Optimal. Leaf size=56 \[ \frac{a^4 x^5}{5}+\frac{4}{7} a^3 b x^7+\frac{2}{3} a^2 b^2 x^9+\frac{4}{11} a b^3 x^{11}+\frac{b^4 x^{13}}{13} \]
[Out]
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Rubi [A] time = 0.0738783, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{a^4 x^5}{5}+\frac{4}{7} a^3 b x^7+\frac{2}{3} a^2 b^2 x^9+\frac{4}{11} a b^3 x^{11}+\frac{b^4 x^{13}}{13} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 17.5397, size = 53, normalized size = 0.95 \[ \frac{a^{4} x^{5}}{5} + \frac{4 a^{3} b x^{7}}{7} + \frac{2 a^{2} b^{2} x^{9}}{3} + \frac{4 a b^{3} x^{11}}{11} + \frac{b^{4} x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b**2*x**4+2*a*b*x**2+a**2)**2,x)
[Out]
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Mathematica [A] time = 0.0036894, size = 56, normalized size = 1. \[ \frac{a^4 x^5}{5}+\frac{4}{7} a^3 b x^7+\frac{2}{3} a^2 b^2 x^9+\frac{4}{11} a b^3 x^{11}+\frac{b^4 x^{13}}{13} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a^2 + 2*a*b*x^2 + b^2*x^4)^2,x]
[Out]
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Maple [A] time = 0.002, size = 47, normalized size = 0.8 \[{\frac{{a}^{4}{x}^{5}}{5}}+{\frac{4\,{a}^{3}b{x}^{7}}{7}}+{\frac{2\,{a}^{2}{b}^{2}{x}^{9}}{3}}+{\frac{4\,a{b}^{3}{x}^{11}}{11}}+{\frac{{b}^{4}{x}^{13}}{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^2,x)
[Out]
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Maxima [A] time = 0.682261, size = 62, normalized size = 1.11 \[ \frac{1}{13} \, b^{4} x^{13} + \frac{4}{11} \, a b^{3} x^{11} + \frac{2}{3} \, a^{2} b^{2} x^{9} + \frac{4}{7} \, a^{3} b x^{7} + \frac{1}{5} \, a^{4} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241833, size = 1, normalized size = 0.02 \[ \frac{1}{13} x^{13} b^{4} + \frac{4}{11} x^{11} b^{3} a + \frac{2}{3} x^{9} b^{2} a^{2} + \frac{4}{7} x^{7} b a^{3} + \frac{1}{5} x^{5} a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.105919, size = 53, normalized size = 0.95 \[ \frac{a^{4} x^{5}}{5} + \frac{4 a^{3} b x^{7}}{7} + \frac{2 a^{2} b^{2} x^{9}}{3} + \frac{4 a b^{3} x^{11}}{11} + \frac{b^{4} x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b**2*x**4+2*a*b*x**2+a**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.267534, size = 62, normalized size = 1.11 \[ \frac{1}{13} \, b^{4} x^{13} + \frac{4}{11} \, a b^{3} x^{11} + \frac{2}{3} \, a^{2} b^{2} x^{9} + \frac{4}{7} \, a^{3} b x^{7} + \frac{1}{5} \, a^{4} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2*x^4,x, algorithm="giac")
[Out]