Question

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

Answer 1

We have,

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

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

$I=\frac{x^3}{3}+\frac{2x^2}{2}+3x-log(x+2)+C$

$I=\frac{x^3}{3}+x^2+3x-log(x+2)+C$

Hence, this is the answer.