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
$\displaystyle \frac{\sin^2(x) }{1 + \sin^2(x) } = 1 - \frac{1}{ 1 + \sin^2(x)} $
and
$\displaystyle \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)} $
$\displaystyle = \frac{\sec^2(x)}{ 1 + 2 \tan^2(x) } $