Mathematics

Mathematics

Problem

Evaluate ∫(3x−2x+1+1x−4)dx\displaystyle \int \left( \dfrac{3}{x}-\dfrac{2}{x+1}+\dfrac{1}{x-4} \right)dx. a) 3ln⁡∣x∣−12ln⁡∣x+1∣+ln⁡∣x−4∣+C3\ln|x| - \dfrac12\ln|x+1| + \ln|x-4| + C b) 3ln⁡∣x∣+2ln⁡∣x+1∣+ln⁡∣x−4∣+C3\ln|x| + 2\ln|x+1| + \ln|x-4| + C c) 3ln⁡∣x∣−2ln⁡∣x+1∣+ln⁡∣x−4∣+C3\ln|x| - 2\ln|x+1| + \ln|x-4| + C d) 3ln⁡∣x∣−2ln⁡∣x+1∣−ln⁡∣x−4∣+C3\ln|x| - 2\ln|x+1| - \ln|x-4| + C

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