# Indefinite Integration with Logarithms and Substitution

1. Dec 6, 2009

### Brilliant

Hi, I missed a few days of my calculus class. I've managed to figure out how to use substitution to solve an indefinite integral, and can apply the log properties to some extent. I just can't figure out this problem.

1. The problem statement, all variables and given/known data
Find the indefinite integral:
$$\int{\frac{1}{x ln(x^3)}}dx$$

2. The attempt at a solution
Well, since d/dx ln(x) is u'/u I know something is kinda wack with the bottom. I first tried to substitute with u=x^3, but then du is 3x^2 and there is only x on the bottom not x squared. I then thought it might be backwards, since the x on bottom is like x^-1 and it would have an integral with a natural log in it, but that wasn't really working out either.

I'm pretty stumped, I've attempted it several times.

2. Dec 6, 2009

### grief

Hint: ln(x^3)=3ln(x).

3. Dec 6, 2009

### Brilliant

I hate it when that happens. so 1/3*ln|ln(x)|

Thanks grief!