Optimal. Leaf size=41 \[ \frac{1}{7} x \left (1-x^4\right )^{3/2}+\frac{2}{7} x \sqrt{1-x^4}+\frac{4}{7} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
[Out]
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Rubi [A] time = 0.0182557, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{1}{7} x \left (1-x^4\right )^{3/2}+\frac{2}{7} x \sqrt{1-x^4}+\frac{4}{7} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 - x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.42777, size = 34, normalized size = 0.83 \[ \frac{x \left (- x^{4} + 1\right )^{\frac{3}{2}}}{7} + \frac{2 x \sqrt{- x^{4} + 1}}{7} + \frac{4 F\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**4+1)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0356835, size = 44, normalized size = 1.07 \[ \frac{x^9-4 x^5+4 \sqrt{1-x^4} F\left (\left .\sin ^{-1}(x)\right |-1\right )+3 x}{7 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.009, size = 59, normalized size = 1.4 \[ -{\frac{{x}^{5}}{7}\sqrt{-{x}^{4}+1}}+{\frac{3\,x}{7}\sqrt{-{x}^{4}+1}}+{\frac{4\,{\it EllipticF} \left ( x,i \right ) }{7}\sqrt{-{x}^{2}+1}\sqrt{{x}^{2}+1}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^4+1)^(3/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (-x^{4} + 1\right )}^{\frac{3}{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (-x^{4} + 1\right )}^{\frac{3}{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.37815, size = 31, normalized size = 0.76 \[ \frac{x \Gamma \left (\frac{1}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{3}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle |{x^{4} e^{2 i \pi }} \right )}}{4 \Gamma \left (\frac{5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**4+1)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (-x^{4} + 1\right )}^{\frac{3}{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^4 + 1)^(3/2),x, algorithm="giac")
[Out]