Optimal. Leaf size=16 \[ \frac{1}{2 b \left (a+\frac{b}{x^2}\right )} \]
[Out]
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Rubi [A] time = 0.0186636, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{2 b \left (a+\frac{b}{x^2}\right )} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)^2*x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.13541, size = 10, normalized size = 0.62 \[ \frac{1}{2 b \left (a + \frac{b}{x^{2}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**2/x**3,x)
[Out]
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Mathematica [A] time = 0.00401547, size = 16, normalized size = 1. \[ -\frac{1}{2 a \left (a x^2+b\right )} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)^2*x^3),x]
[Out]
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Maple [A] time = 0., size = 15, normalized size = 0.9 \[ -{\frac{1}{ \left ( 2\,a{x}^{2}+2\,b \right ) a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^2/x^3,x)
[Out]
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Maxima [A] time = 1.44247, size = 19, normalized size = 1.19 \[ \frac{1}{2 \,{\left (a + \frac{b}{x^{2}}\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^2*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214873, size = 20, normalized size = 1.25 \[ -\frac{1}{2 \,{\left (a^{2} x^{2} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^2*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.27337, size = 15, normalized size = 0.94 \[ - \frac{1}{2 a^{2} x^{2} + 2 a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**2/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220764, size = 19, normalized size = 1.19 \[ -\frac{1}{2 \,{\left (a x^{2} + b\right )} a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^2*x^3),x, algorithm="giac")
[Out]