AP

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Evaluate

\displaystyle\int \frac{4x^{3}+x^{2}-2x+3}{x^{2}-x-2}\,dx

. (a)

2x^{2}+5x+5\ln|x^{2}-x-2|+C

(b)

2x^{2}+5x-\dfrac{35}{3}\ln|x-2|+\dfrac{2}{3}\ln|x+1|+C

(c)

2x^{2}+5x+\dfrac{35}{3}\ln|x-2|-\dfrac{2}{3}\ln|x+1|+C

(d)

2x^{2}+5x+\dfrac{35}{3}\ln|x+1|-\dfrac{2}{3}\ln|x-2|+C