Answer
$\int \frac{x^3-6x-20}{x+5}dx = \frac{x^3}{3}-\frac{5x^2}{2}+19x-115\ln|x+5|+C$
Work Step by Step
To evaluate $\int \frac{x^3-6x-20}{x+5}dx$, begin by dividing the fraction using long polynomial division. See the photo to view how the long polynomial division is performed.
Once you get that:
$\frac{x^3-6x-20}{x+5} = x^2-5x+19-\frac{115}{x+5}$,
Set up the integral:
$\int x^2-5x+19-\frac{115}{x+5}dx$
Separate the integral:
$\int x^2dx-\int5xdx+\int19dx-\int\frac{115}{x+5}dx$
Integrate:
$\frac{x^3}{3}-\frac{5x^2}{2}+19x-115\ln|x+5|+C$
