A Level

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

Problem

Evaluate

\displaystyle \int \frac{x^{3}+2x^{2}+3x+5}{x^{2}+1}\,dx

. (a)

\displaystyle \frac{x^{2}}{2}+2x+\tfrac12\ln\!\big(x^{2}+1\big)+3\arctan x+C

(b)

\displaystyle \frac{x^{2}}{2}+2x+\ln\!\big(x^{2}+1\big)+3\arctan x+C

(c)

\displaystyle x^{2}+2x+\ln\!\big(x^{2}+1\big)+3\arctan x+C

(d)

\displaystyle \frac{x^{2}}{2}+2x+\ln\!\big(x^{2}+1\big)+\arctan x+C