Find ( x^ 4 -x^ 2 +1 x^ 2 +1 ,dx ).

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

Problem

Find

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

. (a)

\dfrac{x^{3}}{3}-2x+3\ln|x^{2}+1|+C

(b)

\dfrac{x^{3}}{3}-2x+3\arctan x+C

(c)

\dfrac{x^{3}}{3}-2x+\arctan x+C

(d)

\dfrac{x^{3}}{3}-x+2\arctan x+C