Question

Evaluate :
$\int \frac{{\left(logx\right)}^2}{x}dx$

Answer 1

$\int \frac{{\left(\log x\right)}^2}{x}dx$

Let $t=\log x\Rightarrow dt=\frac{1}{x}dx$

$=\int t^{2}dt$

$=\frac{t^3}{3}+c$ where $c$ is the constant of integration.

$=\frac{{\left(\log x\right)}^3}{3}+c$