Optimal. Leaf size=16 \[ \frac{x \sqrt{a+\frac{b}{x^2}}}{a} \]
[Out]
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Rubi [A] time = 0.0108583, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x \sqrt{a+\frac{b}{x^2}}}{a} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[a + b/x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.24666, size = 12, normalized size = 0.75 \[ \frac{x \sqrt{a + \frac{b}{x^{2}}}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0112631, size = 16, normalized size = 1. \[ \frac{x \sqrt{a+\frac{b}{x^2}}}{a} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[a + b/x^2],x]
[Out]
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Maple [A] time = 0.003, size = 28, normalized size = 1.8 \[{\frac{a{x}^{2}+b}{ax}{\frac{1}{\sqrt{{\frac{a{x}^{2}+b}{{x}^{2}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.44192, size = 19, normalized size = 1.19 \[ \frac{\sqrt{a + \frac{b}{x^{2}}} x}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(a + b/x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229905, size = 24, normalized size = 1.5 \[ \frac{x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(a + b/x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.07586, size = 17, normalized size = 1.06 \[ \frac{\sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.224326, size = 38, normalized size = 2.38 \[ -\frac{\sqrt{b}{\rm sign}\left (x\right )}{a} + \frac{\sqrt{a x^{2} + b}}{a{\rm sign}\left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(a + b/x^2),x, algorithm="giac")
[Out]