A Level

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

Problem

Evaluate

\displaystyle \int \frac{x^{3}+2x^{2}+3}{x^{2}+1}\,dx

. (a)

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

(b)

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

(c)

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

(d)

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