Optimal. Leaf size=15 \[ -\frac{1}{12} \left (-4 x^2-9\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.00875601, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{12} \left (-4 x^2-9\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[x*Sqrt[-9 - 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.97019, size = 14, normalized size = 0.93 \[ - \frac{\left (- 4 x^{2} - 9\right )^{\frac{3}{2}}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(-4*x**2-9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00321487, size = 15, normalized size = 1. \[ -\frac{1}{12} \left (-4 x^2-9\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[x*Sqrt[-9 - 4*x^2],x]
[Out]
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Maple [A] time = 0.003, size = 12, normalized size = 0.8 \[ -{\frac{1}{12} \left ( -4\,{x}^{2}-9 \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(-4*x^2-9)^(1/2),x)
[Out]
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Maxima [A] time = 1.34706, size = 15, normalized size = 1. \[ -\frac{1}{12} \,{\left (-4 \, x^{2} - 9\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-4*x^2 - 9)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230497, size = 24, normalized size = 1.6 \[ \frac{1}{12} \,{\left (4 \, x^{2} + 9\right )} \sqrt{-4 \, x^{2} - 9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-4*x^2 - 9)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.511571, size = 31, normalized size = 2.07 \[ \frac{x^{2} \sqrt{- 4 x^{2} - 9}}{3} + \frac{3 \sqrt{- 4 x^{2} - 9}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(-4*x**2-9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.20191, size = 16, normalized size = 1.07 \[ \frac{1}{12} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} i \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-4*x^2 - 9)*x,x, algorithm="giac")
[Out]