# Math Help - Integration by parts or by Substitution

1. ## Integration by parts or by Substitution

$\int_{1}^{4} (x^2-2) *ln(x) \, dx$.
Which type of integration I should use? and how?
If I dicede to use integration by substitution:
u= $x^2-2$
du=2xdx
dx=du/2x
Then
$\int_{x=1}^{x=4} u *ln(x)*du/2x \, dx=\frac{1}{2}\int_{x=1}^{x=4}\frac{lnx)*du}{x}$.

2. You can use the integration by part.

$\int_{1}^{4}(x^2 - 2)*ln(x)dx = ln(x)( x^3/3 - 2x) - \int( x^3/3 - 2x)*1/x*dx$

now proceed.