Optimal. Leaf size=45 \[ -\frac{27}{128} \sqrt{9-4 x^2} x-\frac{1}{16} \sqrt{9-4 x^2} x^3+\frac{243}{256} \sin ^{-1}\left (\frac{2 x}{3}\right ) \]
[Out]
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Rubi [A] time = 0.040779, antiderivative size = 45, 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 \[ -\frac{27}{128} \sqrt{9-4 x^2} x-\frac{1}{16} \sqrt{9-4 x^2} x^3+\frac{243}{256} \sin ^{-1}\left (\frac{2 x}{3}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^4/Sqrt[9 - 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.48068, size = 39, normalized size = 0.87 \[ - \frac{x^{3} \sqrt{- 4 x^{2} + 9}}{16} - \frac{27 x \sqrt{- 4 x^{2} + 9}}{128} + \frac{243 \operatorname{asin}{\left (\frac{2 x}{3} \right )}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(-4*x**2+9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0308707, size = 36, normalized size = 0.8 \[ \sqrt{9-4 x^2} \left (-\frac{x^3}{16}-\frac{27 x}{128}\right )+\frac{243}{256} \sin ^{-1}\left (\frac{2 x}{3}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^4/Sqrt[9 - 4*x^2],x]
[Out]
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Maple [A] time = 0.01, size = 34, normalized size = 0.8 \[{\frac{243}{256}\arcsin \left ({\frac{2\,x}{3}} \right ) }-{\frac{27\,x}{128}\sqrt{-4\,{x}^{2}+9}}-{\frac{{x}^{3}}{16}\sqrt{-4\,{x}^{2}+9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(-4*x^2+9)^(1/2),x)
[Out]
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Maxima [A] time = 1.53899, size = 45, normalized size = 1. \[ -\frac{1}{16} \, \sqrt{-4 \, x^{2} + 9} x^{3} - \frac{27}{128} \, \sqrt{-4 \, x^{2} + 9} x + \frac{243}{256} \, \arcsin \left (\frac{2}{3} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-4*x^2 + 9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230018, size = 178, normalized size = 3.96 \[ \frac{192 \, x^{7} - 648 \, x^{5} - 2430 \, x^{3} - 243 \,{\left (2 \, x^{4} - 36 \, x^{2} + 3 \,{\left (2 \, x^{2} - 9\right )} \sqrt{-4 \, x^{2} + 9} + 81\right )} \arctan \left (\frac{\sqrt{-4 \, x^{2} + 9} - 3}{2 \, x}\right ) -{\left (16 \, x^{7} - 234 \, x^{5} - 324 \, x^{3} + 2187 \, x\right )} \sqrt{-4 \, x^{2} + 9} + 6561 \, x}{128 \,{\left (2 \, x^{4} - 36 \, x^{2} + 3 \,{\left (2 \, x^{2} - 9\right )} \sqrt{-4 \, x^{2} + 9} + 81\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-4*x^2 + 9),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.99993, size = 39, normalized size = 0.87 \[ - \frac{x^{3} \sqrt{- 4 x^{2} + 9}}{16} - \frac{27 x \sqrt{- 4 x^{2} + 9}}{128} + \frac{243 \operatorname{asin}{\left (\frac{2 x}{3} \right )}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(-4*x**2+9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21582, size = 35, normalized size = 0.78 \[ -\frac{1}{128} \,{\left (8 \, x^{2} + 27\right )} \sqrt{-4 \, x^{2} + 9} x + \frac{243}{256} \, \arcsin \left (\frac{2}{3} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-4*x^2 + 9),x, algorithm="giac")
[Out]