Solve the Problem by Integration $y = \frac { 1 } { x ^ { 3 } + 6 x ^ { 2 } + 5 x } , x = 4 , x = 5$

Multiple Choice

Solve the problem by integration.
-Find the volume generated by rotating the area bounded by $y = \frac { 1 } { x ^ { 3 } + 6 x ^ { 2 } + 5 x } , x = 4 , x = 5$ , and $y = 0$ about the $\mathrm { y }$ -axis.

A) $2 \pi \ln \frac { 25 } { 27 }$
B) $\frac { 1 } { 2 } \pi \ln \frac { 3 } { 5 }$
C) $\frac { 1 } { 2 } \pi \ln \frac { 27 } { 25 }$
D) $\frac { 1 } { 4 } \pi \ln \frac { 27 } { 25 }$