Question

Integrate :
$\int log\frac{(1-x)}{x^2}dx$

Answer 1

To Integrate this

$\int log\frac{(1-x)}{x^2}dx$

Here , We are using Integration by part

$\int u.vdx=u\int vdx-[\frac{du}{dx}\int (\int vdx)dx]$

$log\frac{(1-x)}{x^2}\int 1.dx-\left[(\frac{d}{dx}log\frac{(1-x)}{x^2}\int 1.dx)dx\right]$

$xlog\frac{(1-x)}{x^2}+[\int \left(\frac{2-x}{1-x}\right)dx]$

$=xln\frac{(1-x)}{x^2}+x-ln|1-x|-1+C$

$=ln\frac{(1-x)}{x}+x-ln|1-x|-1+C$

Where C is the Integration Constant