Optimal. Leaf size=29 \[ -\frac{2 \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{\sqrt{a} \sqrt{b}} \]
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Rubi [A] time = 0.025614, antiderivative size = 29, 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 \[ -\frac{2 \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{\sqrt{a} \sqrt{b}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[x]*(-a + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 4.86987, size = 29, normalized size = 1. \[ - \frac{2 \operatorname{atanh}{\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right )}}{\sqrt{a} \sqrt{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x-a)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00796534, size = 29, normalized size = 1. \[ -\frac{2 \tanh ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{\sqrt{a} \sqrt{b}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[x]*(-a + b*x)),x]
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Maple [A] time = 0.007, size = 19, normalized size = 0.7 \[ -2\,{\frac{1}{\sqrt{ab}}{\it Artanh} \left ({\frac{b\sqrt{x}}{\sqrt{ab}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x-a)/x^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - a)*sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218475, size = 1, normalized size = 0.03 \[ \left [\frac{\log \left (-\frac{2 \, a b \sqrt{x} - \sqrt{a b}{\left (b x + a\right )}}{b x - a}\right )}{\sqrt{a b}}, \frac{2 \, \arctan \left (\frac{a}{\sqrt{-a b} \sqrt{x}}\right )}{\sqrt{-a b}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - a)*sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.96851, size = 65, normalized size = 2.24 \[ \begin{cases} - \frac{2 \operatorname{acoth}{\left (\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right )}}{\sqrt{a} \sqrt{b}} & \text{for}\: \left |{\frac{a}{b x}}\right | > 1 \\- \frac{2 \operatorname{atanh}{\left (\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right )}}{\sqrt{a} \sqrt{b}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x-a)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215732, size = 27, normalized size = 0.93 \[ \frac{2 \, \arctan \left (\frac{b \sqrt{x}}{\sqrt{-a b}}\right )}{\sqrt{-a b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - a)*sqrt(x)),x, algorithm="giac")
[Out]