Question

Evaluate the following integral using a trigonometric substitution.

${\displaystyle \underset{0}{\overset{\frac{7\sqrt[\phantom{2}]{3}}{2}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{784-16x^2}}dx$

Enter an exact answer.

Provide your answer below:

${\displaystyle \underset{0}{\overset{\frac{7\sqrt[\phantom{2}]{3}}{2}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{784-16x^2}}dx=$