Compute the integral .

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

Problem

Compute the integral ∫x2 ln⁡(1+x) dx\displaystyle \int x^{2}\,\ln(1+x)\,dx. (a) x3+13 ln⁡(1+x) − x39−x26−x3+C\dfrac{x^{3}+1}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{9} - \dfrac{x^{2}}{6} - \dfrac{x}{3} + C (b) x3+13 ln⁡(1+x) − x33+x22−x+C\dfrac{x^{3}+1}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{3} + \dfrac{x^{2}}{2} - x + C (c) x3+13 ln⁡(1+x) − x39+x26−x3+C\dfrac{x^{3}+1}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{9} + \dfrac{x^{2}}{6} - \dfrac{x}{3} + C (d) x33 ln⁡(1+x) − x39+x26−x3+C\dfrac{x^{3}}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{9} + \dfrac{x^{2}}{6} - \dfrac{x}{3} + C

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