# Homework Help: Calculus II - Improper Integral Problem

1. Dec 1, 2012

### BaxterCorner

1. The problem statement, all variables and given/known data

Evaluate the integral: ∫(0 to ∞) [dv/((1+v^2)(1+tan^-1(v))]

2. Relevant equations

U-substitution, taking limit to evaluate improper integrals

3. The attempt at a solution

http://imgur.com/CjkRF
As you can see in the image, I try u-substitution and then take the integral. I end up with ln(0), though, because arctan(0) = 0. The correct answer is ln(1 + ∏/2), but I'm not sure how to get there.

Last edited: Dec 1, 2012
2. Dec 1, 2012

### LCKurtz

With your substitution the denominator is $1+u$, not just $u$. It works either way, but I would suggest the substitution $u=1+\arctan v$ in the first place.

3. Dec 1, 2012

### BaxterCorner

Sorry, I intended to write u = 1 + arctan(v), not u = arctan(v). The 1 goes to zero either way though, so I still have the same problem of getting ln(0).

4. Dec 1, 2012

### BaxterCorner

Nevermind, I see what you're saying, that would change the bounds. Thanks!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook