Find the indefinite integral. $$\int \cos ^ { 3 } 3 x d x$$
A) $\frac { \sin 3 x \left( 3 - \sin ^ { 2 } 3 x \right) } { 9 } + C$
B) $\frac { \sin 3 x \left( 3 - \sin ^ { 4 } 3 x \right) } { 9 } + C$
C) $\frac { \sin 3 x \left( 3 + \sin ^ { 2 } 3 x \right) } { 3 } + C$
D) $\frac { \sin 3 x \left( 3 + \sin ^ { 4 } 3 x \right) } { 9 } + C$
E) $\frac { \sin 3 x \left( 3 + \sin ^ { 2 } 3 x \right) } { 9 } + C$

Question

Quizplus · Accepted Answer

To solve the integral $\int \cos^3 3x dx$, use the identity $\cos^2 x = 1 - \sin^2 x$ to rewrite $\cos^3 3x$ as $\cos 3x (1 - \sin^2 3x)$. Then, apply substitution for $\sin 3x$, integrate, and simplify to get the correct answer.

Find the Indefinite Integral ∫cos⁡33xdx\int \cos ^ { 3 } 3 x d x∫cos33xdx

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