A Level

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Evaluate ∫3x−4(x+3)(2x−5)(x−1) dx\displaystyle \int \frac{3x-4}{(x+3)(2x-5)(x-1)}\,dx. (a) −1344ln⁡∣x+3∣+766ln⁡∣2x−5∣+112ln⁡∣x−1∣+C-\dfrac{13}{44}\ln|x+3|+\dfrac{7}{66}\ln|2x-5|+\dfrac{1}{12}\ln|x-1|+C (b) 1344ln⁡∣x+3∣+733ln⁡∣2x−5∣+112ln⁡∣x−1∣+C\dfrac{13}{44}\ln|x+3|+\dfrac{7}{33}\ln|2x-5|+\dfrac{1}{12}\ln|x-1|+C (c) −1344ln⁡∣x+3∣+733ln⁡∣2x−5∣+112ln⁡∣x−1∣+C-\dfrac{13}{44}\ln|x+3|+\dfrac{7}{33}\ln|2x-5|+\dfrac{1}{12}\ln|x-1|+C (d) −1344ln⁡∣x+3∣+1433ln⁡∣2x−5∣+112ln⁡∣x−1∣+C-\dfrac{13}{44}\ln|x+3|+\dfrac{14}{33}\ln|2x-5|+\dfrac{1}{12}\ln|x-1|+C

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