Optimal. Leaf size=28 \[ \frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}} \]
[Out]
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Rubi [A] time = 0.01856, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}} \]
Antiderivative was successfully verified.
[In] Int[1/((3 - 6*x)^(3/2)*(2 + 4*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.86188, size = 19, normalized size = 0.68 \[ \frac{x}{6 \sqrt{- 6 x + 3} \sqrt{4 x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3-6*x)**(3/2)/(2+4*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.049143, size = 16, normalized size = 0.57 \[ \frac{x}{6 \sqrt{6-24 x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((3 - 6*x)^(3/2)*(2 + 4*x)^(3/2)),x]
[Out]
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Maple [A] time = 0.004, size = 28, normalized size = 1. \[ -{ \left ( -1+2\,x \right ) \left ( 1+2\,x \right ) x \left ( 3-6\,x \right ) ^{-{\frac{3}{2}}} \left ( 2+4\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3-6*x)^(3/2)/(2+4*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.33208, size = 16, normalized size = 0.57 \[ \frac{x}{6 \, \sqrt{-24 \, x^{2} + 6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((4*x + 2)^(3/2)*(-6*x + 3)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207193, size = 35, normalized size = 1.25 \[ -\frac{\sqrt{4 \, x + 2} x \sqrt{-6 \, x + 3}}{36 \,{\left (4 \, x^{2} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((4*x + 2)^(3/2)*(-6*x + 3)^(3/2)),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(1/(3-6*x)**(3/2)/(2+4*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219771, size = 96, normalized size = 3.43 \[ -\frac{\sqrt{6}{\left (\sqrt{-4 \, x + 2} - 2\right )}}{288 \, \sqrt{4 \, x + 2}} - \frac{\sqrt{6} \sqrt{4 \, x + 2} \sqrt{-4 \, x + 2}}{288 \,{\left (2 \, x - 1\right )}} + \frac{\sqrt{6} \sqrt{4 \, x + 2}}{288 \,{\left (\sqrt{-4 \, x + 2} - 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((4*x + 2)^(3/2)*(-6*x + 3)^(3/2)),x, algorithm="giac")
[Out]