Question

Evaluate

$\int \frac{(logx{)}^2}{x}dx$

Answer 1

$I=\int \frac{(logx{)}^2}{x}dx$

Let $\log x=t$

$\frac{1}{x}dx=dt$

$I=\int t^{2}dt$

$I=\frac{t^3}{3}+C$

$I=\frac{(\log x{)}^3}{3}+C$