A Level

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

Problem

Evaluate

\displaystyle\int \frac{6x+1}{x^{2}+4x+10}\,dx

. (a)

\dfrac{3}{2}\ln|x^{2}+4x+10|-\dfrac{11}{\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C

(b)

3\ln|x^{2}+4x+10|-\dfrac{11}{\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C

(c)

3\ln|x^{2}+4x+10|-\dfrac{11}{2\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C

(d)

3\ln|x^{2}+4x+10|+\dfrac{11}{\sqrt{6}}\arctan\!\left(\dfrac{x+2}{\sqrt{6}}\right)+C