\(\int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx\) [672]

Optimal result

Integrand size = 13, antiderivative size = 9 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 e^{\sqrt [3]{x}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2240} \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 e^{\sqrt [3]{x}} \]

[In]

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

[Out]

3*E^x^(1/3)

Rule 2240

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*} \text {integral}& = 3 e^{\sqrt [3]{x}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 e^{\sqrt [3]{x}} \]

[In]

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

[Out]

3*E^x^(1/3)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78

method	result	size
derivativedivides	\(3 \,{\mathrm e}^{x^{\frac {1}{3}}}\)	\(7\)
default	\(3 \,{\mathrm e}^{x^{\frac {1}{3}}}\)	\(7\)
meijerg	\(-3+3 \,{\mathrm e}^{x^{\frac {1}{3}}}\)	\(9\)

[In]

int(exp(x^(1/3))/x^(2/3),x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 \, e^{\left (x^{\frac {1}{3}}\right )} \]

[In]

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

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.13 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 e^{\sqrt [3]{x}} \]

[In]

integrate(exp(x**(1/3))/x**(2/3),x)

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 \, e^{\left (x^{\frac {1}{3}}\right )} \]

[In]

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

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3 \, e^{\left (x^{\frac {1}{3}}\right )} \]

[In]

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

[Out]

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

Mupad [B] (verification not implemented)

Time = 0.29 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt [3]{x}}}{x^{2/3}} \, dx=3\,{\mathrm {e}}^{x^{1/3}} \]

[In]

int(exp(x^(1/3))/x^(2/3),x)

[Out]

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