Question

Integrate the function: $\frac{(1+\log x{)}^2}{x}$

Answer 1

Given:
$\int \frac{(1+\log x{)}^2}{x}dx$
Let $1+\log x=t$
Differentiating both sides w.r.t.$x$
$\frac{1}{x}=\frac{dt}{dx}\Rightarrow \frac{dx}{x}=dt$
On substituting,
$=\int t^{2}dt$
$=\frac{t^3}{3}+C$
$=\frac{1}{3}(1+\log x{)}^3+C$
Where $C$ is constant of integration