3.655 \(\int \frac{e^{\sqrt [3]{x}}}{x^{2/3}} \, dx\)

Optimal. Leaf size=9 \[ 3 e^{\sqrt [3]{x}} \]

[Out]

3*E^x^(1/3)

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Rubi [A]  time = 0.0184409, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ 3 e^{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]  Int[E^x^(1/3)/x^(2/3),x]

[Out]

3*E^x^(1/3)

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Rubi in Sympy [A]  time = 2.76859, size = 7, normalized size = 0.78 \[ 3 e^{\sqrt [3]{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*exp(x**(1/3))

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Mathematica [A]  time = 0.00318319, size = 9, normalized size = 1. \[ 3 e^{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^(1/3)/x^(2/3),x]

[Out]

3*E^x^(1/3)

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Maple [A]  time = 0.001, size = 7, normalized size = 0.8 \[ 3\,{{\rm e}^{\sqrt [3]{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^(1/3))/x^(2/3),x)

[Out]

3*exp(x^(1/3))

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Maxima [A]  time = 0.768142, size = 8, normalized size = 0.89 \[ 3 \, e^{\left (x^{\frac{1}{3}}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(x^(1/3))/x^(2/3),x, algorithm="maxima")

[Out]

3*e^(x^(1/3))

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Fricas [A]  time = 0.250086, size = 8, normalized size = 0.89 \[ 3 \, e^{\left (x^{\frac{1}{3}}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(x^(1/3))/x^(2/3),x, algorithm="fricas")

[Out]

3*e^(x^(1/3))

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Sympy [A]  time = 0.502216, size = 7, normalized size = 0.78 \[ 3 e^{\sqrt [3]{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*exp(x**(1/3))

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GIAC/XCAS [A]  time = 0.298076, size = 8, normalized size = 0.89 \[ 3 \, e^{\left (x^{\frac{1}{3}}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^(x^(1/3))/x^(2/3),x, algorithm="giac")

[Out]

3*e^(x^(1/3))