(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find or evaluate the integral using substitution first, then using integration by parts.

[tex]\int \ln (x^2 + 1) \, dx [/tex]

3. The attempt at a solution

[tex]Let \: u = x^2 + 1[/tex]

[tex]du = 2x \, dx[/tex]

[tex]dx = \pm \frac{du}{2 \sqrt{u - 1}}[/tex]

Then

[tex]\int \ln (x^2 + 1) \, dx = \pm \frac{1}{2} \int \frac{\ln u}{\sqrt{u-1}}\, du[/tex]

I don't know where to go from here. I tried to integrate by parts and it just turned into a mess. Am I approaching this the wrong way?

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# Homework Help: Integration by Parts

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