\(\int -2 e^{e^{e^8}-x} \, dx\) [7478]

Optimal result

Integrand size = 13, antiderivative size = 15 \[ \int -2 e^{e^{e^8}-x} \, dx=16+2 e^{e^{e^8}-x} \]

[Out]

2/exp(-exp(exp(4)^2)+x)+16

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2225} \[ \int -2 e^{e^{e^8}-x} \, dx=2 e^{e^{e^8}-x} \]

[In]

Int[-2*E^(E^E^8 - x),x]

[Out]

2*E^(E^E^8 - x)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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}& = -\left (2 \int e^{e^{e^8}-x} \, dx\right ) \\ & = 2 e^{e^{e^8}-x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int -2 e^{e^{e^8}-x} \, dx=2 e^{e^{e^8}-x} \]

[In]

Integrate[-2*E^(E^E^8 - x),x]

[Out]

2*E^(E^E^8 - x)

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73

method	result	size
risch	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(11\)
gosper	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(15\)
derivativedivides	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(15\)
default	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(15\)
norman	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(15\)
parallelrisch	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(15\)

[In]

int(-2/exp(-exp(exp(4)^2)+x),x,method=_RETURNVERBOSE)

[Out]

2*exp(exp(exp(8))-x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int -2 e^{e^{e^8}-x} \, dx=2 \, e^{\left (-x + e^{\left (e^{8}\right )}\right )} \]

[In]

integrate(-2/exp(-exp(exp(4)^2)+x),x, algorithm="fricas")

[Out]

2*e^(-x + e^(e^8))

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -2 e^{e^{e^8}-x} \, dx=2 e^{- x + e^{e^{8}}} \]

[In]

integrate(-2/exp(-exp(exp(4)**2)+x),x)

[Out]

2*exp(-x + exp(exp(8)))

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int -2 e^{e^{e^8}-x} \, dx=2 \, e^{\left (-x + e^{\left (e^{8}\right )}\right )} \]

[In]

integrate(-2/exp(-exp(exp(4)^2)+x),x, algorithm="maxima")

[Out]

2*e^(-x + e^(e^8))

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int -2 e^{e^{e^8}-x} \, dx=2 \, e^{\left (-x + e^{\left (e^{8}\right )}\right )} \]

[In]

integrate(-2/exp(-exp(exp(4)^2)+x),x, algorithm="giac")

[Out]

2*e^(-x + e^(e^8))

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int -2 e^{e^{e^8}-x} \, dx=2\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^8}}\,{\mathrm {e}}^{-x} \]

[In]

int(-2*exp(exp(exp(8)) - x),x)

[Out]

2*exp(exp(exp(8)))*exp(-x)