Optimal. Leaf size=46 \[ -\frac{1}{10} \left (1-x^4\right )^{5/2}+\frac{1}{3} \left (1-x^4\right )^{3/2}-\frac{\sqrt{1-x^4}}{2} \]
[Out]
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Rubi [A] time = 0.0531364, 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 \[ -\frac{1}{10} \left (1-x^4\right )^{5/2}+\frac{1}{3} \left (1-x^4\right )^{3/2}-\frac{\sqrt{1-x^4}}{2} \]
Antiderivative was successfully verified.
[In] Int[x^11/Sqrt[1 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 5.08847, size = 29, normalized size = 0.63 \[ - \frac{\left (- x^{4} + 1\right )^{\frac{5}{2}}}{10} + \frac{\left (- x^{4} + 1\right )^{\frac{3}{2}}}{3} - \frac{\sqrt{- x^{4} + 1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(-x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0161124, size = 27, normalized size = 0.59 \[ -\frac{1}{30} \sqrt{1-x^4} \left (3 x^8+4 x^4+8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^11/Sqrt[1 - x^4],x]
[Out]
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Maple [A] time = 0.007, size = 35, normalized size = 0.8 \[{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ) \left ( 3\,{x}^{8}+4\,{x}^{4}+8 \right ) }{30}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(-x^4+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.44005, size = 46, normalized size = 1. \[ -\frac{1}{10} \,{\left (-x^{4} + 1\right )}^{\frac{5}{2}} + \frac{1}{3} \,{\left (-x^{4} + 1\right )}^{\frac{3}{2}} - \frac{1}{2} \, \sqrt{-x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(-x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26617, size = 31, normalized size = 0.67 \[ -\frac{1}{30} \,{\left (3 \, x^{8} + 4 \, x^{4} + 8\right )} \sqrt{-x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(-x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.08342, size = 41, normalized size = 0.89 \[ - \frac{x^{8} \sqrt{- x^{4} + 1}}{10} - \frac{2 x^{4} \sqrt{- x^{4} + 1}}{15} - \frac{4 \sqrt{- x^{4} + 1}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(-x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21244, size = 55, normalized size = 1.2 \[ -\frac{1}{10} \,{\left (x^{4} - 1\right )}^{2} \sqrt{-x^{4} + 1} + \frac{1}{3} \,{\left (-x^{4} + 1\right )}^{\frac{3}{2}} - \frac{1}{2} \, \sqrt{-x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(-x^4 + 1),x, algorithm="giac")
[Out]