Determine the Integral by Making an Appropriate Substitution $\int \frac { \sin \theta \cos ^ { 2 } \theta } { 1 + \cos ^ { 3 } \theta }$

Multiple Choice

Determine the integral by making an appropriate substitution.
- $\int \frac { \sin \theta \cos ^ { 2 } \theta } { 1 + \cos ^ { 3 } \theta }$ dθ

A) $\frac { 1 } { 2 }$ $\left( 1 + \cos ^ { 3 } \theta \right) ^ { 2 }$ + C
B) - $\frac { 1 } { 3 }$ ln $\left| 1 + \cos ^ { 3 } \theta \right|$ + C
C) $\frac { 1 } { 2 }$ $\left( \sin \theta \cos ^ { 2 } \theta \right) ^ { 2 }$ + C
D) $\sin ^ { 2 }$ θ $\cos ^ { 2 }$ θ + C
E) none of these