Evaluate the integral.
$\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x$
A) $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 }$
B) $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 } + C$
C) $\frac { ( 3 x + 5 x ) ^ { 6 } } { 6 } + C$
D) $\frac { ( 3 x + 5 ) ^ { 6 } } { 3 } + C$
E) $\frac { ( 3 x + 5 ) ^ { 6 } } { 6 } + C$

Question

Evaluate the integral.  
  $\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x$ 
A)  $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 }$
B)   $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 } + C$
C)   $\frac { ( 3 x + 5 x ) ^ { 6 } } { 6 } + C$
D)   $\frac { ( 3 x + 5 ) ^ { 6 } } { 3 } + C$
E)   $\frac { ( 3 x + 5 ) ^ { 6 } } { 6 } + C$

Quizplus · Accepted Answer

The integral of a function in the form of $(ax + b)^n$ with respect to $x$ is $\frac{(ax + b)^{n+1}}{(n+1)a} + C$, where $C$ is the constant of integration. Applying this rule to $\int (3x + 5)^5 \,dx$, we get $\frac{(3x + 5)^6}{6 \cdot 3} + C = \frac{(3x + 5)^6}{18} + C$, which matches option B.

Evaluate the Integral ∫(3x+5)5 dx\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x∫(3x+5)5 dx

Evaluate the Integral $\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x$