A Level

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

Problem

Find ∫4x+1(x−2)(x+1)(x−5) dx\displaystyle \int \frac{4x+1}{(x-2)(x+1)(x-5)}\,dx. (a) −ln⁡∣x−2∣−16ln⁡∣x+1∣+76ln⁡∣x−5∣+C-\ln|x-2|-\dfrac{1}{6}\ln|x+1|+\dfrac{7}{6}\ln|x-5|+C (b) ln⁡∣x−2∣−16ln⁡∣x+1∣+76ln⁡∣x−5∣+C\ln|x-2|-\dfrac{1}{6}\ln|x+1|+\dfrac{7}{6}\ln|x-5|+C (c) −ln⁡∣x−2∣+16ln⁡∣x+1∣+76ln⁡∣x−5∣+C-\ln|x-2|+\dfrac{1}{6}\ln|x+1|+\dfrac{7}{6}\ln|x-5|+C (d) −ln⁡∣x−2∣−16ln⁡∣x+1∣+ln⁡∣x−5∣+C-\ln|x-2|-\dfrac{1}{6}\ln|x+1|+\ln|x-5|+C

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