Optimal. Leaf size=43 \[ -\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]
[Out]
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Rubi [A] time = 0.0530241, 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 \[ -\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^3/x^19,x]
[Out]
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Rubi in Sympy [A] time = 8.88161, size = 37, normalized size = 0.86 \[ - \frac{a^{3}}{18 x^{18}} - \frac{a^{2} b}{5 x^{15}} - \frac{a b^{2}}{4 x^{12}} - \frac{b^{3}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**3/x**19,x)
[Out]
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Mathematica [A] time = 0.00680988, size = 43, normalized size = 1. \[ -\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^3/x^19,x]
[Out]
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Maple [A] time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{{a}^{3}}{18\,{x}^{18}}}-{\frac{{a}^{2}b}{5\,{x}^{15}}}-{\frac{a{b}^{2}}{4\,{x}^{12}}}-{\frac{{b}^{3}}{9\,{x}^{9}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^3/x^19,x)
[Out]
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Maxima [A] time = 1.44141, size = 50, normalized size = 1.16 \[ -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^19,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204639, size = 50, normalized size = 1.16 \[ -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^19,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.11828, size = 39, normalized size = 0.91 \[ - \frac{10 a^{3} + 36 a^{2} b x^{3} + 45 a b^{2} x^{6} + 20 b^{3} x^{9}}{180 x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**3/x**19,x)
[Out]
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GIAC/XCAS [A] time = 0.221604, size = 50, normalized size = 1.16 \[ -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3/x^19,x, algorithm="giac")
[Out]