x/(1+(x^4))?

Question

How to integrate that?
Thank you

Answer 1

I = (1/2) ∫ (2x) / ( 1 + x ² ) dx
Let u = x ²
du = 2x dx
I = (1/2) ∫ du / ( 1 + u ² )
I = (1/2) tan ^(-1) u + C
I = (1/2) tan ^(-1) x ² + C

Answer 2

∫ x/(1+x^4)dx

Use integration by substituion.
Let u = x²
du = 2xdx
(1/2)du = xdx

∫ x/(1+x^4)dx
= ∫(1/2)(1/(1+u²) du
= (1/2)arctan(u) + c
= (1/2)arctan(x²) + c