\(\int -e^{e^{\frac {1}{e^4}}-x} \, dx\) [5792]

Optimal result

Integrand size = 13, antiderivative size = 11 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{e^{\frac {1}{e^4}}-x} \]

[Out]

exp(exp(exp(-4))-x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, 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 = {2225} \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{e^{\frac {1}{e^4}}-x} \]

[In]

Int[-E^(E^E^(-4) - x),x]

[Out]

E^(E^E^(-4) - x)

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = e^{e^{\frac {1}{e^4}}-x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{e^{\frac {1}{e^4}}-x} \]

[In]

Integrate[-E^(E^E^(-4) - x),x]

[Out]

E^(E^E^(-4) - x)

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(9\)
gosper	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
derivativedivides	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
default	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
norman	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
parallelrisch	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
parts	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
meijerg	\(-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}} \left (1-{\mathrm e}^{-x}\right )\)	\(15\)

[In]

int(-exp(exp(1/exp(4))-x),x,method=_RETURNVERBOSE)

[Out]

exp(exp(exp(-4))-x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \]

[In]

integrate(-exp(exp(1/exp(4))-x),x, algorithm="fricas")

[Out]

e^(-x + e^(e^(-4)))

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{- x + e^{e^{-4}}} \]

[In]

integrate(-exp(exp(1/exp(4))-x),x)

[Out]

exp(-x + exp(exp(-4)))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \]

[In]

integrate(-exp(exp(1/exp(4))-x),x, algorithm="maxima")

[Out]

e^(-x + e^(e^(-4)))

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \]

[In]

integrate(-exp(exp(1/exp(4))-x),x, algorithm="giac")

[Out]

e^(-x + e^(e^(-4)))

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx={\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-4}}}\,{\mathrm {e}}^{-x} \]

[In]

int(-exp(exp(exp(-4)) - x),x)

[Out]

exp(exp(exp(-4)))*exp(-x)