Optimal. Leaf size=47 \[ \frac{\sqrt{\frac{11}{2}} \sqrt{5-2 x} E\left (\left .\sin ^{-1}\left (\frac{\sqrt{4 x+1}}{\sqrt{11}}\right )\right |3\right )}{2 \sqrt{2 x-5}} \]
[Out]
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Rubi [A] time = 0.101281, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{\sqrt{\frac{11}{2}} \sqrt{5-2 x} E\left (\left .\sin ^{-1}\left (\frac{\sqrt{4 x+1}}{\sqrt{11}}\right )\right |3\right )}{2 \sqrt{2 x-5}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]
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Rubi in Sympy [A] time = 8.73329, size = 65, normalized size = 1.38 \[ \frac{\sqrt{11} \sqrt{- 3 x + 2} \sqrt{- \frac{4 x}{11} + \frac{10}{11}} E\left (\operatorname{asin}{\left (\frac{\sqrt{11} \sqrt{4 x + 1}}{11} \right )}\middle | 3\right )}{2 \sqrt{- \frac{12 x}{11} + \frac{8}{11}} \sqrt{2 x - 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2-3*x)**(1/2)/(-5+2*x)**(1/2)/(1+4*x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.732478, size = 111, normalized size = 2.36 \[ -\frac{\frac{2 (2 x-5) (3 x-2)}{\sqrt{2 x+\frac{1}{2}}}+\sqrt{11} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{\frac{3 x-2}{4 x+1}} (4 x+1) E\left (\left .\sin ^{-1}\left (\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right )\right |3\right )}{2 \sqrt{2-3 x} \sqrt{4 x-10}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[2 - 3*x]/(Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]
[Out]
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Maple [C] time = 0.018, size = 61, normalized size = 1.3 \[{\frac{\sqrt{11}}{2} \left ({\it EllipticF} \left ({\frac{2\,\sqrt{11}}{11}\sqrt{2-3\,x}},{\frac{i}{2}}\sqrt{2} \right ) -{\it EllipticE} \left ({\frac{2\,\sqrt{11}}{11}\sqrt{2-3\,x}},{\frac{i}{2}}\sqrt{2} \right ) \right ) \sqrt{5-2\,x}{\frac{1}{\sqrt{-5+2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-3 \, x + 2}}{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*x + 2)/(sqrt(4*x + 1)*sqrt(2*x - 5)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{-3 \, x + 2}}{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*x + 2)/(sqrt(4*x + 1)*sqrt(2*x - 5)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- 3 x + 2}}{\sqrt{2 x - 5} \sqrt{4 x + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2-3*x)**(1/2)/(-5+2*x)**(1/2)/(1+4*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-3 \, x + 2}}{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*x + 2)/(sqrt(4*x + 1)*sqrt(2*x - 5)),x, algorithm="giac")
[Out]