Use integration by parts to evaluate the integral $\int \frac { x } { \sqrt { x + 8 } } d x$ .
A) $\frac { 2 } { 3 } ( x - 8 ) ^ { 1 / 2 } ( x + 16 ) + C$
B) $\frac { 2 } { 3 } ( x + 8 ) ^ { 1 / 2 } ( x - 16 ) + C$
C) $\frac { 3 } { 2 } ( x + 8 ) ^ { 1 / 2 } ( x - 16 ) + C$
D) $\frac { 2 } { 3 } ( x + 8 ) ^ { 3 / 2 } ( x - 16 ) + C$

Question

Quizplus · Accepted Answer

Integration by parts is used with $ u = x $ and $ dv = \frac{1}{\sqrt{x+8}} dx $. After solving, the correct answer is $\frac { 2 } { 3 } ( x + 8 ) ^ { 1 / 2 } ( x - 16 ) + C$.

Use Integration by Parts to Evaluate the Integral ∫xx+8dx\int \frac { x } { \sqrt { x + 8 } } d x∫x+8​x​dx

Use Integration by Parts to Evaluate the Integral $\int \frac { x } { \sqrt { x + 8 } } d x$