Question

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

Answer 1

According to question,

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

$=\int \frac{(x+2)(x^2+2x-11)+27}{x+2}dx$

$=\int (x^2+2x-11)dx+\int \frac{27}{x+2}dx$

$=\frac{x^3}{3}+\frac{2x^2}{2}-11x+27\ln (x+2)+C$

$=\frac{x^3}{3}+x^2-11x+27\ln (x+2)+C$