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Difficult

Trigonometric Substitution 4

SVCALC-TRGUXR

Evaluate the integral:

$$\int \frac{x^2}{\sqrt{25-x^2}} dx$$

A

$25\arcsin\cfrac{x}{5}+x\sqrt{25-x^2}+C$

B

$\cfrac{5}{2}\arcsin\cfrac{x}{25}+\cfrac{25}{2}x\sqrt{25-x^2}+C$

C

$\cfrac{25}{2}\arccos\cfrac{x}{5}-\cfrac{1}{2}x\sqrt{25-x^2}+C$

D

$\cfrac{25}{2}\arcsin\cfrac{x}{5}+\cfrac{1}{2}x\sqrt{25-x^2}+C$