Question

Solve $\int xlogxdx$

Answer 1

$\int \underset{\left(i\right)}{x}\underset{\left(ii\right)}{\log x}dx$

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

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

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