CBSE

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

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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