Question

Evaluate :

$\int \frac{(1+\log x{)}^2}{x}dx$

Answer 1

$I=\int \frac{(1+\log x{)}^2}{x}dx$

Let $1+\log x=t$

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

Thus, $I=\int \frac{t^2}{x}\times xdt=\int t^{2}dt=\frac{t^3}{3}+C=\frac{(1+\log x{)}^3}{3}+C$