Optimal. Leaf size=66 \[ \frac{a^5 x^2}{2}+a^4 b x^5+\frac{5}{4} a^3 b^2 x^8+\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{14} a b^4 x^{14}+\frac{b^5 x^{17}}{17} \]
[Out]
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Rubi [A] time = 0.0646452, antiderivative size = 66, 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 \[ \frac{a^5 x^2}{2}+a^4 b x^5+\frac{5}{4} a^3 b^2 x^8+\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{14} a b^4 x^{14}+\frac{b^5 x^{17}}{17} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^3)^5,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{5} \int x\, dx + a^{4} b x^{5} + \frac{5 a^{3} b^{2} x^{8}}{4} + \frac{10 a^{2} b^{3} x^{11}}{11} + \frac{5 a b^{4} x^{14}}{14} + \frac{b^{5} x^{17}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**3+a)**5,x)
[Out]
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Mathematica [A] time = 0.00360333, size = 66, normalized size = 1. \[ \frac{a^5 x^2}{2}+a^4 b x^5+\frac{5}{4} a^3 b^2 x^8+\frac{10}{11} a^2 b^3 x^{11}+\frac{5}{14} a b^4 x^{14}+\frac{b^5 x^{17}}{17} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^3)^5,x]
[Out]
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Maple [A] time = 0.001, size = 57, normalized size = 0.9 \[{\frac{{a}^{5}{x}^{2}}{2}}+{a}^{4}b{x}^{5}+{\frac{5\,{a}^{3}{b}^{2}{x}^{8}}{4}}+{\frac{10\,{a}^{2}{b}^{3}{x}^{11}}{11}}+{\frac{5\,a{b}^{4}{x}^{14}}{14}}+{\frac{{b}^{5}{x}^{17}}{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^3+a)^5,x)
[Out]
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Maxima [A] time = 1.43203, size = 76, normalized size = 1.15 \[ \frac{1}{17} \, b^{5} x^{17} + \frac{5}{14} \, a b^{4} x^{14} + \frac{10}{11} \, a^{2} b^{3} x^{11} + \frac{5}{4} \, a^{3} b^{2} x^{8} + a^{4} b x^{5} + \frac{1}{2} \, a^{5} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.187279, size = 1, normalized size = 0.02 \[ \frac{1}{17} x^{17} b^{5} + \frac{5}{14} x^{14} b^{4} a + \frac{10}{11} x^{11} b^{3} a^{2} + \frac{5}{4} x^{8} b^{2} a^{3} + x^{5} b a^{4} + \frac{1}{2} x^{2} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.12257, size = 63, normalized size = 0.95 \[ \frac{a^{5} x^{2}}{2} + a^{4} b x^{5} + \frac{5 a^{3} b^{2} x^{8}}{4} + \frac{10 a^{2} b^{3} x^{11}}{11} + \frac{5 a b^{4} x^{14}}{14} + \frac{b^{5} x^{17}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**3+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.221125, size = 76, normalized size = 1.15 \[ \frac{1}{17} \, b^{5} x^{17} + \frac{5}{14} \, a b^{4} x^{14} + \frac{10}{11} \, a^{2} b^{3} x^{11} + \frac{5}{4} \, a^{3} b^{2} x^{8} + a^{4} b x^{5} + \frac{1}{2} \, a^{5} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x,x, algorithm="giac")
[Out]