Optimal. Leaf size=30 \[ -\frac{a^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{b^2}{9 x^9} \]
[Out]
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Rubi [A] time = 0.0414464, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{b^2}{9 x^9} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2/x^6,x]
[Out]
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Rubi in Sympy [A] time = 6.91994, size = 27, normalized size = 0.9 \[ - \frac{a^{2}}{5 x^{5}} - \frac{2 a b}{7 x^{7}} - \frac{b^{2}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2/x**6,x)
[Out]
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Mathematica [A] time = 0.0021906, size = 30, normalized size = 1. \[ -\frac{a^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{b^2}{9 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{b}^{2}}{9\,{x}^{9}}}-{\frac{2\,ab}{7\,{x}^{7}}}-{\frac{{a}^{2}}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2/x^6,x)
[Out]
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Maxima [A] time = 1.43788, size = 35, normalized size = 1.17 \[ -\frac{63 \, a^{2} x^{4} + 90 \, a b x^{2} + 35 \, b^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214745, size = 35, normalized size = 1.17 \[ -\frac{63 \, a^{2} x^{4} + 90 \, a b x^{2} + 35 \, b^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.50328, size = 27, normalized size = 0.9 \[ - \frac{63 a^{2} x^{4} + 90 a b x^{2} + 35 b^{2}}{315 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.224208, size = 35, normalized size = 1.17 \[ -\frac{63 \, a^{2} x^{4} + 90 \, a b x^{2} + 35 \, b^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^6,x, algorithm="giac")
[Out]