Question

$\int \frac{1}{x\sqrt{1+\ln x}}dx=m\sqrt{(1+\ln x)}+c$.Find $m$

Answer 1

$1+lnx=t^2\left(\frac{1}{x}\right)dx=2tdt\therefore I=\int \left(\frac{2tdt}{\sqrt{t^2}}\right)=2\int dt=2t+C=2\sqrt{1+lnx}+C\therefore m=2$