Optimal. Leaf size=20 \[ -\frac{2 (2-e x)^{3/2}}{\sqrt{3} e} \]
[Out]
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Rubi [A] time = 0.0396517, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{2 (2-e x)^{3/2}}{\sqrt{3} e} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[12 - 3*e^2*x^2]/Sqrt[2 + e*x],x]
[Out]
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Rubi in Sympy [A] time = 4.22721, size = 15, normalized size = 0.75 \[ - \frac{2 \left (- 3 e x + 6\right )^{\frac{3}{2}}}{9 e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-3*e**2*x**2+12)**(1/2)/(e*x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0285834, size = 34, normalized size = 1.7 \[ \frac{2 (e x-2) \sqrt{4-e^2 x^2}}{e \sqrt{3 e x+6}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[12 - 3*e^2*x^2]/Sqrt[2 + e*x],x]
[Out]
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Maple [A] time = 0.003, size = 30, normalized size = 1.5 \[{\frac{2\,ex-4}{3\,e}\sqrt{-3\,{e}^{2}{x}^{2}+12}{\frac{1}{\sqrt{ex+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(1/2),x)
[Out]
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Maxima [A] time = 0.786002, size = 34, normalized size = 1.7 \[ \frac{{\left (2 i \, \sqrt{3} e x - 4 i \, \sqrt{3}\right )} \sqrt{e x - 2}}{3 \, e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*e^2*x^2 + 12)/sqrt(e*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225133, size = 61, normalized size = 3.05 \[ -\frac{2 \,{\left (e^{3} x^{3} - 2 \, e^{2} x^{2} - 4 \, e x + 8\right )}}{\sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*e^2*x^2 + 12)/sqrt(e*x + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \sqrt{3} \int \frac{\sqrt{- e^{2} x^{2} + 4}}{\sqrt{e x + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*e**2*x**2+12)**(1/2)/(e*x+2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-3 \, e^{2} x^{2} + 12}}{\sqrt{e x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*e^2*x^2 + 12)/sqrt(e*x + 2),x, algorithm="giac")
[Out]