Optimal. Leaf size=35 \[ -\frac{\sqrt [4]{3} \left (4-e^2 x^2\right )^{5/4}}{5 e (e x+2)^{5/2}} \]
[Out]
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Rubi [A] time = 0.0456917, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{\sqrt [4]{3} \left (4-e^2 x^2\right )^{5/4}}{5 e (e x+2)^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 4.20868, size = 26, normalized size = 0.74 \[ - \frac{\left (- 3 e^{2} x^{2} + 12\right )^{\frac{5}{4}}}{15 e \left (e x + 2\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0395077, size = 35, normalized size = 1. \[ \frac{(e x-2) \sqrt [4]{12-3 e^2 x^2}}{5 e (e x+2)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(12 - 3*e^2*x^2)^(1/4)/(2 + e*x)^(5/2),x]
[Out]
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Maple [A] time = 0.007, size = 30, normalized size = 0.9 \[{\frac{ex-2}{5\,e}\sqrt [4]{-3\,{e}^{2}{x}^{2}+12} \left ( ex+2 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(5/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-3 \, e^{2} x^{2} + 12\right )}^{\frac{1}{4}}}{{\left (e x + 2\right )}^{\frac{5}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*e^2*x^2 + 12)^(1/4)/(e*x + 2)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228555, size = 61, normalized size = 1.74 \[ \frac{{\left (-3 \, e^{2} x^{2} + 12\right )}^{\frac{1}{4}} \sqrt{e x + 2}{\left (e x - 2\right )}}{5 \,{\left (e^{3} x^{2} + 4 \, e^{2} x + 4 \, e\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*e^2*x^2 + 12)^(1/4)/(e*x + 2)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*e**2*x**2+12)**(1/4)/(e*x+2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.230931, size = 62, normalized size = 1.77 \[ -\frac{3^{\frac{1}{4}}{\left (-{\left (x e + 2\right )}^{2} + 4 \, x e + 8\right )}^{\frac{1}{4}}{\left (\frac{4}{x e + 2} - 1\right )} e^{\left (-1\right )}}{5 \, \sqrt{x e + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*e^2*x^2 + 12)^(1/4)/(e*x + 2)^(5/2),x, algorithm="giac")
[Out]