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

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

To integrate 1/(x^2+1), we can use the substitution u = x^2 + 1. This gives us du/dx = 2x, or dx = du/(2x). Substituting these into the integral, we get:

∫ 1/(x^2+1) dx = ∫ 1/(u) * (1/(2x)) du
= (1/2) ∫ u^(-1/2) du
= (1/2) * 2(u^(1/2)) + C
= √(x^2+1) + C

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