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

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

Integrating x^2/(x^2+1) requires substitution. Let u = x^2+1, then du = 2x dx. Rewrite the integral in terms of u:

∫ x^2/(x^2+1) dx = ∫ (u-1)/(u) du

Simplify the integrand:

∫ (u-1)/(u) du = ∫ (u/u) - (1/u) du = ∫ 1 - 1/u du

Integrate each term separately:

∫ 1 - 1/u du = u - ln|u| + C

Substitute back in for u:

u - ln|u| + C = x^2+1 - ln|x^2+1| + C

Therefore, the integral of x^2/(x^2+1) is x^2+1 - ln|x^2+1| + C.