# Thread: Trouble with this integral

1. ## Trouble with this integral

Hi,

I'm trying to solve this integral:

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

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?

Thank you in advance

2. Originally Posted by noname
Hi,

I'm trying to solve this integral:

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

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?

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

3. Thank you

Now I feel a little silly