Answer
$\displaystyle \frac{1}{2}x^{2}-2x+6\ln|x+2|+C$
Work Step by Step
$\displaystyle \frac{x^{2}+2}{x+2}=\frac{x(x+2)-2x+2}{x+2}=x+\frac{-2x+2}{x+2}$
$=x+\displaystyle \frac{-2(x+2)+6}{x+2}=x-2+\frac{6}{x+2}$
$\displaystyle \int\frac{x^{2}+2}{x+2}dx=\int\left(x-2+\frac{6}{x+2}\right)dx $
$=\displaystyle \frac{1}{2}x^{2}-2x+6\ln|x+2|+C$
