Optimal. Leaf size=14 \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]
[Out]
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Rubi [A] time = 0.00683868, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[b/x^2],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x \sqrt{\frac{b}{x^{2}}} \int x\, dx}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0036718, size = 14, normalized size = 1. \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[b/x^2],x]
[Out]
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Maple [A] time = 0.003, size = 11, normalized size = 0.8 \[{\frac{x}{2}{\frac{1}{\sqrt{{\frac{b}{{x}^{2}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.46196, size = 14, normalized size = 1. \[ \frac{x}{2 \, \sqrt{\frac{b}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b/x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250505, size = 20, normalized size = 1.43 \[ \frac{x^{3} \sqrt{\frac{b}{x^{2}}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b/x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.57395, size = 15, normalized size = 1.07 \[ \frac{x}{2 \sqrt{b} \sqrt{\frac{1}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221745, size = 16, normalized size = 1.14 \[ \frac{x^{2}}{2 \, \sqrt{b}{\rm sign}\left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b/x^2),x, algorithm="giac")
[Out]