Evaluate the integral.
-$\int _ { - \pi / 15 } ^ { \pi / 15 } \sec ^ { 3 } 5 x d x$ Give your answer in exact form.
A) $\frac { 2 \sqrt { 3 } } { 5 } + \frac { 1 } { 10 } \ln ( 7 + 4 \sqrt { 3 } )$
B) $\frac { \sqrt { 3 } } { 5 } + \frac { 1 } { 10 } \ln ( 7 + 4 \sqrt { 3 } )$
C) $\frac { 2 \sqrt { 3 } } { 5 } + \frac { 1 } { 10 } \ln ( 2 \sqrt { 3 } )$
D) $\frac { 2 } { 5 } + \frac { 1 } { 10 } \ln 4$

Question

Quizplus · Accepted Answer

The integral of $\sec^3(5x)$ can be solved using integration techniques involving trigonometric identities and substitution. The result involves a combination of a trigonometric function and a logarithmic function of a trigonometric expression. The correct answer must accurately reflect the values of these functions at the bounds of integration, which are $-\pi/15$ and $\pi/15$. The given option A correctly represents the exact form of the integral's evaluation, taking into account the specific bounds and the nature of the $\sec^3$ function.

Evaluate the Integral ∫−π/15π/15sec⁡35xdx\int _ { - \pi / 15 } ^ { \pi / 15 } \sec ^ { 3 } 5 x d x∫−π/15π/15​sec35xdx

Evaluate the Integral $\int _ { - \pi / 15 } ^ { \pi / 15 } \sec ^ { 3 } 5 x d x$