Question

Integrate the following functions.
$\int \frac{(1+logx{)}^2}{x}dx.$

Answer 1

$\int \frac{(1+logx{)}^2}{x}dx.$
Let $1+logx=t\Rightarrow \frac{1}{x}=\frac{dt}{dx}\Rightarrow dx=xdt$
$\therefore \int \frac{(1+logx{)}^2}{x}dx=\int \frac{t^2}{x}xdt=\int t^{2}dt=\frac{t^3}{3}+C=\frac{(1+logx{)}^3}{3}+C$