Optimal. Leaf size=16 \[ \frac{1}{4 b \left (a+\frac{b}{x^2}\right )^2} \]
[Out]
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Rubi [A] time = 0.0186982, 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 \[ \frac{1}{4 b \left (a+\frac{b}{x^2}\right )^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)^3*x^3),x]
[Out]
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Rubi in Sympy [A] time = 2.142, size = 12, normalized size = 0.75 \[ \frac{1}{4 b \left (a + \frac{b}{x^{2}}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**3/x**3,x)
[Out]
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Mathematica [A] time = 0.0125049, size = 24, normalized size = 1.5 \[ -\frac{2 a x^2+b}{4 a^2 \left (a x^2+b\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)^3*x^3),x]
[Out]
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Maple [B] time = 0.01, size = 31, normalized size = 1.9 \[ -{\frac{1}{ \left ( 2\,a{x}^{2}+2\,b \right ){a}^{2}}}+{\frac{b}{4\,{a}^{2} \left ( a{x}^{2}+b \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^3/x^3,x)
[Out]
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Maxima [A] time = 1.4225, size = 19, normalized size = 1.19 \[ \frac{1}{4 \,{\left (a + \frac{b}{x^{2}}\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^3*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218064, size = 49, normalized size = 3.06 \[ -\frac{2 \, a x^{2} + b}{4 \,{\left (a^{4} x^{4} + 2 \, a^{3} b x^{2} + a^{2} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^3*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.71308, size = 36, normalized size = 2.25 \[ - \frac{2 a x^{2} + b}{4 a^{4} x^{4} + 8 a^{3} b x^{2} + 4 a^{2} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.225683, size = 30, normalized size = 1.88 \[ -\frac{2 \, a x^{2} + b}{4 \,{\left (a x^{2} + b\right )}^{2} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^3*x^3),x, algorithm="giac")
[Out]