$\text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. }$
A)$\frac { ( 1 + 4 z ) ^ { 6 } } { 20 } + C$
B) $\frac { ( 1 + 4 z ) ^ { 6 } } { 6 } + C$
C) $\frac { ( 1 + 4 z ) ^ { 6 } } { 24 } + C$
D) $6 ( 1 + 4 z ) ^ { 6 } + C$
E) $\frac { ( 1 + 4 z ) ^ { 6 } } { 5 } + C$

Question

$\text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. }$ 
A)$\frac { ( 1 + 4 z ) ^ { 6 } } { 20 } + C$
B) $\frac { ( 1 + 4 z ) ^ { 6 } } { 6 } + C$
C) $\frac { ( 1 + 4 z ) ^ { 6 } } { 24 } + C$
D) $6 ( 1 + 4 z ) ^ { 6 } + C$
E) $\frac { ( 1 + 4 z ) ^ { 6 } } { 5 } + C$

Quizplus · Accepted Answer

Using substitution, let $ u = 1 + 4z $, then $ du = 4dz $ or $ dz = \frac{1}{4}du $. The integral becomes $\int u^5 \cdot \frac{1}{4} du = \frac{1}{4} \int u^5 du$. Integrating gives $\frac{1}{4} \cdot \frac{u^6}{6} = \frac{u^6}{24}$. Substituting back $ u = 1 + 4z $, the result is $\frac{(1 + 4z)^6}{24} + C$.

Find the indefinite integral ∫(1+4z)5dz. \text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. } Find the indefinite integral ∫(1+4z)5dz.

$\text { Find the indefinite integral } \int ( 1 + 4 z ) ^ { 5 } d z \text {. }$