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} + \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)}{\sin{\left(2 x \right)} - 1} + \frac{64 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{6 \left(\sin{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{8 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \frac{36 \left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}} - \frac{24 \left(\sin{\left(2 x \right)} - 1\right) \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{4}} - \sin{\left(2 x \right)} + \frac{6 \sin^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} - \frac{8 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{36 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} + \frac{24 \cos^{4}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{3}}\right)}{\sin{\left(2 x \right)} - 1} + \frac{160 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)^{2}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} + \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right) \left(\sin{\left(2 x \right)} + 1\right)} - \frac{160 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right)^{2}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} - \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \sin{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2}} + \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{2} \left(\sin{\left(2 x \right)} + 1\right)} - \frac{384 \left(\frac{\left(\sin{\left(2 x \right)} - 1\right) \sin{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1} + \frac{2 \left(\sin{\left(2 x \right)} - 1\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} + 1\right)^{2}} - \sin{\left(2 x \right)} - \frac{2 \cos^{2}{\left(2 x \right)}}{\sin{\left(2 x \right)} + 1}\right) \cos^{2}{\left(2 x \right)}}{\left(\sin{\left(2 x \right)} - 1\right)^{3}}\right) \cos{\left(2 x \right)}}{\sin{\left(2 x \right)} - 1}$$
The graph