Optimal. Leaf size=43 \[ \frac{a^3 x^{15}}{15}+\frac{1}{6} a^2 b x^{18}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24} \]
[Out]
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Rubi [A] time = 0.078271, 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 \[ \frac{a^3 x^{15}}{15}+\frac{1}{6} a^2 b x^{18}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24} \]
Antiderivative was successfully verified.
[In] Int[x^14*(a + b*x^3)^3,x]
[Out]
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Rubi in Sympy [A] time = 10.1258, size = 36, normalized size = 0.84 \[ \frac{a^{3} x^{15}}{15} + \frac{a^{2} b x^{18}}{6} + \frac{a b^{2} x^{21}}{7} + \frac{b^{3} x^{24}}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**14*(b*x**3+a)**3,x)
[Out]
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Mathematica [A] time = 0.00345326, size = 43, normalized size = 1. \[ \frac{a^3 x^{15}}{15}+\frac{1}{6} a^2 b x^{18}+\frac{1}{7} a b^2 x^{21}+\frac{b^3 x^{24}}{24} \]
Antiderivative was successfully verified.
[In] Integrate[x^14*(a + b*x^3)^3,x]
[Out]
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Maple [A] time = 0.002, size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{15}}{15}}+{\frac{{a}^{2}b{x}^{18}}{6}}+{\frac{a{b}^{2}{x}^{21}}{7}}+{\frac{{b}^{3}{x}^{24}}{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^14*(b*x^3+a)^3,x)
[Out]
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Maxima [A] time = 1.43878, size = 47, normalized size = 1.09 \[ \frac{1}{24} \, b^{3} x^{24} + \frac{1}{7} \, a b^{2} x^{21} + \frac{1}{6} \, a^{2} b x^{18} + \frac{1}{15} \, a^{3} x^{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3*x^14,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.195559, size = 1, normalized size = 0.02 \[ \frac{1}{24} x^{24} b^{3} + \frac{1}{7} x^{21} b^{2} a + \frac{1}{6} x^{18} b a^{2} + \frac{1}{15} x^{15} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3*x^14,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.102098, size = 36, normalized size = 0.84 \[ \frac{a^{3} x^{15}}{15} + \frac{a^{2} b x^{18}}{6} + \frac{a b^{2} x^{21}}{7} + \frac{b^{3} x^{24}}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**14*(b*x**3+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.216466, size = 47, normalized size = 1.09 \[ \frac{1}{24} \, b^{3} x^{24} + \frac{1}{7} \, a b^{2} x^{21} + \frac{1}{6} \, a^{2} b x^{18} + \frac{1}{15} \, a^{3} x^{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^3*x^14,x, algorithm="giac")
[Out]