Question

Evaluate the following integral for $x>8$ using the substitution $x=8cosh.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{\sqrt[\phantom{2}]{81x^2-5184}}dx$

Express the final answer in terms of the variable $x.$ Be sure to include parentheses around the arguments of any inverse hyperbolic functions in your answer.

Provide your answer below:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{\sqrt[\phantom{2}]{81x^2-5184}}dx=$