Optimal. Leaf size=46 \[ -\frac{2}{15} \left (-x^3-1\right )^{5/2}-\frac{4}{9} \left (-x^3-1\right )^{3/2}-\frac{2}{3} \sqrt{-x^3-1} \]
[Out]
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Rubi [A] time = 0.0532925, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2}{15} \left (-x^3-1\right )^{5/2}-\frac{4}{9} \left (-x^3-1\right )^{3/2}-\frac{2}{3} \sqrt{-x^3-1} \]
Antiderivative was successfully verified.
[In] Int[x^8/Sqrt[-1 - x^3],x]
[Out]
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Rubi in Sympy [A] time = 5.44626, size = 41, normalized size = 0.89 \[ - \frac{2 \left (- x^{3} - 1\right )^{\frac{5}{2}}}{15} - \frac{4 \left (- x^{3} - 1\right )^{\frac{3}{2}}}{9} - \frac{2 \sqrt{- x^{3} - 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(-x**3-1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0138172, size = 27, normalized size = 0.59 \[ -\frac{2}{45} \sqrt{-x^3-1} \left (3 x^6-4 x^3+8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^8/Sqrt[-1 - x^3],x]
[Out]
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Maple [A] time = 0.007, size = 35, normalized size = 0.8 \[{\frac{ \left ( 2+2\,x \right ) \left ({x}^{2}-x+1 \right ) \left ( 3\,{x}^{6}-4\,{x}^{3}+8 \right ) }{45}{\frac{1}{\sqrt{-{x}^{3}-1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(-x^3-1)^(1/2),x)
[Out]
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Maxima [A] time = 1.43819, size = 46, normalized size = 1. \[ -\frac{2}{15} \,{\left (-x^{3} - 1\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (-x^{3} - 1\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(-x^3 - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225062, size = 31, normalized size = 0.67 \[ -\frac{2}{45} \,{\left (3 \, x^{6} - 4 \, x^{3} + 8\right )} \sqrt{-x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(-x^3 - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.89103, size = 46, normalized size = 1. \[ - \frac{2 x^{6} \sqrt{- x^{3} - 1}}{15} + \frac{8 x^{3} \sqrt{- x^{3} - 1}}{45} - \frac{16 \sqrt{- x^{3} - 1}}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(-x**3-1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216902, size = 55, normalized size = 1.2 \[ -\frac{2}{15} \,{\left (x^{3} + 1\right )}^{2} \sqrt{-x^{3} - 1} - \frac{4}{9} \,{\left (-x^{3} - 1\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(-x^3 - 1),x, algorithm="giac")
[Out]