Optimal. Leaf size=66 \[ \frac{a^5 x^4}{4}+\frac{5}{7} a^4 b x^7+a^3 b^2 x^{10}+\frac{10}{13} a^2 b^3 x^{13}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{19}}{19} \]
[Out]
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Rubi [A] time = 0.0705057, antiderivative size = 66, 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 \[ \frac{a^5 x^4}{4}+\frac{5}{7} a^4 b x^7+a^3 b^2 x^{10}+\frac{10}{13} a^2 b^3 x^{13}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{19}}{19} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^3)^5,x]
[Out]
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Rubi in Sympy [A] time = 11.4048, size = 63, normalized size = 0.95 \[ \frac{a^{5} x^{4}}{4} + \frac{5 a^{4} b x^{7}}{7} + a^{3} b^{2} x^{10} + \frac{10 a^{2} b^{3} x^{13}}{13} + \frac{5 a b^{4} x^{16}}{16} + \frac{b^{5} x^{19}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**3+a)**5,x)
[Out]
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Mathematica [A] time = 0.00375532, size = 66, normalized size = 1. \[ \frac{a^5 x^4}{4}+\frac{5}{7} a^4 b x^7+a^3 b^2 x^{10}+\frac{10}{13} a^2 b^3 x^{13}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{19}}{19} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^3)^5,x]
[Out]
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Maple [A] time = 0.002, size = 57, normalized size = 0.9 \[{\frac{{a}^{5}{x}^{4}}{4}}+{\frac{5\,{a}^{4}b{x}^{7}}{7}}+{a}^{3}{b}^{2}{x}^{10}+{\frac{10\,{a}^{2}{b}^{3}{x}^{13}}{13}}+{\frac{5\,a{b}^{4}{x}^{16}}{16}}+{\frac{{b}^{5}{x}^{19}}{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^3+a)^5,x)
[Out]
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Maxima [A] time = 1.44216, size = 76, normalized size = 1.15 \[ \frac{1}{19} \, b^{5} x^{19} + \frac{5}{16} \, a b^{4} x^{16} + \frac{10}{13} \, a^{2} b^{3} x^{13} + a^{3} b^{2} x^{10} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{4} \, a^{5} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.188246, size = 1, normalized size = 0.02 \[ \frac{1}{19} x^{19} b^{5} + \frac{5}{16} x^{16} b^{4} a + \frac{10}{13} x^{13} b^{3} a^{2} + x^{10} b^{2} a^{3} + \frac{5}{7} x^{7} b a^{4} + \frac{1}{4} x^{4} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.121037, size = 63, normalized size = 0.95 \[ \frac{a^{5} x^{4}}{4} + \frac{5 a^{4} b x^{7}}{7} + a^{3} b^{2} x^{10} + \frac{10 a^{2} b^{3} x^{13}}{13} + \frac{5 a b^{4} x^{16}}{16} + \frac{b^{5} x^{19}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**3+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.221913, size = 76, normalized size = 1.15 \[ \frac{1}{19} \, b^{5} x^{19} + \frac{5}{16} \, a b^{4} x^{16} + \frac{10}{13} \, a^{2} b^{3} x^{13} + a^{3} b^{2} x^{10} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{4} \, a^{5} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^5*x^3,x, algorithm="giac")
[Out]