Optimal. Leaf size=50 \[ \frac{37 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{10 \sqrt{10}}-\frac{3}{10} \sqrt{1-2 x} \sqrt{5 x+3} \]
[Out]
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Rubi [A] time = 0.0556831, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{37 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{10 \sqrt{10}}-\frac{3}{10} \sqrt{1-2 x} \sqrt{5 x+3} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 5.13679, size = 44, normalized size = 0.88 \[ - \frac{3 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{10} + \frac{37 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{100} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)/(1-2*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0324248, size = 50, normalized size = 1. \[ \frac{1}{100} \left (-30 \sqrt{1-2 x} \sqrt{5 x+3}-37 \sqrt{10} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)/(Sqrt[1 - 2*x]*Sqrt[3 + 5*x]),x]
[Out]
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Maple [A] time = 0.017, size = 55, normalized size = 1.1 \[{\frac{1}{200}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 37\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -60\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.49134, size = 35, normalized size = 0.7 \[ -\frac{37}{200} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) - \frac{3}{10} \, \sqrt{-10 \, x^{2} - x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(sqrt(5*x + 3)*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216072, size = 70, normalized size = 1.4 \[ -\frac{1}{200} \, \sqrt{10}{\left (6 \, \sqrt{10} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 37 \, \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(sqrt(5*x + 3)*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{3 x + 2}{\sqrt{- 2 x + 1} \sqrt{5 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)/(1-2*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227213, size = 54, normalized size = 1.08 \[ \frac{1}{100} \, \sqrt{5}{\left (37 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) - 6 \, \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(sqrt(5*x + 3)*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]