Evaluate the integral.
-$$\int 9 \sec ^ { 4 } x d x$$
A) $3 \tan ^ { 3 } x + C$
B) $- 3 \tan ^ { 3 } x + C$
C) $9 ( \sec x + \tan x ) ^ { 5 } + C$
D) $9 \tan x + 3 \tan ^ { 3 } x + C$

Question

Quizplus · Accepted Answer

The integral of $9 \sec^4 x dx$ can be solved by recognizing it as a standard integral form. The integral of $\sec^n x dx$ for even powers can be approached by reducing the power using trigonometric identities. Specifically, $\sec^4 x$ can be integrated by expressing it in terms of $\sec^2 x$ and $\tan^2 x + 1$, which are related through the identity $\sec^2 x = \tan^2 x + 1$. The integral then becomes a sum of simpler integrals, leading to the result $9 \tan x + 3 \tan^3 x + C$, which matches option D.

Evaluate the Integral ∫9sec⁡4xdx\int 9 \sec ^ { 4 } x d x∫9sec4xdx

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