Find the indefinite integral. $$\int \sec ^ { 6 } 6 x d x$$
A) $\frac { 15 \tan ( 6 x ) - 10 \tan ( 6 x ) ^ { 3 } - 3 \tan ( 6 x ) ^ { 5 } } { 90 } + C$
B) $\frac { 15 \tan ( 6 x ) + 10 \tan ( 6 x ) ^ { 3 } + 3 \tan ( 6 x ) ^ { 5 } } { 15 } + C$
C) $\frac { 15 \tan ( 6 x ) + 10 \tan ( 6 x ) ^ { 3 } + 3 \tan ( 6 x ) ^ { 5 } } { 90 } + C$
D) $\frac { 15 \tan ( 6 x ) + 10 \tan ( 6 x ) ^ { 3 } + 3 \tan ( 6 x ) ^ { 5 } } { 270 } + C$
E) $\frac { 15 \tan ( 6 x ) - 10 \tan ( 6 x ) ^ { 3 } - 3 \tan ( 6 x ) ^ { 5 } } { 15 } + C$

Question

Quizplus · Accepted Answer

The correct answer is obtained through the integration of $\sec^6(6x)$ using integration techniques involving trigonometric identities and substitution. The result involves a combination of $\tan(6x)$ and its higher powers, divided by a constant, which matches option C.

Find the Indefinite Integral ∫sec⁡66xdx\int \sec ^ { 6 } 6 x d x∫sec66xdx

Find the Indefinite Integral $\int \sec ^ { 6 } 6 x d x$