Evaluate the following integral for $x>4$ using a trigonometric substitution.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{(64x^2-1024{)}^{\frac{3}{2}}}dx$

Provide your answer below:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{(64x^2-1024{)}^{\frac{1}{2}}}dx=$

$$