Optimal. Leaf size=47 \[ \frac{a^3 x^5}{5}+\frac{9}{14} a^2 b x^{14/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4} \]
[Out]
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Rubi [A] time = 0.0933029, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{a^3 x^5}{5}+\frac{9}{14} a^2 b x^{14/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^(1/3))^3*x^4,x]
[Out]
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Rubi in Sympy [A] time = 14.6472, size = 42, normalized size = 0.89 \[ \frac{a^{3} x^{5}}{5} + \frac{9 a^{2} b x^{\frac{14}{3}}}{14} + \frac{9 a b^{2} x^{\frac{13}{3}}}{13} + \frac{b^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**(1/3))**3*x**4,x)
[Out]
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Mathematica [A] time = 0.0142908, size = 47, normalized size = 1. \[ \frac{a^3 x^5}{5}+\frac{9}{14} a^2 b x^{14/3}+\frac{9}{13} a b^2 x^{13/3}+\frac{b^3 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^(1/3))^3*x^4,x]
[Out]
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Maple [A] time = 0.002, size = 36, normalized size = 0.8 \[{\frac{{b}^{3}{x}^{4}}{4}}+{\frac{9\,a{b}^{2}}{13}{x}^{{\frac{13}{3}}}}+{\frac{9\,{a}^{2}b}{14}{x}^{{\frac{14}{3}}}}+{\frac{{a}^{3}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^(1/3))^3*x^4,x)
[Out]
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Maxima [A] time = 1.43955, size = 50, normalized size = 1.06 \[ \frac{1}{1820} \,{\left (364 \, a^{3} + \frac{1170 \, a^{2} b}{x^{\frac{1}{3}}} + \frac{1260 \, a b^{2}}{x^{\frac{2}{3}}} + \frac{455 \, b^{3}}{x}\right )} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21962, size = 47, normalized size = 1. \[ \frac{1}{5} \, a^{3} x^{5} + \frac{9}{14} \, a^{2} b x^{\frac{14}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{1}{4} \, b^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.4227, size = 42, normalized size = 0.89 \[ \frac{a^{3} x^{5}}{5} + \frac{9 a^{2} b x^{\frac{14}{3}}}{14} + \frac{9 a b^{2} x^{\frac{13}{3}}}{13} + \frac{b^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**(1/3))**3*x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.210331, size = 47, normalized size = 1. \[ \frac{1}{5} \, a^{3} x^{5} + \frac{9}{14} \, a^{2} b x^{\frac{14}{3}} + \frac{9}{13} \, a b^{2} x^{\frac{13}{3}} + \frac{1}{4} \, b^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^(1/3))^3*x^4,x, algorithm="giac")
[Out]