Use a Table of Integrals to Evaluate the Integral $\int x \sqrt{2+2 x} d x$

Multiple Choice

Use a table of integrals to evaluate the integral. $\int x \sqrt{2+2 x} d x$

A) $\frac{2 \sqrt{2}}{15}(2 x-1) (x+1) ^{3 / 2}+C$
B) $\frac{2 \sqrt{2}}{15}(3 x-2) (x+1) ^{3 / 2}+C$
C) $\frac{2}{15}(3 x-2) \sqrt{x+1}+C$
D) $\frac{2 \sqrt{2}}{15}(3 x-2) \sqrt{x+1}+C$