3.807 \(\int \frac{1-\sqrt{x}}{\sqrt [3]{x}} \, dx\)

Optimal. Leaf size=19 \[ \frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7} \]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

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Rubi [A]  time = 0.00994923, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7} \]

Antiderivative was successfully verified.

[In]  Int[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

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Rubi in Sympy [A]  time = 1.23819, size = 15, normalized size = 0.79 \[ - \frac{6 x^{\frac{7}{6}}}{7} + \frac{3 x^{\frac{2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-x**(1/2))/x**(1/3),x)

[Out]

-6*x**(7/6)/7 + 3*x**(2/3)/2

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Mathematica [A]  time = 0.00578017, size = 19, normalized size = 1. \[ \frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7} \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

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Maple [A]  time = 0.002, size = 12, normalized size = 0.6 \[{\frac{3}{2}{x}^{{\frac{2}{3}}}}-{\frac{6}{7}{x}^{{\frac{7}{6}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-x^(1/2))/x^(1/3),x)

[Out]

3/2*x^(2/3)-6/7*x^(7/6)

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Maxima [A]  time = 0.67822, size = 15, normalized size = 0.79 \[ -\frac{6}{7} \, x^{\frac{7}{6}} + \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(sqrt(x) - 1)/x^(1/3),x, algorithm="maxima")

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

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Fricas [A]  time = 0.260389, size = 15, normalized size = 0.79 \[ -\frac{6}{7} \, x^{\frac{7}{6}} + \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(sqrt(x) - 1)/x^(1/3),x, algorithm="fricas")

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

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Sympy [A]  time = 1.31166, size = 15, normalized size = 0.79 \[ - \frac{6 x^{\frac{7}{6}}}{7} + \frac{3 x^{\frac{2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-x**(1/2))/x**(1/3),x)

[Out]

-6*x**(7/6)/7 + 3*x**(2/3)/2

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GIAC/XCAS [A]  time = 0.261083, size = 15, normalized size = 0.79 \[ -\frac{6}{7} \, x^{\frac{7}{6}} + \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(sqrt(x) - 1)/x^(1/3),x, algorithm="giac")

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)