Optimal. Leaf size=19 \[ -\frac{1}{a x \sqrt{a+\frac{b}{x^2}}} \]
[Out]
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Rubi [A] time = 0.0298115, antiderivative size = 19, 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 \[ -\frac{1}{a x \sqrt{a+\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)^(3/2)*x^2),x]
[Out]
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Rubi in Sympy [A] time = 2.79089, size = 15, normalized size = 0.79 \[ - \frac{1}{a x \sqrt{a + \frac{b}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**(3/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.010665, size = 19, normalized size = 1. \[ -\frac{1}{a x \sqrt{a+\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)^(3/2)*x^2),x]
[Out]
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Maple [A] time = 0.006, size = 29, normalized size = 1.5 \[ -{\frac{a{x}^{2}+b}{a{x}^{3}} \left ({\frac{a{x}^{2}+b}{{x}^{2}}} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^(3/2)/x^2,x)
[Out]
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Maxima [A] time = 1.4321, size = 23, normalized size = 1.21 \[ -\frac{1}{\sqrt{a + \frac{b}{x^{2}}} a x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230548, size = 39, normalized size = 2.05 \[ -\frac{x \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a^{2} x^{2} + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.57052, size = 20, normalized size = 1.05 \[ - \frac{1}{a \sqrt{b} \sqrt{\frac{a x^{2}}{b} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**(3/2)/x**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (a + \frac{b}{x^{2}}\right )}^{\frac{3}{2}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^2),x, algorithm="giac")
[Out]