Optimal. Leaf size=16 \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]
[Out]
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Rubi [A] time = 0.0118253, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]
Antiderivative was successfully verified.
[In] Int[(-1 + x^3)/(-1 + x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{3}}{3} + x + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-1)/(-1+x),x)
[Out]
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Mathematica [A] time = 0.000656925, size = 16, normalized size = 1. \[ \frac{x^3}{3}+\frac{x^2}{2}+x \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + x^3)/(-1 + x),x]
[Out]
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Maple [A] time = 0.001, size = 13, normalized size = 0.8 \[ x+{\frac{{x}^{2}}{2}}+{\frac{{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-1)/(-1+x),x)
[Out]
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Maxima [A] time = 0.785423, size = 16, normalized size = 1. \[ \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)/(x - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24503, size = 16, normalized size = 1. \[ \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)/(x - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.07334, size = 10, normalized size = 0.62 \[ \frac{x^{3}}{3} + \frac{x^{2}}{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-1)/(-1+x),x)
[Out]
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GIAC/XCAS [A] time = 0.259049, size = 16, normalized size = 1. \[ \frac{1}{3} \, x^{3} + \frac{1}{2} \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)/(x - 1),x, algorithm="giac")
[Out]