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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(3x²-1)^4
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Integral of x*sin(x)^2
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Integral of dx/(5-12*x-9*x^2)
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Integral of 4/x^2
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Identical expressions
- one /(three +2cos(3x)-sin(3x))
- 1 divide by (3 plus 2 co sinus of e of (3x) minus sinus of (3x))
- one divide by (three plus 2 co sinus of e of (3x) minus sinus of (3x))
- 1/3+2cos3x-sin3x
- 1 divide by (3+2cos(3x)-sin(3x))
- 1/(3+2cos(3x)-sin(3x))dx
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Similar expressions
- 1/(3-2cos(3x)-sin(3x))
- 1/(3+2cos(3x)+sin(3x))
Integral of 1/(3+2cos(3x)-sin(3x)) dx
The solution
You have entered
[src]
1 / | | 1 | ------------------------- dx | 3 + 2*cos(3*x) - sin(3*x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(2 \cos{\left(3 x \right)} + 3\right) - \sin{\left(3 x \right)}}\, dx$$
Integral(1/(3 + 2*cos(3*x) - sin(3*x)), (x, 0, 1))
The answer (Indefinite)
[src]
/ /3*x\\ / pi 3*x\
| tan|---|| |- -- + ---|
/ | 1 \ 2 /| | 2 2 |
| atan|- - + --------| pi*floor|----------|
| 1 \ 2 2 / \ pi /
| ------------------------- dx = C + -------------------- + --------------------
| 3 + 2*cos(3*x) - sin(3*x) 3 3
|
/
$$\int \frac{1}{\left(2 \cos{\left(3 x \right)} + 3\right) - \sin{\left(3 x \right)}}\, dx = C + \frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{3 x}{2} \right)}}{2} - \frac{1}{2} \right)}}{3} + \frac{\pi \left\lfloor{\frac{\frac{3 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor}{3}$$
The graph
The answer
[src]
/1 tan(3/2)\
atan|- - --------|
\2 2 / atan(1/2)
- ------------------ + ---------
3 3
$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3} - \frac{\operatorname{atan}{\left(\frac{1}{2} - \frac{\tan{\left(\frac{3}{2} \right)}}{2} \right)}}{3}$$
=
=
/1 tan(3/2)\
atan|- - --------|
\2 2 / atan(1/2)
- ------------------ + ---------
3 3
$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3} - \frac{\operatorname{atan}{\left(\frac{1}{2} - \frac{\tan{\left(\frac{3}{2} \right)}}{2} \right)}}{3}$$
-atan(1/2 - tan(3/2)/2)/3 + atan(1/2)/3
Use the examples entering the upper and lower limits of integration.