3.75.78 \(\int -2 e^{e^{e^8}-x} \, dx\)

Optimal. Leaf size=15 \[ 16+2 e^{e^{e^8}-x} \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2194} \begin {gather*} 2 e^{e^{e^8}-x} \end {gather*}

Antiderivative was successfully verified.

[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 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} &=-\left (2 \int e^{e^{e^8}-x} \, dx\right )\\ &=2 e^{e^{e^8}-x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 13, normalized size = 0.87 \begin {gather*} 2 e^{e^{e^8}-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*E^(E^E^8 - x),x]

[Out]

2*E^(E^E^8 - x)

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fricas [A]  time = 1.07, size = 10, normalized size = 0.67 \begin {gather*} 2 \, e^{\left (-x + e^{\left (e^{8}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^(-x + e^(e^8))

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giac [A]  time = 0.23, size = 10, normalized size = 0.67 \begin {gather*} 2 \, e^{\left (-x + e^{\left (e^{8}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^(-x + e^(e^8))

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maple [A]  time = 0.02, size = 11, normalized size = 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	\(2 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{8}}-x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.39, size = 10, normalized size = 0.67 \begin {gather*} 2 \, e^{\left (-x + e^{\left (e^{8}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^(-x + e^(e^8))

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mupad [B]  time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} 2\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^8}}\,{\mathrm {e}}^{-x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(exp(exp(8)) - x),x)

[Out]

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

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sympy [A]  time = 0.08, size = 8, normalized size = 0.53 \begin {gather*} 2 e^{- x + e^{e^{8}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp(-x + exp(exp(8)))

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