# Math Help - Integral

1. ## Integral

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

Any help?

Thanks

2. Originally Posted by usagi_killer
$\int \frac{x\log_e(x)}{\sqrt{x^2-1}} dx ~{\color{red}= I}$

Any help?

Thanks
first: use integration by parts with $u = \ln x$ and $dv = \frac x{\sqrt{x^2 - 1}}~dx$ to get

$I = \sqrt{x^2 - 1} \cdot \ln x - \int \frac {\sqrt{x^2 - 1}}x~dx$

Finish off the last integral with a trig sub of $x = \sec \theta$