Question

Integrate the function: $\frac{1}{x(\log x)^m}, x>0$

Answer 1

Let log x = t

∴ $\frac{1}{x}$dx= dt

$\Rightarrow \int \frac{1}{x(\log x)^m}dx=\int\frac{dt}{(t)^m}$

=$\bigg(\frac{t^{-m+1}}{1-m}\bigg)+C$

= $\frac{(\log x)^{1-m}}{(1-m)}+C$