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

Question

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

Quizplus · Accepted Answer

The Answer of 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

Determine the Integral by Making an Appropriate Substitution ∫sin⁡θcos⁡2θ1+cos⁡3θ\int \frac { \sin \theta \cos ^ { 2 } \theta } { 1 + \cos ^ { 3 } \theta }∫1+cos3θsinθcos2θ​

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