Optimal. Leaf size=43 \[ \frac{a^3 x^5}{5}+\frac{1}{3} a^2 b x^9+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17} \]
[Out]
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Rubi [A] time = 0.0420275, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a^3 x^5}{5}+\frac{1}{3} a^2 b x^9+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 7.0113, size = 37, normalized size = 0.86 \[ \frac{a^{3} x^{5}}{5} + \frac{a^{2} b x^{9}}{3} + \frac{3 a b^{2} x^{13}}{13} + \frac{b^{3} x^{17}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x**4+a)**3,x)
[Out]
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Mathematica [A] time = 0.00315055, size = 43, normalized size = 1. \[ \frac{a^3 x^5}{5}+\frac{1}{3} a^2 b x^9+\frac{3}{13} a b^2 x^{13}+\frac{b^3 x^{17}}{17} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x^4)^3,x]
[Out]
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Maple [A] time = 0.001, size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{5}}{5}}+{\frac{{a}^{2}b{x}^{9}}{3}}+{\frac{3\,a{b}^{2}{x}^{13}}{13}}+{\frac{{b}^{3}{x}^{17}}{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x^4+a)^3,x)
[Out]
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Maxima [A] time = 1.42694, size = 47, normalized size = 1.09 \[ \frac{1}{17} \, b^{3} x^{17} + \frac{3}{13} \, a b^{2} x^{13} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{5} \, a^{3} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201435, size = 1, normalized size = 0.02 \[ \frac{1}{17} x^{17} b^{3} + \frac{3}{13} x^{13} b^{2} a + \frac{1}{3} x^{9} b a^{2} + \frac{1}{5} x^{5} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.098659, size = 37, normalized size = 0.86 \[ \frac{a^{3} x^{5}}{5} + \frac{a^{2} b x^{9}}{3} + \frac{3 a b^{2} x^{13}}{13} + \frac{b^{3} x^{17}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x**4+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.217194, size = 47, normalized size = 1.09 \[ \frac{1}{17} \, b^{3} x^{17} + \frac{3}{13} \, a b^{2} x^{13} + \frac{1}{3} \, a^{2} b x^{9} + \frac{1}{5} \, a^{3} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^3*x^4,x, algorithm="giac")
[Out]