Find the indefinite integral of the following function and check the result by differentiation. $\int ( 1 + 4 z ) ^ { 3 } d z$
A) $4 ( 1 + 4 z ) ^ { 4 } + C$
B) $\frac { ( 1 + 4 z ) ^ { 4 } } { 3 } + C$
C) $\frac { ( 1 + 4 z ) ^ { 4 } } { 4 } + C$
D) $\frac { ( 1 + 4 z ) ^ { 4 } } { 16 } + C$
E)none of the above

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = 1 + 4z $, then $ du = 4dz $ or $ dz = \frac{1}{4}du $. The integral becomes $\int u^3 \cdot \frac{1}{4} du = \frac{1}{4} \int u^3 du = \frac{1}{4} \cdot \frac{u^4}{4} + C = \frac{(1 + 4z)^4}{16} + C$. Differentiating this result gives back the original function.

Find the Indefinite Integral of the Following Function and Check ∫(1+4z)3dz\int ( 1 + 4 z ) ^ { 3 } d z∫(1+4z)3dz

Find the Indefinite Integral of the Following Function and Check $\int ( 1 + 4 z ) ^ { 3 } d z$