Optimal. Leaf size=17 \[ -\frac{\sqrt{2-b x}}{\sqrt{x}} \]
[Out]
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Rubi [A] time = 0.0116922, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{\sqrt{2-b x}}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(3/2)*Sqrt[2 - b*x]),x]
[Out]
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Rubi in Sympy [A] time = 2.55384, size = 14, normalized size = 0.82 \[ - \frac{\sqrt{- b x + 2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(3/2)/(-b*x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.011696, size = 17, normalized size = 1. \[ -\frac{\sqrt{2-b x}}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(3/2)*Sqrt[2 - b*x]),x]
[Out]
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Maple [A] time = 0.005, size = 14, normalized size = 0.8 \[ -{1\sqrt{-bx+2}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(3/2)/(-b*x+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.32228, size = 18, normalized size = 1.06 \[ -\frac{\sqrt{-b x + 2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + 2)*x^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20879, size = 18, normalized size = 1.06 \[ -\frac{\sqrt{-b x + 2}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + 2)*x^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.63751, size = 41, normalized size = 2.41 \[ \begin{cases} - \sqrt{b} \sqrt{-1 + \frac{2}{b x}} & \text{for}\: 2 \left |{\frac{1}{b x}}\right | > 1 \\- i \sqrt{b} \sqrt{1 - \frac{2}{b x}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(3/2)/(-b*x+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.224528, size = 41, normalized size = 2.41 \[ -\frac{\sqrt{-b x + 2} b^{2}}{\sqrt{{\left (b x - 2\right )} b + 2 \, b}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + 2)*x^(3/2)),x, algorithm="giac")
[Out]