\(\int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx\) [6566]

Optimal result

Integrand size = 34, antiderivative size = 16 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx=e^{\frac {e^{-x/3}}{16 x^4}} \]

[Out]

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

Rubi [F]

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

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx=e^{\frac {e^{-x/3}}{16 x^4}} \]

[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))

Maple [A] (verified)

Time = 0.24 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.69

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

[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))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (10) = 20\).

Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx=e^{\left (\frac {1}{3} \, x - \frac {16 \, x^{5} - 3 \, e^{\left (-\frac {1}{3} \, x\right )}}{48 \, x^{4}}\right )} \]

[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)

Sympy [A] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx=e^{\frac {e^{- \frac {x}{3}}}{16 x^{4}}} \]

[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))

Maxima [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx=e^{\left (\frac {e^{\left (-\frac {1}{3} \, x\right )}}{16 \, x^{4}}\right )} \]

[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)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 22 vs. \(2 (10) = 20\).

Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.38 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx=e^{\left (\frac {1}{3} \, x - \frac {16 \, x^{5} - 3 \, e^{\left (-\frac {1}{3} \, x\right )}}{48 \, x^{4}}\right )} \]

[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)

Mupad [B] (verification not implemented)

Time = 13.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {e^{\frac {e^{-x/3}}{16 x^4}-\frac {x}{3}} (-12-x)}{48 x^5} \, dx={\mathrm {e}}^{\frac {{\mathrm {e}}^{-\frac {x}{3}}}{16\,x^4}} \]

[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))