calculus - Need some advice to solve this integral $intfrac{sin^2x}{1+sin^2x}mathrm dx$

I'm trying to use this subtitution $t=\tan(x/2)$. But I don´t get anywhere. I've tried $t=\tan(x)$ too. Appreciate your help.

$$\int\dfrac{\sin^2x}{1+\sin^2x}\mathrm dx$$

Answer

You can use the substitution $x=\arctan(t/2)$ and you will need the identity

$$\sin( \arctan(t/2) ) = \frac{t}{\sqrt{t^2+1}}$$

to reach the form

$$I= \int \frac{t^2}{(t^2+2)(t^2+4)}dt.$$

I think you can finish it now!