Evaluate the integral using integration by parts.
-$\int x$ $\sqrt { x + 1 }$ dx
A) $\frac { 2 } { 3 }$ $( x + 1 ) ^ { 3 / 2 }$ - $\frac { 4 } { 15 }$ $( x + 1 ) ^ { 5 / 2 }$ + C
B) $\frac { 2 } { 3 }$ x $( x + 1 ) ^ { 3 / 2 }$ - $\frac { 4 } { 15 }$ $( x + 1 ) ^ { 5 / 2 }$ + C
C) x $( x + 1 ) ^ { 3 / 2 }$ - $( x + 1 ) ^ { 5 / 2 }$ + C
D) $( x + 1 ) ^ { 3 / 2 }$ + $( x + 1 ) ^ { 5 / 2 }$ + C

Question

Quizplus · Accepted Answer

Integration by parts is used with $ u = x $ and $ dv = \sqrt{x+1} \, dx $. After applying the formula and simplifying, the result is option B.

Evaluate the Integral Using Integration by Parts ∫x\int x∫x x+1\sqrt { x + 1 }x+1​

Evaluate the Integral Using Integration by Parts $\int x$ $\sqrt { x + 1 }$