# Integration by Parts Problem

• Sep 13th 2009, 10:48 AM
uberbandgeek6
Integration by Parts Problem
According to the directions, I should be using u-substitution and integration by parts to find the indefinite integral of:

x ln(1 + x) dx

This is the only problem that I am having an immense amount of trouble with. It seems useless to use any u-substitution (at least at this point). I tried to use integration by parts with u = ln(1 + x) and dv = x dx, but that gave me an integral of (x^2)/(1 + x) which I cannot seem to make go anywhere from that. Am I approaching this problem the wrong way?
• Sep 13th 2009, 11:13 AM
stapel
If u = 1 + x, then you have x = u - 1, ln(1 + x) = ln(u), and du = dx.... (Wink)
• Sep 13th 2009, 11:22 AM
skeeter
Quote:

Originally Posted by uberbandgeek6
According to the directions, I should be using u-substitution and integration by parts to find the indefinite integral of:

x ln(1 + x) dx

This is the only problem that I am having an immense amount of trouble with. It seems useless to use any u-substitution (at least at this point). I tried to use integration by parts with u = ln(1 + x) and dv = x dx, but that gave me an integral of (x^2)/(1 + x) which I cannot seem to make go anywhere from that. Am I approaching this problem the wrong way?

$\frac{x^2}{1+x} = \frac{x^2-1+1}{1+x} = x - 1 + \frac{1}{1+x}$