$\displaystyle \int_{1}^{4} (x^2-2) *ln(x) \, dx$.

Which type of integration I should use? and how?

If I dicede to use integration by substitution:

u=$\displaystyle x^2-2$

du=2xdx

dx=du/2x

Then

$\displaystyle \int_{x=1}^{x=4} u *ln(x)*du/2x \, dx=\frac{1}{2}\int_{x=1}^{x=4}\frac{lnx)*du}{x}$.