Question

Evaluate:

$\int \frac{(x^3+8)(x-1)}{x^2-2x+4}dx$

Answer 1

$\int \frac{(x^3+8)(x-1)}{(x^2-2x+4)}dx$

$\Rightarrow \int \frac{(x+2)(x-1)(x^2-2x+4)}{(x^2-2x+4)}dx$

$\Rightarrow \int (x^2+x-2)dx$

$=\frac{x^3}{3}+\frac{x^2}{2}-2x+c$