Optimal. Leaf size=16 \[ -\frac{2 \sinh ^{-1}\left (\sqrt{2-b x}\right )}{b} \]
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Rubi [A] time = 0.0259772, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ -\frac{2 \sinh ^{-1}\left (\sqrt{2-b x}\right )}{b} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[2 - b*x]*Sqrt[3 - b*x]),x]
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Rubi in Sympy [A] time = 6.87606, size = 14, normalized size = 0.88 \[ - \frac{2 \operatorname{asinh}{\left (\sqrt{- b x + 2} \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-b*x+2)**(1/2)/(-b*x+3)**(1/2),x)
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Mathematica [A] time = 0.0120554, size = 16, normalized size = 1. \[ -\frac{2 \sinh ^{-1}\left (\sqrt{2-b x}\right )}{b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[2 - b*x]*Sqrt[3 - b*x]),x]
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Maple [B] time = 0.008, size = 70, normalized size = 4.4 \[{1\sqrt{ \left ( -bx+2 \right ) \left ( -bx+3 \right ) }\ln \left ({1 \left ( -{\frac{5\,b}{2}}+{b}^{2}x \right ){\frac{1}{\sqrt{{b}^{2}}}}}+\sqrt{{b}^{2}{x}^{2}-5\,bx+6} \right ){\frac{1}{\sqrt{-bx+2}}}{\frac{1}{\sqrt{-bx+3}}}{\frac{1}{\sqrt{{b}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-b*x+2)^(1/2)/(-b*x+3)^(1/2),x)
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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/(sqrt(-b*x + 3)*sqrt(-b*x + 2)),x, algorithm="maxima")
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Fricas [A] time = 0.208236, size = 41, normalized size = 2.56 \[ -\frac{\log \left (-2 \, b x + 2 \, \sqrt{-b x + 3} \sqrt{-b x + 2} + 5\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + 3)*sqrt(-b*x + 2)),x, algorithm="fricas")
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- b x + 2} \sqrt{- b x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-b*x+2)**(1/2)/(-b*x+3)**(1/2),x)
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GIAC/XCAS [A] time = 0.273011, size = 35, normalized size = 2.19 \[ \frac{2 \,{\rm ln}\left ({\left | -\sqrt{-b x + 3} + \sqrt{-b x + 2} \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + 3)*sqrt(-b*x + 2)),x, algorithm="giac")
[Out]