Optimal. Leaf size=106 \[ \frac{a^8 x^2}{2}+\frac{8}{5} a^7 b x^5+\frac{7}{2} a^6 b^2 x^8+\frac{56}{11} a^5 b^3 x^{11}+5 a^4 b^4 x^{14}+\frac{56}{17} a^3 b^5 x^{17}+\frac{7}{5} a^2 b^6 x^{20}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{26}}{26} \]
[Out]
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Rubi [A] time = 0.102032, antiderivative size = 106, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a^8 x^2}{2}+\frac{8}{5} a^7 b x^5+\frac{7}{2} a^6 b^2 x^8+\frac{56}{11} a^5 b^3 x^{11}+5 a^4 b^4 x^{14}+\frac{56}{17} a^3 b^5 x^{17}+\frac{7}{5} a^2 b^6 x^{20}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{26}}{26} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^3)^8,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{8} \int x\, dx + \frac{8 a^{7} b x^{5}}{5} + \frac{7 a^{6} b^{2} x^{8}}{2} + \frac{56 a^{5} b^{3} x^{11}}{11} + 5 a^{4} b^{4} x^{14} + \frac{56 a^{3} b^{5} x^{17}}{17} + \frac{7 a^{2} b^{6} x^{20}}{5} + \frac{8 a b^{7} x^{23}}{23} + \frac{b^{8} x^{26}}{26} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**3+a)**8,x)
[Out]
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Mathematica [A] time = 0.00422346, size = 106, normalized size = 1. \[ \frac{a^8 x^2}{2}+\frac{8}{5} a^7 b x^5+\frac{7}{2} a^6 b^2 x^8+\frac{56}{11} a^5 b^3 x^{11}+5 a^4 b^4 x^{14}+\frac{56}{17} a^3 b^5 x^{17}+\frac{7}{5} a^2 b^6 x^{20}+\frac{8}{23} a b^7 x^{23}+\frac{b^8 x^{26}}{26} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^3)^8,x]
[Out]
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Maple [A] time = 0.002, size = 91, normalized size = 0.9 \[{\frac{{a}^{8}{x}^{2}}{2}}+{\frac{8\,{a}^{7}b{x}^{5}}{5}}+{\frac{7\,{a}^{6}{b}^{2}{x}^{8}}{2}}+{\frac{56\,{a}^{5}{b}^{3}{x}^{11}}{11}}+5\,{a}^{4}{b}^{4}{x}^{14}+{\frac{56\,{a}^{3}{b}^{5}{x}^{17}}{17}}+{\frac{7\,{a}^{2}{b}^{6}{x}^{20}}{5}}+{\frac{8\,a{b}^{7}{x}^{23}}{23}}+{\frac{{b}^{8}{x}^{26}}{26}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^3+a)^8,x)
[Out]
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Maxima [A] time = 1.43848, size = 122, normalized size = 1.15 \[ \frac{1}{26} \, b^{8} x^{26} + \frac{8}{23} \, a b^{7} x^{23} + \frac{7}{5} \, a^{2} b^{6} x^{20} + \frac{56}{17} \, a^{3} b^{5} x^{17} + 5 \, a^{4} b^{4} x^{14} + \frac{56}{11} \, a^{5} b^{3} x^{11} + \frac{7}{2} \, a^{6} b^{2} x^{8} + \frac{8}{5} \, a^{7} b x^{5} + \frac{1}{2} \, a^{8} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.189635, size = 1, normalized size = 0.01 \[ \frac{1}{26} x^{26} b^{8} + \frac{8}{23} x^{23} b^{7} a + \frac{7}{5} x^{20} b^{6} a^{2} + \frac{56}{17} x^{17} b^{5} a^{3} + 5 x^{14} b^{4} a^{4} + \frac{56}{11} x^{11} b^{3} a^{5} + \frac{7}{2} x^{8} b^{2} a^{6} + \frac{8}{5} x^{5} b a^{7} + \frac{1}{2} x^{2} a^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.172866, size = 105, normalized size = 0.99 \[ \frac{a^{8} x^{2}}{2} + \frac{8 a^{7} b x^{5}}{5} + \frac{7 a^{6} b^{2} x^{8}}{2} + \frac{56 a^{5} b^{3} x^{11}}{11} + 5 a^{4} b^{4} x^{14} + \frac{56 a^{3} b^{5} x^{17}}{17} + \frac{7 a^{2} b^{6} x^{20}}{5} + \frac{8 a b^{7} x^{23}}{23} + \frac{b^{8} x^{26}}{26} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**3+a)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.22281, size = 122, normalized size = 1.15 \[ \frac{1}{26} \, b^{8} x^{26} + \frac{8}{23} \, a b^{7} x^{23} + \frac{7}{5} \, a^{2} b^{6} x^{20} + \frac{56}{17} \, a^{3} b^{5} x^{17} + 5 \, a^{4} b^{4} x^{14} + \frac{56}{11} \, a^{5} b^{3} x^{11} + \frac{7}{2} \, a^{6} b^{2} x^{8} + \frac{8}{5} \, a^{7} b x^{5} + \frac{1}{2} \, a^{8} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8*x,x, algorithm="giac")
[Out]