Optimal. Leaf size=19 \[ \frac{a x^3}{3}+\frac{3}{10} b x^{10/3} \]
[Out]
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Rubi [A] time = 0.0153745, antiderivative size = 19, 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 \[ \frac{a x^3}{3}+\frac{3}{10} b x^{10/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))*x^2,x]
[Out]
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Rubi in Sympy [A] time = 2.89902, size = 15, normalized size = 0.79 \[ \frac{a x^{3}}{3} + \frac{3 b x^{\frac{10}{3}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))*x**2,x)
[Out]
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Mathematica [A] time = 0.00614047, size = 19, normalized size = 1. \[ \frac{a x^3}{3}+\frac{3}{10} b x^{10/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))*x^2,x]
[Out]
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Maple [A] time = 0.001, size = 14, normalized size = 0.7 \[{\frac{a{x}^{3}}{3}}+{\frac{3\,b}{10}{x}^{{\frac{10}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))*x^2,x)
[Out]
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Maxima [A] time = 1.43704, size = 201, normalized size = 10.58 \[ \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{10}}{10 \, b^{9}} - \frac{8 \,{\left (b x^{\frac{1}{3}} + a\right )}^{9} a}{3 \, b^{9}} + \frac{21 \,{\left (b x^{\frac{1}{3}} + a\right )}^{8} a^{2}}{2 \, b^{9}} - \frac{24 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7} a^{3}}{b^{9}} + \frac{35 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a^{4}}{b^{9}} - \frac{168 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{5}}{5 \, b^{9}} + \frac{21 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{6}}{b^{9}} - \frac{8 \,{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{7}}{b^{9}} + \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{2} a^{8}}{2 \, b^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212913, size = 18, normalized size = 0.95 \[ \frac{3}{10} \, b x^{\frac{10}{3}} + \frac{1}{3} \, a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.89655, size = 15, normalized size = 0.79 \[ \frac{a x^{3}}{3} + \frac{3 b x^{\frac{10}{3}}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))*x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.256131, size = 18, normalized size = 0.95 \[ \frac{3}{10} \, b x^{\frac{10}{3}} + \frac{1}{3} \, a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)*x^2,x, algorithm="giac")
[Out]