Question

Evaluate : $\int (\log x{)}^{2}dx$

Answer 1

$\begin{array}{c}Integratingbypartweget:-\\ {\int }^{}{\left(\log x\right)}^{2}dx\\ ={\left(\log x\right)}^2{\int }^{}dx-{\int }^{}\left[2\left(\frac{\log x}{x}\right){\int }^{}dx\right]dx\\ =x{\left(\log x\right)}^2-2{\int }^{}\left(\log x\right)dx\\ =x{\left(\log x\right)}^2-2x\left(\log x\right)+2x+C\end{array}$

Hence, this is the answer.