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Problem Compute the integral ∫ x 2 ln ( 1 + x ) d x \displaystyle \int x^{2}\,\ln(1+x)\,dx ∫ x 2 ln ( 1 + x ) d x x 3 + 1 3 ln ( 1 + x ) − x 3 9 − x 2 6 − x 3 + C \dfrac{x^{3}+1}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{9} - \dfrac{x^{2}}{6} - \dfrac{x}{3} + C 3 x 3 + 1 ln ( 1 + x ) − 9 x 3 − 6 x 2 − 3 x + C x 3 + 1 3 ln ( 1 + x ) − x 3 3 + x 2 2 − x + C \dfrac{x^{3}+1}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{3} + \dfrac{x^{2}}{2} - x + C 3 x 3 + 1 ln ( 1 + x ) − 3 x 3 + 2 x 2 − x + C x 3 + 1 3 ln ( 1 + x ) − x 3 9 + x 2 6 − x 3 + C \dfrac{x^{3}+1}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{9} + \dfrac{x^{2}}{6} - \dfrac{x}{3} + C 3 x 3 + 1 ln ( 1 + x ) − 9 x 3 + 6 x 2 − 3 x + C x 3 3 ln ( 1 + x ) − x 3 9 + x 2 6 − x 3 + C \dfrac{x^{3}}{3}\,\ln(1+x) \, -\, \dfrac{x^{3}}{9} + \dfrac{x^{2}}{6} - \dfrac{x}{3} + C 3 x 3 ln ( 1 + x ) − 9 x 3 + 6 x 2 − 3 x + C Browse the problem library