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

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

To integrate (x+1)/(x^2+1), use substitution with u = x^2 + 1. Then du/dx = 2x, so dx = du/2x. Substituting these into the integral gives:

∫(x+1)/(x^2+1) dx = ∫(x+1)/(u) (du/2x)
= 1/2 ∫(1 + u^-1) du
= 1/2 (u + ln|u|) + C
= 1/2 (x^2 + 1 + ln|x^2 + 1|) + C

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

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