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!
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