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) $\frac { 2 \sqrt { 2 } } { 15 } ( 3 x - 2 ) \sqrt { x + 1 } + C$

Question

Quizplus · Accepted Answer

The integral can be solved using a substitution method. Let $ u = 2 + 2x $, then $ du = 2 dx $ and $ x = \frac{u - 2}{2} $. Substituting these into the integral and simplifying, we find that choice B matches the evaluated integral.

Use a Table of Integrals to Evaluate the Integral ∫x2+2xdx\int x \sqrt { 2 + 2 x } d x∫x2+2x​dx

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