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

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

[Out]

3*E^x^(1/3)

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Rubi [A]  time = 0.0109865, 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, Rules used = {2209} \[ 3 e^{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]

Int[E^x^(1/3)/x^(2/3),x]

[Out]

3*E^x^(1/3)

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin{align*} \int \frac{e^{\sqrt [3]{x}}}{x^{2/3}} \, dx &=3 e^{\sqrt [3]{x}}\\ \end{align*}

Mathematica [A]  time = 0.0018391, 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 = 0.02, size = 7, normalized size = 0.8 \begin{align*} 3\,{{\rm e}^{\sqrt [3]{x}}} \end{align*}

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 = 0.95909, size = 8, normalized size = 0.89 \begin{align*} 3 \, e^{\left (x^{\frac{1}{3}}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x^(1/3))/x^(2/3),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.803634, size = 20, normalized size = 2.22 \begin{align*} 3 \, e^{\left (x^{\frac{1}{3}}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x^(1/3))/x^(2/3),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0.372059, size = 7, normalized size = 0.78 \begin{align*} 3 e^{\sqrt [3]{x}} \end{align*}

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 [A]  time = 1.27028, size = 8, normalized size = 0.89 \begin{align*} 3 \, e^{\left (x^{\frac{1}{3}}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x^(1/3))/x^(2/3),x, algorithm="giac")

[Out]

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