Question

Solve: $\int \frac{\ln \frac{x}{e}}{{\left(lnx\right)}^2}dx$

Answer 1

$\begin{array}{c}\int \frac{\ln \frac{x}{e}}{{\left(lnx\right)}^2}dx\\ =\int \frac{1}{\ln \left(x\right)}-\frac{1}{{\ln }^2\left(x\right)}dx\\ =\frac{x}{\ln x}-\int -\left(\frac{1}{{\ln }^{2}x}\right)dx-\int \left(\frac{1}{{\ln }^{2}x}\right)dx\\ =\frac{x}{\ln x}+C\end{array}$