Mathematics

Mathematics

Problem

Determine ∫x tan⁡−1x dx\displaystyle \int x\,\tan^{-1} x\,dx. a) x tan⁡−1x−12ln⁡(1+x2)+Cx\,\tan^{-1}x - \dfrac12\ln(1+x^{2}) + C b) x2+12 tan⁡−1x−x2+C\dfrac{x^{2}+1}{2}\,\tan^{-1} x - \dfrac{x}{2} + C c) x2+12 tan⁡−1x+x2+C\dfrac{x^{2}+1}{2}\,\tan^{-1} x + \dfrac{x}{2} + C d) (x2+1) tan⁡−1x−x2+C(x^{2}+1)\,\tan^{-1} x - \dfrac{x}{2} + C

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