# Homework Help: Indefinite integral involving arctan and ln

1. Apr 19, 2012

### appplejack

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

∫ 1/x arctan (lnx) dx

2. Relevant equations

3. The attempt at a solution
1.U substitution. SO u = ln x, du= 1/x dx
∫ arctan u du

2.by parts: u = arctan u du = 1/ 1+u^2
v = 1 dv = du

3. uv - ∫vdu = artan u - ∫ 1/ 1+u^2
= arctan u - artan u = 0

2. Apr 19, 2012

### Dick

If du=dv, then v=u, not v=1! I'd also suggest when you get to ∫ arctan u du and if you want to use u and v for the variables in the integration by parts you change that to ∫ arctan w dw. Otherwise the variable naming gets really confusing.

Last edited: Apr 19, 2012
3. Apr 19, 2012

### scurty

Also, u = arctan(u) du doesn't make sense! If you already did u-substitution, use v and w for integration by parts so your variables don't get mixed up.

4. Apr 19, 2012

### Dick

I think applejack meant u=arctan(u), which also doesn't make sense, and is part of the variable naming problem.

5. Apr 19, 2012

### scurty

You're right, he did, the du part is when he took the derivative.

I'm used to putting the four equations (u, dv, du, v) in a box shape in my scratch work so I always get confused when it is formatted poorly on websites. Regardless, in addition to changing the variable, there should have been a comma inserted there.