Question

Integrate the function [(logx)²/x].dx

Answer 1

Given, $\int{\frac{(logx)^2}{x}}\,dx$ ----(1)
Let logx = t
differentiate both sides,
1/x dx = dt
dx = x.dt , put it equation (1) ,

$\int{\frac{(logx)^2}{x}}\,dx=\int{\frac{t^2}{x}}\,xdt$

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

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

put , t = logx

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