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

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

To integrate (x^2+1)^2, use the substitution u = x^2 + 1. This will give us du/dx = 2x, which means that dx = du/2x. Substituting these into the integral, we get:

∫(x^2+1)^2 dx = ∫(u)^2 (du/2x)
= 1/2 ∫u^2 du
= 1/2 (u^3/3) + C
= 1/2 (x^2+1)^3/3 + C

Therefore, the integral of (x^2+1)^2 is (x^2+1)^3/6 + C.