Optimal. Leaf size=13 \[ \frac{2 \sqrt{x^3-1}}{3} \]
[Out]
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Rubi [A] time = 0.00691803, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2 \sqrt{x^3-1}}{3} \]
Antiderivative was successfully verified.
[In] Int[x^2/Sqrt[-1 + x^3],x]
[Out]
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Rubi in Sympy [A] time = 1.65482, size = 10, normalized size = 0.77 \[ \frac{2 \sqrt{x^{3} - 1}}{3} \]
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 = 0.00507269, size = 13, normalized size = 1. \[ \frac{2 \sqrt{x^3-1}}{3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/Sqrt[-1 + x^3],x]
[Out]
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Maple [A] time = 0.006, size = 19, normalized size = 1.5 \[{\frac{ \left ( -2+2\,x \right ) \left ({x}^{2}+x+1 \right ) }{3}{\frac{1}{\sqrt{{x}^{3}-1}}}} \]
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 = 1.4261, size = 12, normalized size = 0.92 \[ \frac{2}{3} \, \sqrt{x^{3} - 1} \]
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 = 0.224821, size = 12, normalized size = 0.92 \[ \frac{2}{3} \, \sqrt{x^{3} - 1} \]
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 = 0.343646, size = 10, normalized size = 0.77 \[ \frac{2 \sqrt{x^{3} - 1}}{3} \]
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 = 0.218604, size = 12, normalized size = 0.92 \[ \frac{2}{3} \, \sqrt{x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(x^3 - 1),x, algorithm="giac")
[Out]