Evaluate the integral.
-$\int \operatorname { coth } ( 9 x ) d x$
A) $\frac { 1 } { 9 } \ln | \sinh 9 x | + C$
B) $\ln | \sinh 9 x | + C$
C) $\frac { 1 } { 9 } \operatorname { csch } ^ { 2 } 9 x + C$
D) $9 \ln \left( \sinh \frac { x } { 9 } \right) + C$

Question

Quizplus · Accepted Answer

The integral of $\operatorname{coth}(9x)$ is $\frac{1}{9}\ln|\sinh(9x)| + C$, because the antiderivative of $\operatorname{coth}x$ is $\ln|\sinh x|$, and applying the chain rule for integration results in a factor of $\frac{1}{9}$ due to the inner derivative of $9x$.

Evaluate the Integral ∫coth⁡(9x)dx\int \operatorname { coth } ( 9 x ) d x∫coth(9x)dx

Evaluate the Integral $\int \operatorname { coth } ( 9 x ) d x$