Optimal. Leaf size=15 \[ \frac{1}{b \sqrt{a+\frac{b}{x^2}}} \]
[Out]
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Rubi [A] time = 0.0291111, antiderivative size = 15, 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 \[ \frac{1}{b \sqrt{a+\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)^(3/2)*x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.13514, size = 12, normalized size = 0.8 \[ \frac{1}{b \sqrt{a + \frac{b}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**(3/2)/x**3,x)
[Out]
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Mathematica [A] time = 0.0166078, size = 15, normalized size = 1. \[ \frac{1}{b \sqrt{a+\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)^(3/2)*x^3),x]
[Out]
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Maple [B] time = 0.006, size = 28, normalized size = 1.9 \[{\frac{a{x}^{2}+b}{b{x}^{2}} \left ({\frac{a{x}^{2}+b}{{x}^{2}}} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^(3/2)/x^3,x)
[Out]
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Maxima [A] time = 1.43849, size = 18, normalized size = 1.2 \[ \frac{1}{\sqrt{a + \frac{b}{x^{2}}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237408, size = 39, normalized size = 2.6 \[ \frac{x^{2} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a b x^{2} + b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.96624, size = 26, normalized size = 1.73 \[ \begin{cases} \frac{1}{b \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{2 a^{\frac{3}{2}} x^{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**(3/2)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (a + \frac{b}{x^{2}}\right )}^{\frac{3}{2}} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^3),x, algorithm="giac")
[Out]