Optimal. Leaf size=20 \[ \sqrt{2} \sin ^{-1}\left (\sqrt{\frac{2}{3}} \sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.0194492, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \sqrt{2} \sin ^{-1}\left (\sqrt{\frac{2}{3}} \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[3 - 2*x]*Sqrt[x]),x]
[Out]
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Rubi in Sympy [A] time = 2.56503, size = 17, normalized size = 0.85 \[ \sqrt{2} \operatorname{asin}{\left (\frac{\sqrt{6} \sqrt{x}}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3-2*x)**(1/2)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00934318, size = 20, normalized size = 1. \[ \sqrt{2} \sin ^{-1}\left (\sqrt{\frac{2}{3}} \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[3 - 2*x]*Sqrt[x]),x]
[Out]
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Maple [B] time = 0.008, size = 31, normalized size = 1.6 \[{\frac{\sqrt{2}}{2}\sqrt{ \left ( 3-2\,x \right ) x}\arcsin \left ({\frac{4\,x}{3}}-1 \right ){\frac{1}{\sqrt{3-2\,x}}}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3-2*x)^(1/2)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.50453, size = 28, normalized size = 1.4 \[ -\sqrt{2} \arctan \left (\frac{\sqrt{2} \sqrt{-2 \, x + 3}}{2 \, \sqrt{x}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x)*sqrt(-2*x + 3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208743, size = 28, normalized size = 1.4 \[ -\sqrt{2} \arctan \left (\frac{\sqrt{2} \sqrt{-2 \, x + 3}}{2 \, \sqrt{x}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x)*sqrt(-2*x + 3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.70845, size = 44, normalized size = 2.2 \[ \begin{cases} - \sqrt{2} i \operatorname{acosh}{\left (\frac{\sqrt{6} \sqrt{x}}{3} \right )} & \text{for}\: \frac{2 \left |{x}\right |}{3} > 1 \\\sqrt{2} \operatorname{asin}{\left (\frac{\sqrt{6} \sqrt{x}}{3} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3-2*x)**(1/2)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217587, size = 18, normalized size = 0.9 \[ \sqrt{2} \arcsin \left (\frac{1}{3} \, \sqrt{6} \sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x)*sqrt(-2*x + 3)),x, algorithm="giac")
[Out]