Mathematics

Mathematics

Problem

Evaluate ∫tan⁡−1x dx\displaystyle \int \tan^{-1}x\,dx. a) xtan⁡−1x+12ln⁡(1+x2)+Cx\tan^{-1}x+\dfrac{1}{2}\ln(1+x^{2})+C b) 12x2tan⁡−1x−ln⁡(1+x2)+C\dfrac{1}{2}x^{2}\tan^{-1}x-\ln(1+x^{2})+C c) xtan⁡−1x−12ln⁡(1+x2)+Cx\tan^{-1}x-\dfrac{1}{2}\ln(1+x^{2})+C d) xtan⁡−1x−ln⁡(1+x2)+Cx\tan^{-1}x-\ln(1+x^{2})+C

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