AP

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

Problem

Find

\displaystyle \int \frac{4x-1}{x^{2}+4}\,dx

. (a)

\ln\bigl(x^{2}+4\bigr)-\dfrac{1}{2}\arctan\!\left(\dfrac{x}{2}\right)+C

(b)

2\ln\bigl(x^{2}+4\bigr)-\dfrac{1}{2}\arctan\!\left(\dfrac{x}{2}\right)+C

(c)

2\ln\bigl(x^{2}+4\bigr)+\dfrac{1}{2}\arctan\!\left(\dfrac{x}{2}\right)+C

(d)

2\ln\bigl(x^{2}+4\bigr)-\arctan\!\left(\dfrac{x}{2}\right)+C