Question

Evaluate: $\int \frac{1}{x(3+\log x)}dx$

Answer 1

$\int \frac{1}{x(3+\log x)}dx$

Put $\log x=t$

then $\frac{1}{x}.dx=dt$

Substitute these values , we get

$\int \frac{dt}{3+t}$

$=\ln (3+t)+C$

Put value of $t$,

$=\ln (3+\log x)+C$