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How to use it?
- Integral of d{x}:
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Integral of arcsin
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Integral of 1/(2*x)
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Integral of 1/(sqrt(1+x^2))
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Integral of x^3/(x^2+1)
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Identical expressions
- dx/(sin(x)+cos(x))^ two
- dx divide by ( sinus of (x) plus co sinus of e of (x)) squared
- dx divide by ( sinus of (x) plus co sinus of e of (x)) to the power of two
- dx/(sin(x)+cos(x))2
- dx/sinx+cosx2
- dx/(sin(x)+cos(x))²
- dx/(sin(x)+cos(x)) to the power of 2
- dx/sinx+cosx^2
- dx divide by (sin(x)+cos(x))^2
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Similar expressions
- dx/(sin(x)-cos(x))^2
- dx/(sinx+cosx)^2
Integral of dx/(sin(x)+cos(x))^2 dx
The solution
You have entered
[src]
pi -- 3 / | | 1 | ------------------ dx | 2 | (sin(x) + cos(x)) | / 0
$$\int\limits_{0}^{\frac{\pi}{3}} \frac{1}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\, dx$$
Integral(1/((sin(x) + cos(x))^2), (x, 0, pi/3))
The answer (Indefinite)
[src]
/ /x\ | 2*tan|-| | 1 \2/ | ------------------ dx = C - ----------------------- | 2 2/x\ /x\ | (sin(x) + cos(x)) -1 + tan |-| - 2*tan|-| | \2/ \2/ /
$$\int \frac{1}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\, dx = C - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1}$$
The graph
The answer
[src]
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-2*\/ 3
-----------------
/ ___\
| 2 2*\/ 3 |
3*|- - - -------|
\ 3 3 /
$$- \frac{2 \sqrt{3}}{3 \left(- \frac{2 \sqrt{3}}{3} - \frac{2}{3}\right)}$$
=
=
___
-2*\/ 3
-----------------
/ ___\
| 2 2*\/ 3 |
3*|- - - -------|
\ 3 3 /
$$- \frac{2 \sqrt{3}}{3 \left(- \frac{2 \sqrt{3}}{3} - \frac{2}{3}\right)}$$
-2*sqrt(3)/(3*(-2/3 - 2*sqrt(3)/3))
Use the examples entering the upper and lower limits of integration.