Optimal. Leaf size=46 \[ \frac{1}{448} \left (4 x^2+9\right )^{7/2}-\frac{9}{160} \left (4 x^2+9\right )^{5/2}+\frac{27}{64} \left (4 x^2+9\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.0587316, 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 \[ \frac{1}{448} \left (4 x^2+9\right )^{7/2}-\frac{9}{160} \left (4 x^2+9\right )^{5/2}+\frac{27}{64} \left (4 x^2+9\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[x^5*Sqrt[9 + 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 6.62534, size = 37, normalized size = 0.8 \[ \frac{\left (4 x^{2} + 9\right )^{\frac{7}{2}}}{448} - \frac{9 \left (4 x^{2} + 9\right )^{\frac{5}{2}}}{160} + \frac{27 \left (4 x^{2} + 9\right )^{\frac{3}{2}}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5*(4*x**2+9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.016122, size = 27, normalized size = 0.59 \[ \frac{1}{280} \left (4 x^2+9\right )^{3/2} \left (10 x^4-18 x^2+27\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^5*Sqrt[9 + 4*x^2],x]
[Out]
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Maple [A] time = 0.006, size = 24, normalized size = 0.5 \[{\frac{10\,{x}^{4}-18\,{x}^{2}+27}{280} \left ( 4\,{x}^{2}+9 \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5*(4*x^2+9)^(1/2),x)
[Out]
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Maxima [A] time = 1.5017, size = 54, normalized size = 1.17 \[ \frac{1}{28} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} x^{4} - \frac{9}{140} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} x^{2} + \frac{27}{280} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 9)*x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221754, size = 180, normalized size = 3.91 \[ -\frac{655360 \, x^{14} + 3612672 \, x^{12} + 5999616 \, x^{10} + 4844448 \, x^{8} + 14451696 \, x^{6} + 28934010 \, x^{4} + 17360406 \, x^{2} - 2 \,{\left (163840 \, x^{13} + 718848 \, x^{11} + 794880 \, x^{9} + 655128 \, x^{7} + 3031182 \, x^{5} + 4133430 \, x^{3} + 1240029 \, x\right )} \sqrt{4 \, x^{2} + 9} + 1594323}{280 \,{\left (8192 \, x^{7} + 32256 \, x^{5} + 36288 \, x^{3} -{\left (4096 \, x^{6} + 11520 \, x^{4} + 7776 \, x^{2} + 729\right )} \sqrt{4 \, x^{2} + 9} + 10206 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 9)*x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.94183, size = 61, normalized size = 1.33 \[ \frac{x^{6} \sqrt{4 x^{2} + 9}}{7} + \frac{9 x^{4} \sqrt{4 x^{2} + 9}}{140} - \frac{27 x^{2} \sqrt{4 x^{2} + 9}}{140} + \frac{243 \sqrt{4 x^{2} + 9}}{280} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5*(4*x**2+9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.203657, size = 46, normalized size = 1. \[ \frac{1}{448} \,{\left (4 \, x^{2} + 9\right )}^{\frac{7}{2}} - \frac{9}{160} \,{\left (4 \, x^{2} + 9\right )}^{\frac{5}{2}} + \frac{27}{64} \,{\left (4 \, x^{2} + 9\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 9)*x^5,x, algorithm="giac")
[Out]