Question

Evaluate $\int x.\log xdx$

Answer 1

$\int x\log xdx$

Let $u=\log x\Rightarrow du=\frac{1}{x}dx$

$dv=xdx\Rightarrow v=\frac{x^2}{2}$

$=\frac{x^2\log x}{2}-\int \frac{x^2}{2}\frac{1}{x}dx$

$=\frac{x^2\log x}{2}-\frac{1}{2}\int xdx$

$=\frac{x^2\log x}{2}-\frac{x^2}{4}+c$