Optimal. Leaf size=30 \[ -\frac{x^2}{2}+\frac{1}{3} \log \left (x^2-x+1\right )+x-\frac{2}{3} \log (x+1) \]
[Out]
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Rubi [A] time = 0.0687791, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{x^2}{2}+\frac{1}{3} \log \left (x^2-x+1\right )+x-\frac{2}{3} \log (x+1) \]
Antiderivative was successfully verified.
[In] Int[((1 - x)*x^3)/(1 + x^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ x - \frac{2 \log{\left (x + 1 \right )}}{3} + \frac{\log{\left (x^{2} - x + 1 \right )}}{3} - \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-x)*x**3/(x**3+1),x)
[Out]
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Mathematica [A] time = 0.00712826, size = 30, normalized size = 1. \[ -\frac{x^2}{2}+\frac{1}{3} \log \left (x^2-x+1\right )+x-\frac{2}{3} \log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[((1 - x)*x^3)/(1 + x^3),x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.8 \[ x-{\frac{{x}^{2}}{2}}-{\frac{2\,\ln \left ( 1+x \right ) }{3}}+{\frac{\ln \left ({x}^{2}-x+1 \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-x)*x^3/(x^3+1),x)
[Out]
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Maxima [A] time = 1.52492, size = 32, normalized size = 1.07 \[ -\frac{1}{2} \, x^{2} + x + \frac{1}{3} \, \log \left (x^{2} - x + 1\right ) - \frac{2}{3} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 1)*x^3/(x^3 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208356, size = 32, normalized size = 1.07 \[ -\frac{1}{2} \, x^{2} + x + \frac{1}{3} \, \log \left (x^{2} - x + 1\right ) - \frac{2}{3} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 1)*x^3/(x^3 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.094271, size = 24, normalized size = 0.8 \[ - \frac{x^{2}}{2} + x - \frac{2 \log{\left (x + 1 \right )}}{3} + \frac{\log{\left (x^{2} - x + 1 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-x)*x**3/(x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.210913, size = 34, normalized size = 1.13 \[ -\frac{1}{2} \, x^{2} + x + \frac{1}{3} \,{\rm ln}\left (x^{2} - x + 1\right ) - \frac{2}{3} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 1)*x^3/(x^3 + 1),x, algorithm="giac")
[Out]