Optimal. Leaf size=13 \[ x \sqrt{\frac{b}{x^2}} \log (x) \]
[Out]
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Rubi [A] time = 0.00848211, antiderivative size = 13, 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 \[ x \sqrt{\frac{b}{x^2}} \log (x) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b/x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.15439, size = 12, normalized size = 0.92 \[ x \sqrt{\frac{b}{x^{2}}} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b/x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00248467, size = 13, normalized size = 1. \[ x \sqrt{\frac{b}{x^2}} \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b/x^2],x]
[Out]
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Maple [A] time = 0.007, size = 12, normalized size = 0.9 \[ x\ln \left ( x \right ) \sqrt{{\frac{b}{{x}^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b/x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.43562, size = 15, normalized size = 1.15 \[ x \sqrt{\frac{b}{x^{2}}} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b/x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22476, size = 15, normalized size = 1.15 \[ x \sqrt{\frac{b}{x^{2}}} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b/x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{\frac{b}{x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b/x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.239839, size = 12, normalized size = 0.92 \[ \sqrt{b}{\rm ln}\left ({\left | x \right |}\right ){\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b/x^2),x, algorithm="giac")
[Out]