Optimal. Leaf size=20 \[ -\frac{2 \sqrt{2-e x}}{\sqrt{3} e} \]
[Out]
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Rubi [A] time = 0.0405082, 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 \[ -\frac{2 \sqrt{2-e x}}{\sqrt{3} e} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[2 + e*x]/Sqrt[12 - 3*e^2*x^2],x]
[Out]
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Rubi in Sympy [A] time = 4.20868, size = 15, normalized size = 0.75 \[ - \frac{2 \sqrt{- 3 e x + 6}}{3 e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+2)**(1/2)/(-3*e**2*x**2+12)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0266031, size = 33, normalized size = 1.65 \[ \frac{2 (e x-2) \sqrt{e x+2}}{e \sqrt{12-3 e^2 x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[2 + e*x]/Sqrt[12 - 3*e^2*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 30, normalized size = 1.5 \[ 2\,{\frac{ \left ( ex-2 \right ) \sqrt{ex+2}}{e\sqrt{-3\,{e}^{2}{x}^{2}+12}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x)
[Out]
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Maxima [A] time = 0.788501, size = 34, normalized size = 1.7 \[ -\frac{2 i \, \sqrt{3} e x - 4 i \, \sqrt{3}}{3 \, \sqrt{e x - 2} e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(e*x + 2)/sqrt(-3*e^2*x^2 + 12),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22895, size = 45, normalized size = 2.25 \[ \frac{2 \,{\left (e^{2} x^{2} - 4\right )}}{\sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(e*x + 2)/sqrt(-3*e^2*x^2 + 12),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\sqrt{3} \int \frac{\sqrt{e x + 2}}{\sqrt{- e^{2} x^{2} + 4}}\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+2)**(1/2)/(-3*e**2*x**2+12)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{e x + 2}}{\sqrt{-3 \, e^{2} x^{2} + 12}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(e*x + 2)/sqrt(-3*e^2*x^2 + 12),x, algorithm="giac")
[Out]