AP

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Find ∫2x3+3x2+x+4x2+1 dx\displaystyle\int \frac{2x^{3}+3x^{2}+x+4}{x^{2}+1}\,dx. (a) x2+3x+12ln⁡(x2+1)−tan⁡−1x+Cx^{2}+3x+\dfrac{1}{2}\ln(x^{2}+1)-\tan^{-1}x+C (b) x2+3x−ln⁡(x2+1)+tan⁡−1x+Cx^{2}+3x-\ln(x^{2}+1)+\tan^{-1}x+C (c) x2+3x−12ln⁡(x2+1)+tan⁡−1x+Cx^{2}+3x-\dfrac{1}{2}\ln(x^{2}+1)+\tan^{-1}x+C (d) x2+3x−12ln⁡∣x+1∣+tan⁡−1x+Cx^{2}+3x-\dfrac{1}{2}\ln|x+1|+\tan^{-1}x+C

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