Optimal. Leaf size=40 \[ \frac{2}{15} \left (x^3-1\right )^{5/2}+\frac{4}{9} \left (x^3-1\right )^{3/2}+\frac{2 \sqrt{x^3-1}}{3} \]
[Out]
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Rubi [A] time = 0.0413709, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{2}{15} \left (x^3-1\right )^{5/2}+\frac{4}{9} \left (x^3-1\right )^{3/2}+\frac{2 \sqrt{x^3-1}}{3} \]
Antiderivative was successfully verified.
[In] Int[x^8/Sqrt[-1 + x^3],x]
[Out]
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Rubi in Sympy [A] time = 4.19718, size = 34, normalized size = 0.85 \[ \frac{2 \left (x^{3} - 1\right )^{\frac{5}{2}}}{15} + \frac{4 \left (x^{3} - 1\right )^{\frac{3}{2}}}{9} + \frac{2 \sqrt{x^{3} - 1}}{3} \]
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 = 0.0134002, size = 25, normalized size = 0.62 \[ \frac{2}{45} \sqrt{x^3-1} \left (3 x^6+4 x^3+8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^8/Sqrt[-1 + x^3],x]
[Out]
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Maple [A] time = 0.006, size = 31, 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 = 1.43903, size = 38, normalized size = 0.95 \[ \frac{2}{15} \,{\left (x^{3} - 1\right )}^{\frac{5}{2}} + \frac{4}{9} \,{\left (x^{3} - 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} - 1} \]
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 = 0.228316, size = 28, normalized size = 0.7 \[ \frac{2}{45} \,{\left (3 \, x^{6} + 4 \, x^{3} + 8\right )} \sqrt{x^{3} - 1} \]
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 = 1.88879, size = 41, normalized size = 1.02 \[ \frac{2 x^{6} \sqrt{x^{3} - 1}}{15} + \frac{8 x^{3} \sqrt{x^{3} - 1}}{45} + \frac{16 \sqrt{x^{3} - 1}}{45} \]
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 = 0.212981, size = 38, normalized size = 0.95 \[ \frac{2}{15} \,{\left (x^{3} - 1\right )}^{\frac{5}{2}} + \frac{4}{9} \,{\left (x^{3} - 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(x^3 - 1),x, algorithm="giac")
[Out]