Calculus II - Improper Integral Problem

[BaxterCorner]

Homework Statement

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

Homework Equations

U-substitution, taking limit to evaluate improper integrals

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.

 

[LCKurtz]

Homework Statement

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

Homework Equations

U-substitution, taking limit to evaluate improper integrals

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.

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.

 

[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).

 

[BaxterCorner]

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