Question

Integrate the following w.r.t $x:\frac{e^x}{x}\left[x\right(\log x{)}^2+2.\log x]$

Answer 1

$\int \frac{e^x}{x}\left[x\right(\log x{)}^2+2\log x]dx$

$=\int e^{x}dx(\log x{)}^2-\int (e^x.2\log x.\frac{1}{x})dx+\int \frac{e^x}{x}2\log xdx$

$=e^x(\log x{)}^2+c$