Question

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

Answer 1

Let $I=\int \frac{(logx{)}^2}{x}dx$
Let log x =t
On differentiating w.r.t.x, we get $\frac{1}{x}=\frac{dt}{dx}\to dx=xdt$
$\therefore I=\int \frac{t^2}{x}xdt=\int t^{2}dt=\frac{t^3}{3}+C=\frac{(logx{)}^3}{3}+C$