AP

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

Problem

Determine ∫2x+3x(x2+1) dx\displaystyle \int \frac{2x+3}{x(x^{2}+1)}\,dx. (a) 3ln⁡∣x∣−32ln⁡(x2+1)+2tan⁡−1x+C3\ln|x|-\dfrac{3}{2}\ln\left(x^{2}+1\right)+2\tan^{-1}x+C (b) 3ln⁡∣x∣+32ln⁡(x2+1)+2tan⁡−1x+C3\ln|x|+\dfrac{3}{2}\ln\left(x^{2}+1\right)+2\tan^{-1}x+C (c) 3ln⁡∣x∣−32ln⁡(x2+1)+tan⁡−1x+C3\ln|x|-\dfrac{3}{2}\ln\left(x^{2}+1\right)+\tan^{-1}x+C (d) ln⁡∣x∣−32ln⁡(x2+1)+2tan⁡−1x+C\ln|x|-\dfrac{3}{2}\ln\left(x^{2}+1\right)+2\tan^{-1}x+C

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