# Thread: Trouble with this integral

1. ## Trouble with this integral

Hi,

I'm trying to solve this integral:

$\displaystyle \int \frac{dx}{x(log^2x-1)}$

The integration by parts makes the integral more difficult.

The integration by substitution brings me to this solution (show steps):
http://www.wolframalpha.com/input/?i=integrate+1%2F%28x%28%28logx%29^2-1%29%29

But we don't study hyperbolic functions. There must be another way to solve this exercise...

Any hint?

2. Originally Posted by noname
Hi,

I'm trying to solve this integral:

$\displaystyle \int \frac{dx}{x(log^2x-1)}$

The integration by parts makes the integral more difficult.

The integration by substitution brings me to this solution (show steps):
http://www.wolframalpha.com/input/?i=integrate+1%2F%28x%28%28logx%29^2-1%29%29

But we don't study hyperbolic functions. There must be another way to solve this exercise...

Any hint?

Hint: Let $\displaystyle u=\ln(x)$, and then figure out how to apply a partial fraction decomposition.