Optimal. Leaf size=42 \[ a^3 x+\frac{9}{4} a^2 b x^{4/3}+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2} \]
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Rubi [A] time = 0.0607792, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ a^3 x+\frac{9}{4} a^2 b x^{4/3}+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^3,x]
[Out]
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Rubi in Sympy [A] time = 8.2966, size = 39, normalized size = 0.93 \[ a^{3} x + \frac{9 a^{2} b x^{\frac{4}{3}}}{4} + \frac{9 a b^{2} x^{\frac{5}{3}}}{5} + \frac{b^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**3,x)
[Out]
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Mathematica [A] time = 0.00924879, size = 42, normalized size = 1. \[ a^3 x+\frac{9}{4} a^2 b x^{4/3}+\frac{9}{5} a b^2 x^{5/3}+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^3,x]
[Out]
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Maple [A] time = 0.002, size = 33, normalized size = 0.8 \[{a}^{3}x+{\frac{9\,{a}^{2}b}{4}{x}^{{\frac{4}{3}}}}+{\frac{9\,a{b}^{2}}{5}{x}^{{\frac{5}{3}}}}+{\frac{{b}^{3}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^3,x)
[Out]
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Maxima [A] time = 1.4467, size = 43, normalized size = 1.02 \[ \frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214309, size = 43, normalized size = 1.02 \[ \frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.18059, size = 39, normalized size = 0.93 \[ a^{3} x + \frac{9 a^{2} b x^{\frac{4}{3}}}{4} + \frac{9 a b^{2} x^{\frac{5}{3}}}{5} + \frac{b^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212922, size = 43, normalized size = 1.02 \[ \frac{1}{2} \, b^{3} x^{2} + \frac{9}{5} \, a b^{2} x^{\frac{5}{3}} + \frac{9}{4} \, a^{2} b x^{\frac{4}{3}} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3,x, algorithm="giac")
[Out]