Optimal. Leaf size=19 \[ -\sqrt{2} \tanh ^{-1}\left (\sqrt{2} \sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.014124, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\sqrt{2} \tanh ^{-1}\left (\sqrt{2} \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[x]*(-1 + 2*x)),x]
[Out]
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Rubi in Sympy [A] time = 1.11609, size = 17, normalized size = 0.89 \[ - \sqrt{2} \operatorname{atanh}{\left (\sqrt{2} \sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(1/2)/(2*x-1),x)
[Out]
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Mathematica [A] time = 0.00697179, size = 19, normalized size = 1. \[ -\sqrt{2} \tanh ^{-1}\left (\sqrt{2} \sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[x]*(-1 + 2*x)),x]
[Out]
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \[ -{\it Artanh} \left ( \sqrt{2}\sqrt{x} \right ) \sqrt{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(1/2)/(-1+2*x),x)
[Out]
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Maxima [A] time = 1.50511, size = 38, normalized size = 2. \[ \frac{1}{2} \, \sqrt{2} \log \left (-\frac{2 \,{\left (\sqrt{2} - 2 \, \sqrt{x}\right )}}{2 \, \sqrt{2} + 4 \, \sqrt{x}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x - 1)*sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208419, size = 38, normalized size = 2. \[ \frac{1}{2} \, \sqrt{2} \log \left (-\frac{2 \, \sqrt{2} \sqrt{x} - 2 \, x - 1}{2 \, x - 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x - 1)*sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.75927, size = 39, normalized size = 2.05 \[ \begin{cases} - \sqrt{2} \operatorname{acoth}{\left (\sqrt{2} \sqrt{x} \right )} & \text{for}\: 2 \left |{x}\right | > 1 \\- \sqrt{2} \operatorname{atanh}{\left (\sqrt{2} \sqrt{x} \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(1/2)/(2*x-1),x)
[Out]
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GIAC/XCAS [A] time = 0.201376, size = 43, normalized size = 2.26 \[ -\frac{1}{2} \, \sqrt{2}{\rm ln}\left (\frac{1}{2} \, \sqrt{2} + \sqrt{x}\right ) + \frac{1}{2} \, \sqrt{2}{\rm ln}\left ({\left | -\frac{1}{2} \, \sqrt{2} + \sqrt{x} \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((2*x - 1)*sqrt(x)),x, algorithm="giac")
[Out]