Optimal. Leaf size=79 \[ \frac{a^6 x^7}{7}+\frac{2}{3} a^5 b x^9+\frac{15}{11} a^4 b^2 x^{11}+\frac{20}{13} a^3 b^3 x^{13}+a^2 b^4 x^{15}+\frac{6}{17} a b^5 x^{17}+\frac{b^6 x^{19}}{19} \]
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Rubi [A] time = 0.104694, antiderivative size = 79, 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 \[ \frac{a^6 x^7}{7}+\frac{2}{3} a^5 b x^9+\frac{15}{11} a^4 b^2 x^{11}+\frac{20}{13} a^3 b^3 x^{13}+a^2 b^4 x^{15}+\frac{6}{17} a b^5 x^{17}+\frac{b^6 x^{19}}{19} \]
Antiderivative was successfully verified.
[In] Int[x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 23.1571, size = 76, normalized size = 0.96 \[ \frac{a^{6} x^{7}}{7} + \frac{2 a^{5} b x^{9}}{3} + \frac{15 a^{4} b^{2} x^{11}}{11} + \frac{20 a^{3} b^{3} x^{13}}{13} + a^{2} b^{4} x^{15} + \frac{6 a b^{5} x^{17}}{17} + \frac{b^{6} x^{19}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**6*(b**2*x**4+2*a*b*x**2+a**2)**3,x)
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Mathematica [A] time = 0.00407754, size = 79, normalized size = 1. \[ \frac{a^6 x^7}{7}+\frac{2}{3} a^5 b x^9+\frac{15}{11} a^4 b^2 x^{11}+\frac{20}{13} a^3 b^3 x^{13}+a^2 b^4 x^{15}+\frac{6}{17} a b^5 x^{17}+\frac{b^6 x^{19}}{19} \]
Antiderivative was successfully verified.
[In] Integrate[x^6*(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
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Maple [A] time = 0.001, size = 68, normalized size = 0.9 \[{\frac{{a}^{6}{x}^{7}}{7}}+{\frac{2\,{a}^{5}b{x}^{9}}{3}}+{\frac{15\,{a}^{4}{b}^{2}{x}^{11}}{11}}+{\frac{20\,{a}^{3}{b}^{3}{x}^{13}}{13}}+{a}^{2}{b}^{4}{x}^{15}+{\frac{6\,a{b}^{5}{x}^{17}}{17}}+{\frac{{b}^{6}{x}^{19}}{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^6*(b^2*x^4+2*a*b*x^2+a^2)^3,x)
[Out]
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Maxima [A] time = 0.695062, size = 90, normalized size = 1.14 \[ \frac{1}{19} \, b^{6} x^{19} + \frac{6}{17} \, a b^{5} x^{17} + a^{2} b^{4} x^{15} + \frac{20}{13} \, a^{3} b^{3} x^{13} + \frac{15}{11} \, a^{4} b^{2} x^{11} + \frac{2}{3} \, a^{5} b x^{9} + \frac{1}{7} \, a^{6} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3*x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236235, size = 1, normalized size = 0.01 \[ \frac{1}{19} x^{19} b^{6} + \frac{6}{17} x^{17} b^{5} a + x^{15} b^{4} a^{2} + \frac{20}{13} x^{13} b^{3} a^{3} + \frac{15}{11} x^{11} b^{2} a^{4} + \frac{2}{3} x^{9} b a^{5} + \frac{1}{7} x^{7} a^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3*x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.134051, size = 76, normalized size = 0.96 \[ \frac{a^{6} x^{7}}{7} + \frac{2 a^{5} b x^{9}}{3} + \frac{15 a^{4} b^{2} x^{11}}{11} + \frac{20 a^{3} b^{3} x^{13}}{13} + a^{2} b^{4} x^{15} + \frac{6 a b^{5} x^{17}}{17} + \frac{b^{6} x^{19}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**6*(b**2*x**4+2*a*b*x**2+a**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.267808, size = 90, normalized size = 1.14 \[ \frac{1}{19} \, b^{6} x^{19} + \frac{6}{17} \, a b^{5} x^{17} + a^{2} b^{4} x^{15} + \frac{20}{13} \, a^{3} b^{3} x^{13} + \frac{15}{11} \, a^{4} b^{2} x^{11} + \frac{2}{3} \, a^{5} b x^{9} + \frac{1}{7} \, a^{6} x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3*x^6,x, algorithm="giac")
[Out]