Find the indefinite integral. $$\int \sec ^ { 4 } 9 x d x$$
A) $\frac { 1 } { 27 } \tan ( 9 x ) ( 3 + \tan ( 9 x ) ) + C$
B) $\frac { 1 } { 27 } \tan ( 9 x ) \left( 3 + \tan ^ { 2 } ( 9 x ) \right) + C$
C) $- \frac { 1 } { 27 } \tan ( 9 x ) \left( 3 + \tan ^ { 2 } ( 9 x ) \right) + C$
D) $\frac { 1 } { 27 } \tan ( 9 x ) \left( 3 - \tan ^ { 2 } ( 9 x ) \right) + C$
E) $\frac { 1 } { 27 } \tan ( 9 x ) ( 3 - \tan ( 9 x ) ) + C$

Question

Quizplus · Accepted Answer

The integral of $\sec^4(9x)dx$ can be solved using trigonometric identities and substitution. The correct answer involves recognizing that $\sec^2(x) = 1 + \tan^2(x)$ and applying integration techniques accordingly, leading to the expression in choice B.

Find the Indefinite Integral ∫sec⁡49xdx\int \sec ^ { 4 } 9 x d x∫sec49xdx

Find the Indefinite Integral $\int \sec ^ { 4 } 9 x d x$