What are the steps to integrate x/(1+x^4)?

Question

I have the answer ( arctan(x^2)/2 ) but I would like to know the steps to solving it.

Answer 1

If you make the substitution

u=x^2,

then du/dx=2x or du=2x dx

and the integral becomes
integral 1/2 du / (1+u^2)
which leads to the given answer.

Answer 2

Use the substitution u = x^2. Then du = 2x dx and you end up with the integral of
(1/2) du/(1 + u^2)

Answer 3

x^2 = tan(u)
x dx = sec^2(u) du/2
the integral then becomes
int sec^2(u)/(1+tan^2(u)) du/2
= u/2 = tan^-1(x^2)/2 + C