$\displaystyle \int \frac{x\log_e(x)}{\sqrt{x^2-1}} dx$
Any help?
Thanks
first: use integration by parts with $\displaystyle u = \ln x$ and $\displaystyle dv = \frac x{\sqrt{x^2 - 1}}~dx$ to get
$\displaystyle I = \sqrt{x^2 - 1} \cdot \ln x - \int \frac {\sqrt{x^2 - 1}}x~dx$
Finish off the last integral with a trig sub of $\displaystyle x = \sec \theta$