Optimal. Leaf size=28 \[ \frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2} \]
[Out]
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Rubi [A] time = 0.014102, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2} \]
Antiderivative was successfully verified.
[In] Int[(3 - x + x^2)/x^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 2.93399, size = 24, normalized size = 0.86 \[ \frac{3 x^{\frac{8}{3}}}{8} - \frac{3 x^{\frac{5}{3}}}{5} + \frac{9 x^{\frac{2}{3}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-x+3)/x**(1/3),x)
[Out]
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Mathematica [A] time = 0.00726777, size = 19, normalized size = 0.68 \[ \frac{3}{40} x^{2/3} \left (5 x^2-8 x+60\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(3 - x + x^2)/x^(1/3),x]
[Out]
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Maple [A] time = 0.005, size = 16, normalized size = 0.6 \[{\frac{15\,{x}^{2}-24\,x+180}{40}{x}^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-x+3)/x^(1/3),x)
[Out]
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Maxima [A] time = 0.671948, size = 22, normalized size = 0.79 \[ \frac{3}{8} \, x^{\frac{8}{3}} - \frac{3}{5} \, x^{\frac{5}{3}} + \frac{9}{2} \, x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - x + 3)/x^(1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206144, size = 20, normalized size = 0.71 \[ \frac{3}{40} \,{\left (5 \, x^{2} - 8 \, x + 60\right )} x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - x + 3)/x^(1/3),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RecursionError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-x+3)/x**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.22337, size = 22, normalized size = 0.79 \[ \frac{3}{8} \, x^{\frac{8}{3}} - \frac{3}{5} \, x^{\frac{5}{3}} + \frac{9}{2} \, x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - x + 3)/x^(1/3),x, algorithm="giac")
[Out]