Optimal. Leaf size=61 \[ \frac{2}{21} \left (-x^3-1\right )^{7/2}+\frac{2}{5} \left (-x^3-1\right )^{5/2}+\frac{2}{3} \left (-x^3-1\right )^{3/2}+\frac{2}{3} \sqrt{-x^3-1} \]
[Out]
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Rubi [A] time = 0.0659667, antiderivative size = 61, 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 \[ \frac{2}{21} \left (-x^3-1\right )^{7/2}+\frac{2}{5} \left (-x^3-1\right )^{5/2}+\frac{2}{3} \left (-x^3-1\right )^{3/2}+\frac{2}{3} \sqrt{-x^3-1} \]
Antiderivative was successfully verified.
[In] Int[x^11/Sqrt[-1 - x^3],x]
[Out]
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Rubi in Sympy [A] time = 7.32734, size = 53, normalized size = 0.87 \[ \frac{2 \left (- x^{3} - 1\right )^{\frac{7}{2}}}{21} + \frac{2 \left (- x^{3} - 1\right )^{\frac{5}{2}}}{5} + \frac{2 \left (- x^{3} - 1\right )^{\frac{3}{2}}}{3} + \frac{2 \sqrt{- x^{3} - 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(-x**3-1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0167002, size = 32, normalized size = 0.52 \[ -\frac{2}{105} \sqrt{-x^3-1} \left (5 x^9-6 x^6+8 x^3-16\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^11/Sqrt[-1 - x^3],x]
[Out]
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Maple [A] time = 0.007, size = 40, normalized size = 0.7 \[{\frac{ \left ( 2+2\,x \right ) \left ({x}^{2}-x+1 \right ) \left ( 5\,{x}^{9}-6\,{x}^{6}+8\,{x}^{3}-16 \right ) }{105}{\frac{1}{\sqrt{-{x}^{3}-1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(-x^3-1)^(1/2),x)
[Out]
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Maxima [A] time = 1.43992, size = 61, normalized size = 1. \[ \frac{2}{21} \,{\left (-x^{3} - 1\right )}^{\frac{7}{2}} + \frac{2}{5} \,{\left (-x^{3} - 1\right )}^{\frac{5}{2}} + \frac{2}{3} \,{\left (-x^{3} - 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{-x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(-x^3 - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225686, size = 38, normalized size = 0.62 \[ -\frac{2}{105} \,{\left (5 \, x^{9} - 6 \, x^{6} + 8 \, x^{3} - 16\right )} \sqrt{-x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(-x^3 - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.50879, size = 63, normalized size = 1.03 \[ - \frac{2 x^{9} \sqrt{- x^{3} - 1}}{21} + \frac{4 x^{6} \sqrt{- x^{3} - 1}}{35} - \frac{16 x^{3} \sqrt{- x^{3} - 1}}{105} + \frac{32 \sqrt{- x^{3} - 1}}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(-x**3-1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212613, size = 80, normalized size = 1.31 \[ -\frac{2}{21} \,{\left (x^{3} + 1\right )}^{3} \sqrt{-x^{3} - 1} + \frac{2}{5} \,{\left (x^{3} + 1\right )}^{2} \sqrt{-x^{3} - 1} + \frac{2}{3} \,{\left (-x^{3} - 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, \sqrt{-x^{3} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(-x^3 - 1),x, algorithm="giac")
[Out]