Question

Integrate the function: $\frac{1}{x+x\log x}$

Answer 1

$\frac{1}{x+x\log x}$ =$\frac{1}{x(1+\log x)}$

Let 1 + log x = t

∴ $\frac{1}{x} dx$ = dt

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

= log |t| + C

= log |1+ log x| + C