Question

Evaluate
sigma log x dx​

Answer 1

$I = ∫log(x)dx$

$I = ∫log(x). 1dx$

Using Integration by parts, we get

$I = log(x)∫1dx - ∫[\frac{d}{dx}(logx)∫1dx]dx$

$I = log(x)x - ∫[\frac{1}{x}\times x]dx$

$I = log(x)x - ∫1dx$

$I = log(x)x - x+ C$

$I = x(log(x)-1)+ C$