Optimal. Leaf size=43 \[ -\frac{a^3}{5 x^5}-\frac{3 a^2 b}{7 x^7}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}} \]
[Out]
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Rubi [A] time = 0.0506904, antiderivative size = 43, 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 \[ -\frac{a^3}{5 x^5}-\frac{3 a^2 b}{7 x^7}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^3/x^6,x]
[Out]
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Rubi in Sympy [A] time = 8.62173, size = 39, normalized size = 0.91 \[ - \frac{a^{3}}{5 x^{5}} - \frac{3 a^{2} b}{7 x^{7}} - \frac{a b^{2}}{3 x^{9}} - \frac{b^{3}}{11 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**3/x**6,x)
[Out]
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Mathematica [A] time = 0.0125785, size = 43, normalized size = 1. \[ -\frac{a^3}{5 x^5}-\frac{3 a^2 b}{7 x^7}-\frac{a b^2}{3 x^9}-\frac{b^3}{11 x^{11}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^3/x^6,x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{11\,{x}^{11}}}-{\frac{a{b}^{2}}{3\,{x}^{9}}}-{\frac{3\,{a}^{2}b}{7\,{x}^{7}}}-{\frac{{a}^{3}}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^3/x^6,x)
[Out]
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Maxima [A] time = 1.43475, size = 50, normalized size = 1.16 \[ -\frac{231 \, a^{3} x^{6} + 495 \, a^{2} b x^{4} + 385 \, a b^{2} x^{2} + 105 \, b^{3}}{1155 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214452, size = 50, normalized size = 1.16 \[ -\frac{231 \, a^{3} x^{6} + 495 \, a^{2} b x^{4} + 385 \, a b^{2} x^{2} + 105 \, b^{3}}{1155 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.77952, size = 39, normalized size = 0.91 \[ - \frac{231 a^{3} x^{6} + 495 a^{2} b x^{4} + 385 a b^{2} x^{2} + 105 b^{3}}{1155 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**3/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.220084, size = 50, normalized size = 1.16 \[ -\frac{231 \, a^{3} x^{6} + 495 \, a^{2} b x^{4} + 385 \, a b^{2} x^{2} + 105 \, b^{3}}{1155 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^3/x^6,x, algorithm="giac")
[Out]