What is the Integral of ln(2x+1)?

[Sczisnad]

Homework Statement

integral ln(2x+1)dx

Homework Equations

N/A

The Attempt at a Solution

I tried integration by parts,

Let u = ln(2x+1), dv = dx, du = 2/(2x+1)dx, v = x

ln(2x+1)dx = ln(2x+1)*x-(integral)x*(2/(2x+1))dx

 

[foxjwill]

Try u-substitution with $u=2x+1$.

 

[Mark44]

Homework Statement

integral ln(2x+1)dx

Homework Equations

N/A

The Attempt at a Solution

I tried integration by parts,

Let u = ln(2x+1), dv = dx, du = 2/(2x+1)dx, v = x

ln(2x+1)dx = ln(2x+1)*x-(integral)x*(2/(2x+1))dx

So far, so good. The last integral can be turned into a simpler one by dividing 2x by 2x + 1, using polynomial long division. If you don't know that technique, it works out to 1 + -1/(2x + 1) in this problem.

 

[mathstew]

Try u subsitution (the obvious one...)