Find the Indefinite Integral of the Following Function and Check $\int \frac { 5 x } { \left( x ^ { 2 } + 5 \right) ^ { 4 } } d x$

Multiple Choice

Find the indefinite integral of the following function and check the result by differentiation. $\int \frac { 5 x } { \left( x ^ { 2 } + 5 \right) ^ { 4 } } d x$

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