Question

Integrate the following functions.
$\int \frac{1}{x+xlogx}dx.$

Answer 1

Let $I=\int \frac{1}{x(1+logx)}dx$
Let 1+log x=t
On differentiating w.r.t.x, we get $\frac{1}{x}=\frac{dt}{dx}\Rightarrow dx=xdt$
$\therefore I=\int \frac{1}{x\left(t\right)}xdt=\int \frac{1}{t}dt=log|t|+C=log|1+logx|+C$