How to integrate x/(x^2+1)^2?

To integrate x/(x^2+1)^2, use substitution with u = x^2 + 1.

Substitute u = x^2 + 1, then du/dx = 2x, so dx = du/2x.
Rewrite the integral in terms of u: ∫(x/(x^2+1)^2)dx = ∫(1/(2(u)^2))du.
Integrate using the power rule: ∫(1/(2(u)^2))du = -1/(2u) + C.
Substitute back in for u: -1/(2(x^2+1)) + C.