Find the Indefinite Integral of the Following Function and Check $\int x ^ { 4 } \sqrt { \left( 4 + x ^ { 5 } \right) } d x$

Multiple Choice

Find the indefinite integral of the following function and check the result by differentiation. $\int x ^ { 4 } \sqrt { \left( 4 + x ^ { 5 } \right) } d x$

A) $\frac { \left( 4 + x ^ { 5 } \right) ^ { \frac { 3 } { 2 } } } { 10 } + C$
B) $\frac { 2 \left( 4 + x ^ { 5 } \right) ^ { \frac { 2 } { 3 } } } { 15 } + C$
C) $\frac { \left( 4 + x ^ { 5 } \right) ^ { \frac { 3 } { 2 } } } { 15 } + C$
D) $\frac { 2 \left( 4 + x ^ { 5 } \right) ^ { \frac { 3 } { 2 } } } { 15 } + C$
E) none of the above