Question

logx integration by using substitution

Answer 1

Hello,

Solution: I am doing with integration by parts

$\int1.log \: x \: dx$

$\int{uv} dx = U\int \: V \: dx - \int\frac{dU}{dx}\int V \: dx\: dx \\ \\= log \: x \: \int 1.dx -\int\frac{d \: log \: x}{dx}\int1 \: dx \: dx \\ \\ = x \: logx -\int\frac{1}{x} \times x \: dx \\ \\ = x \: logx - \int 1.dx \\ = x \: logx - x + C$
Hope it helps you.