Optimal. Leaf size=47 \[ \frac{a^3 x^4}{4}+\frac{9}{13} a^2 b x^{13/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{b^3 x^5}{5} \]
[Out]
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Rubi [A] time = 0.0823604, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{a^3 x^4}{4}+\frac{9}{13} a^2 b x^{13/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{b^3 x^5}{5} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^3*x^3,x]
[Out]
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Rubi in Sympy [A] time = 13.3222, size = 42, normalized size = 0.89 \[ \frac{a^{3} x^{4}}{4} + \frac{9 a^{2} b x^{\frac{13}{3}}}{13} + \frac{9 a b^{2} x^{\frac{14}{3}}}{14} + \frac{b^{3} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**3*x**3,x)
[Out]
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Mathematica [A] time = 0.0112628, size = 47, normalized size = 1. \[ \frac{a^3 x^4}{4}+\frac{9}{13} a^2 b x^{13/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{b^3 x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^3*x^3,x]
[Out]
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Maple [A] time = 0.002, size = 36, normalized size = 0.8 \[{\frac{{a}^{3}{x}^{4}}{4}}+{\frac{9\,{a}^{2}b}{13}{x}^{{\frac{13}{3}}}}+{\frac{9\,a{b}^{2}}{14}{x}^{{\frac{14}{3}}}}+{\frac{{b}^{3}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^3*x^3,x)
[Out]
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Maxima [A] time = 1.43211, size = 270, normalized size = 5.74 \[ \frac{{\left (b x^{\frac{1}{3}} + a\right )}^{15}}{5 \, b^{12}} - \frac{33 \,{\left (b x^{\frac{1}{3}} + a\right )}^{14} a}{14 \, b^{12}} + \frac{165 \,{\left (b x^{\frac{1}{3}} + a\right )}^{13} a^{2}}{13 \, b^{12}} - \frac{165 \,{\left (b x^{\frac{1}{3}} + a\right )}^{12} a^{3}}{4 \, b^{12}} + \frac{90 \,{\left (b x^{\frac{1}{3}} + a\right )}^{11} a^{4}}{b^{12}} - \frac{693 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10} a^{5}}{5 \, b^{12}} + \frac{154 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a^{6}}{b^{12}} - \frac{495 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{7}}{4 \, b^{12}} + \frac{495 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{8}}{7 \, b^{12}} - \frac{55 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{9}}{2 \, b^{12}} + \frac{33 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{10}}{5 \, b^{12}} - \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{11}}{4 \, b^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21349, size = 47, normalized size = 1. \[ \frac{1}{5} \, b^{3} x^{5} + \frac{9}{14} \, a b^{2} x^{\frac{14}{3}} + \frac{9}{13} \, a^{2} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.90852, size = 42, normalized size = 0.89 \[ \frac{a^{3} x^{4}}{4} + \frac{9 a^{2} b x^{\frac{13}{3}}}{13} + \frac{9 a b^{2} x^{\frac{14}{3}}}{14} + \frac{b^{3} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**3*x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.218989, size = 47, normalized size = 1. \[ \frac{1}{5} \, b^{3} x^{5} + \frac{9}{14} \, a b^{2} x^{\frac{14}{3}} + \frac{9}{13} \, a^{2} b x^{\frac{13}{3}} + \frac{1}{4} \, a^{3} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^3*x^3,x, algorithm="giac")
[Out]