Question

Integrate with respect o $x$:
$\ln x$

Answer 1

$\int \ln xdx=\int 1\times \ln xdx$

integrating by parts

$⟹\int \ln xdx=\left(\ln x\right)\int 1dx-\int \frac{d\left(\ln x\right)}{dx}\int 1dxdx=\left(\ln x\right)x-\int \frac{1}{x}\times xdx=x\left(\ln x\right)-\int 1dx=x\left(\ln x\right)-x$

$=x(\ln x-1)$