Integral of tan^2x/(x^2+1) ?

Question

jennychan12 · Answer

$$\int\limits \frac{ \tan^2 x }{ x^2+1 }dx$$

hartnn · Answer

put x = $\tan^{-1}y$
dx=... ?

jennychan12 · Answer

dx = 1/(1+x^2)

hartnn · Answer

i got stuck actually...i think product rule needs to be use here...

jennychan12 · Answer

product rule? isn't that only for derivatives? :0

anonymous · Answer

This problem would be a lot nicer if it was an arctan, but it's not right @jennychan12 ?

hartnn · Answer

this is not easy, even the uv (product) rule fails here. please verify the question ?

jennychan12 · Answer

no. there's no arctan in the question.

anonymous · Answer

If there is no arctan in the integral, then integration by parts will only make things worse, gradually with each term, I tried with the first 2 terms before I lost faith in that attempt. So an u-substitution sounds the most reasonable, but I don't see any way how it could be applied.

hartnn · Answer

same ^

anonymous · Answer

The denominator looks a bit like a sec^2(x) or like a hyperbolic function. But oh well.

jennychan12 · Answer

well the original question is 
If f is an antiderivative of $$\frac{ \tan^2 x }{ x^2+1 }$$ such that f(1)=1/2, then f(0)=?