Question

Evaluate

$\int \frac{x^3+{4x}^2-7x+5}{x+2}dx$

Answer 1

$\int \frac{x^3+4x^2-7x+5}{x+2}dx$

$x^2+2x-11$

________________

$x+2)x^3+4x^2-7x+5$

$x^3+2x^2$

________________

$2x^2-7x$

$2x^2-4x$

______________

$-11x+5$

$-11x-22$

____________

$27$

____________

So $\int x^2+2x-11+\frac{27}{x+2}dx$

$\Rightarrow \frac{x^3}{3}+\frac{2x^2}{2}-11x+27log(x+2)+c$

$\Rightarrow \frac{x^3}{3}+x^2-11x+27log(x+2)+c$.