Optimal. Leaf size=43 \[ -\frac{a^3}{5 x^5}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8} \]
[Out]
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Rubi [A] time = 0.0467866, 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 \[ -\frac{a^3}{5 x^5}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x^6,x]
[Out]
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Rubi in Sympy [A] time = 8.24555, size = 39, normalized size = 0.91 \[ - \frac{a^{3}}{5 x^{5}} - \frac{a^{2} b}{2 x^{6}} - \frac{3 a b^{2}}{7 x^{7}} - \frac{b^{3}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x**6,x)
[Out]
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Mathematica [A] time = 0.0103863, size = 43, normalized size = 1. \[ -\frac{a^3}{5 x^5}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{8 x^8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{8\,{x}^{8}}}-{\frac{3\,a{b}^{2}}{7\,{x}^{7}}}-{\frac{{a}^{2}b}{2\,{x}^{6}}}-{\frac{{a}^{3}}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x^6,x)
[Out]
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Maxima [A] time = 1.45743, size = 47, normalized size = 1.09 \[ -\frac{56 \, a^{3} x^{3} + 140 \, a^{2} b x^{2} + 120 \, a b^{2} x + 35 \, b^{3}}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210364, size = 47, normalized size = 1.09 \[ -\frac{56 \, a^{3} x^{3} + 140 \, a^{2} b x^{2} + 120 \, a b^{2} x + 35 \, b^{3}}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.62728, size = 37, normalized size = 0.86 \[ - \frac{56 a^{3} x^{3} + 140 a^{2} b x^{2} + 120 a b^{2} x + 35 b^{3}}{280 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.217919, size = 47, normalized size = 1.09 \[ -\frac{56 \, a^{3} x^{3} + 140 \, a^{2} b x^{2} + 120 \, a b^{2} x + 35 \, b^{3}}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^6,x, algorithm="giac")
[Out]