3.66.66 \(\int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx\)

Optimal. Leaf size=16 \[ e^{\frac {e^{-x/3}}{16 x^4}} \]

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Rubi [F]  time = 0.38, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(1/(16*E^(x/3)*x^4) - x/3)*(-12 - x))/(48*x^5),x]

[Out]

-1/4*Defer[Int][E^(1/(16*E^(x/3)*x^4) - x/3)/x^5, x] - Defer[Int][E^(1/(16*E^(x/3)*x^4) - x/3)/x^4, x]/48

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{48} \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{x^5} \, dx\\ &=\frac {1}{48} \int \left (-\frac {12 e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}}}{x^5}-\frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}}}{x^4}\right ) \, dx\\ &=-\left (\frac {1}{48} \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}}}{x^4} \, dx\right )-\frac {1}{4} \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}}}{x^5} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 16, normalized size = 1.00 \begin {gather*} e^{\frac {e^{-x/3}}{16 x^4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(1/(16*E^(x/3)*x^4) - x/3)*(-12 - x))/(48*x^5),x]

[Out]

E^(1/(16*E^(x/3)*x^4))

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fricas [B]  time = 0.71, size = 22, normalized size = 1.38 \begin {gather*} e^{\left (\frac {1}{3} \, x - \frac {16 \, x^{5} - 3 \, e^{\left (-\frac {1}{3} \, x\right )}}{48 \, x^{4}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/48*(-x-12)*exp(1/16/x^4/exp(1/3*x))/x^5/exp(1/3*x),x, algorithm="fricas")

[Out]

e^(1/3*x - 1/48*(16*x^5 - 3*e^(-1/3*x))/x^4)

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giac [B]  time = 0.29, size = 22, normalized size = 1.38 \begin {gather*} e^{\left (\frac {1}{3} \, x - \frac {16 \, x^{5} - 3 \, e^{\left (-\frac {1}{3} \, x\right )}}{48 \, x^{4}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/48*(-x-12)*exp(1/16/x^4/exp(1/3*x))/x^5/exp(1/3*x),x, algorithm="giac")

[Out]

e^(1/3*x - 1/48*(16*x^5 - 3*e^(-1/3*x))/x^4)

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maple [A]  time = 0.06, size = 11, normalized size = 0.69

method	result	size
risch	\({\mathrm e}^{\frac {{\mathrm e}^{-\frac {x}{3}}}{16 x^{4}}}\)	\(11\)
norman	\({\mathrm e}^{\frac {{\mathrm e}^{-\frac {x}{3}}}{16 x^{4}}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/48*(-x-12)*exp(1/16/x^4/exp(1/3*x))/x^5/exp(1/3*x),x,method=_RETURNVERBOSE)

[Out]

exp(1/16/x^4*exp(-1/3*x))

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maxima [A]  time = 0.49, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (\frac {e^{\left (-\frac {1}{3} \, x\right )}}{16 \, x^{4}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/48*(-x-12)*exp(1/16/x^4/exp(1/3*x))/x^5/exp(1/3*x),x, algorithm="maxima")

[Out]

e^(1/16*e^(-1/3*x)/x^4)

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mupad [B]  time = 4.16, size = 10, normalized size = 0.62 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{-\frac {x}{3}}}{16\,x^4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-x/3)*exp(exp(-x/3)/(16*x^4))*(x + 12))/(48*x^5),x)

[Out]

exp(exp(-x/3)/(16*x^4))

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sympy [A]  time = 0.18, size = 12, normalized size = 0.75 \begin {gather*} e^{\frac {e^{- \frac {x}{3}}}{16 x^{4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/48*(-x-12)*exp(1/16/x**4/exp(1/3*x))/x**5/exp(1/3*x),x)

[Out]

exp(exp(-x/3)/(16*x**4))

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