Optimal. Leaf size=43 \[ -\frac{a^3}{7 x^7}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4} \]
[Out]
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Rubi [A] time = 0.03139, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^3}{7 x^7}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^3/x^8,x]
[Out]
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Rubi in Sympy [A] time = 6.35112, size = 39, normalized size = 0.91 \[ - \frac{a^{3}}{7 x^{7}} - \frac{a^{2} b}{2 x^{6}} - \frac{3 a b^{2}}{5 x^{5}} - \frac{b^{3}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3/x**8,x)
[Out]
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Mathematica [A] time = 0.00457256, size = 43, normalized size = 1. \[ -\frac{a^3}{7 x^7}-\frac{a^2 b}{2 x^6}-\frac{3 a b^2}{5 x^5}-\frac{b^3}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^3/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{7\,{x}^{7}}}-{\frac{{a}^{2}b}{2\,{x}^{6}}}-{\frac{3\,a{b}^{2}}{5\,{x}^{5}}}-{\frac{{b}^{3}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3/x^8,x)
[Out]
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Maxima [A] time = 1.33498, size = 47, normalized size = 1.09 \[ -\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.190005, size = 47, normalized size = 1.09 \[ -\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.57391, size = 37, normalized size = 0.86 \[ - \frac{20 a^{3} + 70 a^{2} b x + 84 a b^{2} x^{2} + 35 b^{3} x^{3}}{140 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.213229, size = 47, normalized size = 1.09 \[ -\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^3/x^8,x, algorithm="giac")
[Out]