AP

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

Problem

Evaluate

\displaystyle \int \frac{5x+2}{x^{2}+2x+5}\,dx

. (a)

\dfrac{5}{2}\ln\left(x^{2}+2x+5\right)-3\tan^{-1}\left(\dfrac{x+1}{2}\right)+C

(b)

\dfrac{5}{2}\ln\left(x^{2}+2x+5\right)-\dfrac{3}{2}\tan^{-1}\left(\dfrac{x+1}{2}\right)+C

(c)

\dfrac{5}{2}\ln\left(x^{2}+2x+5\right)+\dfrac{3}{2}\tan^{-1}\left(\dfrac{x+1}{2}\right)+C

(d)

\dfrac{5}{4}\ln\left(x^{2}+2x+5\right)-\dfrac{3}{2}\tan^{-1}\left(\dfrac{x+1}{2}\right)+C