Optimal. Leaf size=43 \[ -\frac{a^3}{4 x^4}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7} \]
[Out]
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Rubi [A] time = 0.0463291, 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 \[ -\frac{a^3}{4 x^4}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^3/x^5,x]
[Out]
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Rubi in Sympy [A] time = 8.07578, size = 39, normalized size = 0.91 \[ - \frac{a^{3}}{4 x^{4}} - \frac{3 a^{2} b}{5 x^{5}} - \frac{a b^{2}}{2 x^{6}} - \frac{b^{3}}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**3/x**5,x)
[Out]
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Mathematica [A] time = 0.00570754, size = 43, normalized size = 1. \[ -\frac{a^3}{4 x^4}-\frac{3 a^2 b}{5 x^5}-\frac{a b^2}{2 x^6}-\frac{b^3}{7 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^3/x^5,x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{{b}^{3}}{7\,{x}^{7}}}-{\frac{a{b}^{2}}{2\,{x}^{6}}}-{\frac{3\,{a}^{2}b}{5\,{x}^{5}}}-{\frac{{a}^{3}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^3/x^5,x)
[Out]
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Maxima [A] time = 1.4368, size = 47, normalized size = 1.09 \[ -\frac{35 \, a^{3} x^{3} + 84 \, a^{2} b x^{2} + 70 \, a b^{2} x + 20 \, b^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214236, size = 47, normalized size = 1.09 \[ -\frac{35 \, a^{3} x^{3} + 84 \, a^{2} b x^{2} + 70 \, a b^{2} x + 20 \, b^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.65233, size = 37, normalized size = 0.86 \[ - \frac{35 a^{3} x^{3} + 84 a^{2} b x^{2} + 70 a b^{2} x + 20 b^{3}}{140 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**3/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.21777, size = 47, normalized size = 1.09 \[ -\frac{35 \, a^{3} x^{3} + 84 \, a^{2} b x^{2} + 70 \, a b^{2} x + 20 \, b^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^3/x^5,x, algorithm="giac")
[Out]