Question

$\int xlogxdx=?$

Answer 1

$\int x\log xdx$

Integrating by parts

$⟹\log x\int xdx-\int (\frac{d\left(\log x\right)}{dx})(\int xdx)dx=\log x(\frac{x^2}{2})-\int \frac{1}{x}\times \frac{x^2}{2}dx=\frac{x^2}{2}\log x-\frac{1}{2}\int xdx=\frac{x^2}{2}\log x-\frac{x^2}{4}+C$