3.2321 \(\int \frac{3-x+x^2}{\sqrt [3]{x}} \, dx\)

Optimal. Leaf size=28 \[ \frac{3 x^{8/3}}{8}-\frac{3 x^{5/3}}{5}+\frac{9 x^{2/3}}{2} \]

[Out]

(9*x^(2/3))/2 - (3*x^(5/3))/5 + (3*x^(8/3))/8

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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]

(9*x^(2/3))/2 - (3*x^(5/3))/5 + (3*x^(8/3))/8

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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]

3*x**(8/3)/8 - 3*x**(5/3)/5 + 9*x**(2/3)/2

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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]

(3*x^(2/3)*(60 - 8*x + 5*x^2))/40

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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]

3/40*x^(2/3)*(5*x^2-8*x+60)

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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]

3/8*x^(8/3) - 3/5*x^(5/3) + 9/2*x^(2/3)

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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]

3/40*(5*x^2 - 8*x + 60)*x^(2/3)

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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]

Exception raised: RecursionError

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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]

3/8*x^(8/3) - 3/5*x^(5/3) + 9/2*x^(2/3)