Optimal. Leaf size=31 \[ \frac{1}{80} \left (4 x^2-9\right )^{5/2}+\frac{3}{16} \left (4 x^2-9\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.0424921, antiderivative size = 31, 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 \[ \frac{1}{80} \left (4 x^2-9\right )^{5/2}+\frac{3}{16} \left (4 x^2-9\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[x^3*Sqrt[-9 + 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.50386, size = 24, normalized size = 0.77 \[ \frac{\left (4 x^{2} - 9\right )^{\frac{5}{2}}}{80} + \frac{3 \left (4 x^{2} - 9\right )^{\frac{3}{2}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(4*x**2-9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00876401, size = 22, normalized size = 0.71 \[ \frac{1}{40} \left (2 x^2+3\right ) \left (4 x^2-9\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*Sqrt[-9 + 4*x^2],x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 0.9 \[{\frac{ \left ( 2\,x-3 \right ) \left ( 2\,x+3 \right ) \left ( 2\,{x}^{2}+3 \right ) }{40}\sqrt{4\,{x}^{2}-9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(4*x^2-9)^(1/2),x)
[Out]
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Maxima [A] time = 1.48749, size = 35, normalized size = 1.13 \[ \frac{1}{20} \,{\left (4 \, x^{2} - 9\right )}^{\frac{3}{2}} x^{2} + \frac{3}{40} \,{\left (4 \, x^{2} - 9\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 - 9)*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22268, size = 139, normalized size = 4.48 \[ -\frac{8192 \, x^{10} - 38400 \, x^{8} + 30240 \, x^{6} + 77760 \, x^{4} - 109350 \, x^{2} - 2 \,{\left (2048 \, x^{9} - 7296 \, x^{7} + 648 \, x^{5} + 17010 \, x^{3} - 10935 \, x\right )} \sqrt{4 \, x^{2} - 9} + 19683}{40 \,{\left (512 \, x^{5} - 1440 \, x^{3} -{\left (256 \, x^{4} - 432 \, x^{2} + 81\right )} \sqrt{4 \, x^{2} - 9} + 810 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 - 9)*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.77854, size = 44, normalized size = 1.42 \[ \frac{x^{4} \sqrt{4 x^{2} - 9}}{5} - \frac{3 x^{2} \sqrt{4 x^{2} - 9}}{20} - \frac{27 \sqrt{4 x^{2} - 9}}{40} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(4*x**2-9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.2021, size = 31, normalized size = 1. \[ \frac{1}{80} \,{\left (4 \, x^{2} - 9\right )}^{\frac{5}{2}} + \frac{3}{16} \,{\left (4 \, x^{2} - 9\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 - 9)*x^3,x, algorithm="giac")
[Out]