Evaluate the following integral using a trigonometric substitution.

${\displaystyle \underset{0}{\overset{3\sqrt[\phantom{2}]{2}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{900-25x^2}}dx$

Enter an exact answer.

Provide your answer below:

${\displaystyle \underset{0}{\overset{3\sqrt[\phantom{2}]{2}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{900-25x^2}}dx=$