# Antiderivative problem

1. Jul 8, 2010

### stau40

1. The problem statement, all variables and given/known data
I'm working on an infinite series problem and need to find the antiderivative of 1/((x(lnx)^3).

2. Relevant equations
u=lnx

3. The attempt at a solution
I know I have to use the substitution u=lnx, but I still can't figure out what the answer is. I know the antiderivative of 1/((x(lnx)) is ln(lnx) but the third power in my problem is giving me trouble. Any advice? Thanks!

2. Jul 8, 2010

### Bohrok

After the u-substitution, what is the integrand in terms of u now?

3. Jul 8, 2010

### stau40

It would be 1/(x(u)^3)

4. Jul 8, 2010

### Staff: Mentor

When you make a substitution, replace everything. Here you still have a factor of x remaining. If u = ln(x), what is x in terms of u? Also, and this is related, did you replace dx by its appropriate expression involving du?

5. Jul 8, 2010

### stau40

Ok, it should be the antiderivative of du/(u^3) but I still don't understand how to work thru the third power. If I solve for the antiderivative and end up with u^4 I would need (1/4) in front of u and that gets me to the wrong result.

6. Jul 8, 2010

### Staff: Mentor

Well, yes. You can't go from du/u^3 to u^4.

du/u^3 = u^(-3)du

7. Jul 8, 2010

### stau40

The light finally came on, Thanks!!!