- #1
GunnaSix
- 35
- 0
Homework Statement
Find or evaluate the integral using substitution first, then using integration by parts.
[tex]\int \ln (x^2 + 1) \, dx [/tex]
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?