# Math Help - Help with hard integral

1. ## Help with hard integral

Hello, this is one of my homework problem, and it's pretty difficult, since I have to use arctan, but I can't figure out how to use it here.. And help would be appreciated.

Find the integral of:

(sin(x))^2 / ( 1 + (sin(x))^2 )

2. Originally Posted by hashshashin715
Hello, this is one of my homework problem, and it's pretty difficult, since I have to use arctan, but I can't figure out how to use it here.. And help would be appreciated.

Find the integral of:

(sin(x))^2 / ( 1 + (sin(x))^2 )

Consider

$\frac{\sin^2(x) }{1 + \sin^2(x) } = 1 - \frac{1}{ 1 + \sin^2(x)}$

and

$\frac{1}{ 1 + \sin^2(x) } = \frac{ 1}{ \sin^2(x) + \cos^2(x) + \sin^2(x) } = \frac{1}{ \cos^2(x) + 2\sin^2(x)}$

$= \frac{\sec^2(x)}{ 1 + 2 \tan^2(x) }$

3. Thanks so much

4. Also, the series of substitutions $x=\arcsin(y)$ and then $y^2=1-z^2$ may be enlightening.