Find the value of .

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

Problem

Find the value of ∫2x2+3x+1x(x+1)(x+2) dx\displaystyle \int \frac{2x^{2}+3x+1}{x(x+1)(x+2)}\,dx. (a) 12ln⁡∣x∣+32ln⁡∣x+1∣+C\dfrac{1}{2}\ln|x|+\dfrac{3}{2}\ln|x+1|+C (b) ln⁡∣x∣+32ln⁡∣x+2∣+C\ln|x|+\dfrac{3}{2}\ln|x+2|+C (c) 12ln⁡∣x∣+32ln⁡∣x+2∣+C\dfrac{1}{2}\ln|x|+\dfrac{3}{2}\ln|x+2|+C (d) 12ln⁡∣x∣+32ln⁡∣x+2∣−ln⁡∣x+1∣+C\dfrac{1}{2}\ln|x|+\dfrac{3}{2}\ln|x+2|-\ln|x+1|+C

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