A Level

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

Problem

Evaluate

\displaystyle \int \frac{2x+9}{x^{2}+5x+10}\,dx

. (a)

\ln|x^{2}+5x+10|-\dfrac{8}{\sqrt{15}}\tan^{-1}\dfrac{2x+5}{\sqrt{15}}+C

(b)

\ln|x^{2}+5x+10|+\dfrac{8}{\sqrt{15}}\tan^{-1}\dfrac{2x+5}{\sqrt{15}}+C

(c)

\ln|x^{2}+5x+10|+\dfrac{4}{\sqrt{15}}\tan^{-1}\dfrac{2x+5}{\sqrt{15}}+C

(d)

\dfrac{8}{\sqrt{15}}\tan^{-1}\dfrac{2x+5}{\sqrt{15}}+C