The integral $\int x \sqrt { 4 x + 5 } d x$ is

A) $\frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x - 5 ) } { 60 } + C$
B) $- \frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x - 5 ) } { 60 } + C$
C) $\frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x + 5 ) } { 60 } + C$
D) $- \frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x + 5 ) } { 60 } + C$
E) $\frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x - 7 ) } { 60 } + C$

Question

The integral $\int x \sqrt { 4 x + 5 } d x$ is

A) $\frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x - 5 ) } { 60 } + C$
B) $- \frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x - 5 ) } { 60 } + C$
C) $\frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x + 5 ) } { 60 } + C$
D) $- \frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x + 5 ) } { 60 } + C$
E) $\frac { ( 4 x + 5 ) ^ { \frac { 3 } { 2 } } ( 6 x - 7 ) } { 60 } + C$

Quizplus · Accepted Answer

To solve the integral $\int x \sqrt { 4 x + 5 } d x$, we can use substitution. Let $u = 4x + 5$, then $du = 4dx$, and $x = \frac{u - 5}{4}$. Substituting these into the integral and simplifying will eventually lead to an integral in terms of $u$ that, when solved, gives a result that matches option A after back-substituting for $x$.

The Integral ∫x4x+5dx\int x \sqrt { 4 x + 5 } d x∫x4x+5​dx

The Integral $\int x \sqrt { 4 x + 5 } d x$