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

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

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

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

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

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