Optimal. Leaf size=39 \[ -\frac{x^3}{9}+\frac{1}{3} x^3 \log (x+1)+\frac{x^2}{6}-\frac{x}{3}+\frac{1}{3} \log (x+1) \]
[Out]
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Rubi [A] time = 0.0310959, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{x^3}{9}+\frac{1}{3} x^3 \log (x+1)+\frac{x^2}{6}-\frac{x}{3}+\frac{1}{3} \log (x+1) \]
Antiderivative was successfully verified.
[In] Int[x^2*Log[1 + x],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{3} \log{\left (x + 1 \right )}}{3} - \frac{x^{3}}{9} - \frac{x}{3} + \frac{\log{\left (x + 1 \right )}}{3} + \frac{\int x\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*ln(1+x),x)
[Out]
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Mathematica [A] time = 0.00314863, size = 39, normalized size = 1. \[ -\frac{x^3}{9}+\frac{1}{3} x^3 \log (x+1)+\frac{x^2}{6}-\frac{x}{3}+\frac{1}{3} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[x^2*Log[1 + x],x]
[Out]
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Maple [A] time = 0.004, size = 46, normalized size = 1.2 \[{\frac{ \left ( 1+x \right ) ^{3}\ln \left ( 1+x \right ) }{3}}-{\frac{{x}^{3}}{9}}+{\frac{{x}^{2}}{6}}-{\frac{x}{3}}-{\frac{11}{18}}- \left ( 1+x \right ) ^{2}\ln \left ( 1+x \right ) +\ln \left ( 1+x \right ) \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*ln(1+x),x)
[Out]
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Maxima [A] time = 1.34187, size = 39, normalized size = 1. \[ \frac{1}{3} \, x^{3} \log \left (x + 1\right ) - \frac{1}{9} \, x^{3} + \frac{1}{6} \, x^{2} - \frac{1}{3} \, x + \frac{1}{3} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*log(x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205935, size = 34, normalized size = 0.87 \[ -\frac{1}{9} \, x^{3} + \frac{1}{6} \, x^{2} + \frac{1}{3} \,{\left (x^{3} + 1\right )} \log \left (x + 1\right ) - \frac{1}{3} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*log(x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.109592, size = 29, normalized size = 0.74 \[ \frac{x^{3} \log{\left (x + 1 \right )}}{3} - \frac{x^{3}}{9} + \frac{x^{2}}{6} - \frac{x}{3} + \frac{\log{\left (x + 1 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*ln(1+x),x)
[Out]
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GIAC/XCAS [A] time = 0.22657, size = 66, normalized size = 1.69 \[ \frac{1}{3} \,{\left (x + 1\right )}^{3}{\rm ln}\left (x + 1\right ) - \frac{1}{9} \,{\left (x + 1\right )}^{3} -{\left (x + 1\right )}^{2}{\rm ln}\left (x + 1\right ) + \frac{1}{2} \,{\left (x + 1\right )}^{2} +{\left (x + 1\right )}{\rm ln}\left (x + 1\right ) - x - 1 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*log(x + 1),x, algorithm="giac")
[Out]