Optimal. Leaf size=15 \[ -\frac{2}{3} \sqrt{1-x^3} \]
[Out]
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Rubi [A] time = 0.00860274, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2}{3} \sqrt{1-x^3} \]
Antiderivative was successfully verified.
[In] Int[x^2/Sqrt[1 - x^3],x]
[Out]
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Rubi in Sympy [A] time = 1.99641, size = 12, normalized size = 0.8 \[ - \frac{2 \sqrt{- x^{3} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-x**3+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0056685, size = 15, normalized size = 1. \[ -\frac{2}{3} \sqrt{1-x^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/Sqrt[1 - x^3],x]
[Out]
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Maple [A] time = 0.006, size = 21, normalized size = 1.4 \[{\frac{ \left ( -2+2\,x \right ) \left ({x}^{2}+x+1 \right ) }{3}{\frac{1}{\sqrt{-{x}^{3}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-x^3+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.42379, size = 15, normalized size = 1. \[ -\frac{2}{3} \, \sqrt{-x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(-x^3 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222621, size = 15, normalized size = 1. \[ -\frac{2}{3} \, \sqrt{-x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(-x^3 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.342876, size = 12, normalized size = 0.8 \[ - \frac{2 \sqrt{- x^{3} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(-x**3+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.218291, size = 15, normalized size = 1. \[ -\frac{2}{3} \, \sqrt{-x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(-x^3 + 1),x, algorithm="giac")
[Out]