Evaluate the following integral using trigonometric substitution.

What substitution will be the most helpful for evaluating this integral?

A$.x=10sin$

B$.x=10sec$

C$.x=10tan$

Rewrite the given integral using this substitution.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{(x^2-100{)}^{\frac{3}{2}}}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}1dd$

$($Type an exact answer.$)$

Evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{(x^2-100{)}^{\frac{3}{2}}}dx=$

$($Type an exact answer.$)$