A Level

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Evaluate

\displaystyle\int \frac{2x^{3}+x^{2}-5x+7}{x^{2}+2x+5}\,dx

. (a)

x^{2}-3x-\dfrac{9}{2}\ln(x^{2}+2x+5)+31\tan^{-1}\left(\dfrac{x+1}{2}\right)+C

(b)

x^{2}-3x-\dfrac{9}{2}\ln(x^{2}+2x+5)+\dfrac{31}{2}\tan^{-1}\left(\dfrac{x+1}{2}\right)+C

(c)

x^{2}-3x+\dfrac{9}{2}\ln(x^{2}+2x+5)+\dfrac{31}{2}\tan^{-1}\left(\dfrac{x+1}{2}\right)+C

(d)

x^{2}-3x-\dfrac{9}{2}\ln(x^{2}+2x+5)+\dfrac{31}{2}\tan^{-1}\left(\dfrac{x+1}{\sqrt{5}}\right)+C