Optimal. Leaf size=16 \[ -\frac{\sqrt{a+\frac{b}{x^2}}}{b} \]
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Rubi [A] time = 0.0289002, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{\sqrt{a+\frac{b}{x^2}}}{b} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[a + b/x^2]*x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.11404, size = 12, normalized size = 0.75 \[ - \frac{\sqrt{a + \frac{b}{x^{2}}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**(1/2)/x**3,x)
[Out]
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Mathematica [A] time = 0.0259794, size = 16, normalized size = 1. \[ -\frac{\sqrt{a+\frac{b}{x^2}}}{b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[a + b/x^2]*x^3),x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 1.8 \[ -{\frac{a{x}^{2}+b}{b{x}^{2}}{\frac{1}{\sqrt{{\frac{a{x}^{2}+b}{{x}^{2}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^(1/2)/x^3,x)
[Out]
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Maxima [A] time = 1.43617, size = 19, normalized size = 1.19 \[ -\frac{\sqrt{a + \frac{b}{x^{2}}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226257, size = 24, normalized size = 1.5 \[ -\frac{\sqrt{\frac{a x^{2} + b}{x^{2}}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.08182, size = 26, normalized size = 1.62 \[ \begin{cases} - \frac{\sqrt{a + \frac{b}{x^{2}}}}{b} & \text{for}\: b \neq 0 \\- \frac{1}{2 \sqrt{a} x^{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**(1/2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.221484, size = 19, normalized size = 1.19 \[ -\frac{\sqrt{a + \frac{b}{x^{2}}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^2)*x^3),x, algorithm="giac")
[Out]