Evaluate the integral.
$$\int _ { x / 6 } ^ { \pi / 3 } \frac { 3 \ln ( \tan x ) } { 7 \sin x \cos x } d x$$
A) $- \frac { 1 } { 5 } ( \ln 2 ) ^ { 2 }$
B) $- \frac { 1 } { 2 } ( \ln 3 ) ^ { 2 }$
C) 0
D) $\frac { 1 } { 6 } ( \ln 3 ) ^ { 2 }$
E) $\frac { 1 } { 2 } ( \ln 3 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The integral is evaluated over a symmetric interval with respect to the function's properties, leading to a result of zero.

Evaluate the Integral ∫x/6π/33ln⁡(tan⁡x)7sin⁡xcos⁡xdx\int _ { x / 6 } ^ { \pi / 3 } \frac { 3 \ln ( \tan x ) } { 7 \sin x \cos x } d x∫x/6π/3​7sinxcosx3ln(tanx)​dx

Evaluate the Integral $\int _ { x / 6 } ^ { \pi / 3 } \frac { 3 \ln ( \tan x ) } { 7 \sin x \cos x } d x$