Evaluation of $\displaystyle \int \frac{x^2}{(x^4-1)\sqrt{x^4+1}}dx$
What I try : Using Substution, $\displaystyle x=\frac{1-t}{1+t}$ and $\displaystyle dx =\frac{2}{(1+t)^2}dt$ also using $\displaystyle x^4-1=\frac{2(1+6t^2+t^4}{(1+t)^4}dt$
And $\displaystyle dx=(4t+4t^3)$
So $\displaystyle I =\frac{1}{2}\int\frac{(1-t)^2}{(1+6t^2+t^4)\sqrt{t+t^3}}dt$
Now I did not understand How I solve it after that step.
Please have a look On that , Thanks