A Level

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Determine

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

. (a)

2\ln|x|+\ln(x^{2}+1)+5\arctan x + C

(b)

\ln|x|+\dfrac{1}{2}\ln(x^{2}+1)+5\arctan x + C

(c)

2\ln|x|+\dfrac{1}{2}\ln(x^{2}+1)+5\arctan x + C

(d)

2\ln|x|+\dfrac{1}{2}\ln(x^{2}+1)+\dfrac{5}{2}\arctan x + C