AP® Calculus AB-BC

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Difficult

Rewriting Integrals to Solve: Improper Rational Functions

APCALC-KI@NRQ

Integrate:

$$\int{\cfrac{x^2+2}{x^2+9}dx}$$

A

$\cfrac{\frac{1}{3}x^3+2x}{\frac{1}{3}x^3+9x}+C$

B

$\left(\cfrac{1}{3}x^3+2x\right)\left(\cfrac{1}{3}\arctan\left(\cfrac{x}{3}\right)\right)+C$

C

$x-\cfrac{7}{3}\arctan\left(\cfrac{x}{3}\right)+C$

D

$x-\cfrac{7}{9}\arctan\left(\cfrac{x}{9}\right)+C$