Find the indefinite integral. $$\int \cos ^ { 3 } 2 x \sin ^ { 2 } 2 x d x$$
A) $\frac { \sin 2 x } { 30 } \left( 4 - 5 \sin ^ { 2 } 2 x + 3 \sin ^ { 4 } 2 x \right) + C$
B) $\frac { \sin 2 x } { 10 } \left( 5 \sin ^ { 2 } 2 x - 3 \sin ^ { 4 } 2 x \right) + C$
C) $\frac { \sin 2 x } { 30 } \left( 5 \sin ^ { 2 } 2 x - 3 \sin ^ { 4 } 2 x \right) + C$
D) $\frac { \sin 2 x } { 10 } \left( 4 - 5 \sin ^ { 2 } 2 x + 3 \sin ^ { 4 } 2 x \right) + C$
E) $\frac { \sin 2 x } { 30 } \left( 5 \sin ^ { 2 } 2 x + 3 \sin ^ { 4 } 2 x \right) + C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution and trigonometric identities. Let $ u = \sin 2x $, then $ du = 2\cos 2x \, dx $. Rewrite the integral in terms of $ u $ and solve, leading to the expression in choice C.

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Find the Indefinite Integral $\int \cos ^ { 3 } 2 x \sin ^ { 2 } 2 x d x$