Mathematics

Mathematics

Problem

Determine ∫xtan⁡−1x dx\displaystyle \int x\tan^{-1}x\,dx. a) x22tan⁡−1x−x2−12tan⁡−1x+C\dfrac{x^{2}}{2}\tan^{-1}x - \dfrac{x}{2} - \dfrac{1}{2}\tan^{-1}x + C b) x2tan⁡−1x−x+tan⁡−1x+Cx^{2}\tan^{-1}x - x + \tan^{-1}x + C c) x22tan⁡−1x−x2+12tan⁡−1x+C\dfrac{x^{2}}{2}\tan^{-1}x - \dfrac{x}{2} + \dfrac{1}{2}\tan^{-1}x + C d) x22tan⁡−1x−12ln⁡(1+x2)+C\dfrac{x^{2}}{2}\tan^{-1}x - \dfrac{1}{2}\ln(1+x^{2}) + C

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