3.58.92 \(\int -e^{e^{\frac {1}{e^4}}-x} \, dx\)

Optimal. Leaf size=11 \[ e^{e^{\frac {1}{e^4}}-x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, 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 = {2194} \begin {gather*} e^{e^{\frac {1}{e^4}}-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^(E^E^(-4) - x),x]

[Out]

E^(E^E^(-4) - x)

Rule 2194

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 {gather*} \begin {aligned} \text {integral} &=e^{e^{\frac {1}{e^4}}-x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} e^{e^{\frac {1}{e^4}}-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^(E^E^(-4) - x),x]

[Out]

E^(E^E^(-4) - x)

________________________________________________________________________________________

fricas [A]  time = 0.70, size = 8, normalized size = 0.73 \begin {gather*} e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(-x + e^(e^(-4)))

________________________________________________________________________________________

giac [A]  time = 0.20, size = 8, normalized size = 0.73 \begin {gather*} e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(-x + e^(e^(-4)))

________________________________________________________________________________________

maple [A]  time = 0.03, size = 9, normalized size = 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	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\)	\(11\)
meijerg	\(-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}} \left (1-{\mathrm e}^{-x}\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.37, size = 8, normalized size = 0.73 \begin {gather*} e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

e^(-x + e^(e^(-4)))

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 9, normalized size = 0.82 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-4}}}\,{\mathrm {e}}^{-x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(exp(-4)) - x),x)

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 8, normalized size = 0.73 \begin {gather*} e^{- x + e^{e^{-4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(-x + exp(exp(-4)))

________________________________________________________________________________________