Question

Evaluate $\int \frac{(1-x)(2+x)}{x}dx$

Answer 1

Let $I=\int \frac{(1-x)(2+x)}{x}dx$
$=\int \frac{(2+x-2x-x^2)}{x}dx$
$=\int \frac{(2-x-x^2)}{x}dx$
$=\int \frac{2}{x}dx-\int 1dx-\int xdx$
$=2{\log }_{e}x-x-\frac{x^2}{2}+C$