Question

Solve: $\int \frac{2x{\tan }^{-1}{x}^2}{(1+x^4)}dx$

Answer 1

$I=\int \frac{2x.ta{n}^{-1}\left(x^2\right)dx}{1+x^4}$

put tan${}^{-1}\left(x^2\right)=t$

Differentiating.

$\left(\frac{1}{1+x^4}\right)2x.dx=dt$

$\therefore I=\int t.dt$

$=\frac{t^2}{2}+c$

$=\frac{1}{2}{\left[ta{n}^{-1}\right(x^2\left)\right]}^2+c$