3.99.94 \(\int e^{e^{-x} (24+2 e^{256})-x} (-24-2 e^{256}) \, dx\)

Optimal. Leaf size=14 \[ e^{2 e^{-x} \left (12+e^{256}\right )} \]

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Rubi [A]  time = 0.10, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2282, 2194} \begin {gather*} e^{2 \left (12+e^{256}\right ) e^{-x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^((24 + 2*E^256)/E^x - x)*(-24 - 2*E^256),x]

[Out]

E^((2*(12 + E^256))/E^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]

Rule 2282

Int[u_, x_Symbol] :> With[{v = FunctionOfExponential[u, x]}, Dist[v/D[v, x], Subst[Int[FunctionOfExponentialFu
nction[u, x]/x, x], x, v], x]] /; FunctionOfExponentialQ[u, x] &&  !MatchQ[u, (w_)*((a_.)*(v_)^(n_))^(m_) /; F
reeQ[{a, m, n}, x] && IntegerQ[m*n]] &&  !MatchQ[u, E^((c_.)*((a_.) + (b_.)*x))*(F_)[v_] /; FreeQ[{a, b, c}, x
] && InverseFunctionQ[F[x]]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 \left (12+e^{256}\right )\right ) \int e^{e^{-x} \left (24+2 e^{256}\right )-x} \, dx\right )\\ &=\left (2 \left (12+e^{256}\right )\right ) \operatorname {Subst}\left (\int e^{2 \left (12+e^{256}\right ) x} \, dx,x,e^{-x}\right )\\ &=e^{2 e^{-x} \left (12+e^{256}\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 14, normalized size = 1.00 \begin {gather*} e^{2 e^{-x} \left (12+e^{256}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^((24 + 2*E^256)/E^x - x)*(-24 - 2*E^256),x]

[Out]

E^((2*(12 + E^256))/E^x)

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fricas [A]  time = 0.54, size = 11, normalized size = 0.79 \begin {gather*} e^{\left (2 \, {\left (e^{256} + 12\right )} e^{\left (-x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*exp(256)-24)*exp((2*exp(256)+24)/exp(x))/exp(x),x, algorithm="fricas")

[Out]

e^(2*(e^256 + 12)*e^(-x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -2 \, {\left (e^{256} + 12\right )} e^{\left (2 \, {\left (e^{256} + 12\right )} e^{\left (-x\right )} - x\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*exp(256)-24)*exp((2*exp(256)+24)/exp(x))/exp(x),x, algorithm="giac")

[Out]

integrate(-2*(e^256 + 12)*e^(2*(e^256 + 12)*e^(-x) - x), x)

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maple [A]  time = 0.04, size = 13, normalized size = 0.93

method	result	size
norman	\({\mathrm e}^{\left (2 \,{\mathrm e}^{256}+24\right ) {\mathrm e}^{-x}}\)	\(13\)
derivativedivides	\(-\frac {\left (-2 \,{\mathrm e}^{256}-24\right ) {\mathrm e}^{\left (2 \,{\mathrm e}^{256}+24\right ) {\mathrm e}^{-x}}}{2 \,{\mathrm e}^{256}+24}\)	\(29\)
default	\(-\frac {\left (-2 \,{\mathrm e}^{256}-24\right ) {\mathrm e}^{\left (2 \,{\mathrm e}^{256}+24\right ) {\mathrm e}^{-x}}}{2 \,{\mathrm e}^{256}+24}\)	\(29\)
risch	\(\frac {{\mathrm e}^{2 \left ({\mathrm e}^{256}+12\right ) {\mathrm e}^{-x}} {\mathrm e}^{256}}{{\mathrm e}^{256}+12}+\frac {12 \,{\mathrm e}^{2 \left ({\mathrm e}^{256}+12\right ) {\mathrm e}^{-x}}}{{\mathrm e}^{256}+12}\)	\(41\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*exp(256)-24)*exp((2*exp(256)+24)/exp(x))/exp(x),x,method=_RETURNVERBOSE)

[Out]

exp((2*exp(256)+24)/exp(x))

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maxima [A]  time = 0.35, size = 16, normalized size = 1.14 \begin {gather*} e^{\left (24 \, e^{\left (-x\right )} + 2 \, e^{\left (-x + 256\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*exp(256)-24)*exp((2*exp(256)+24)/exp(x))/exp(x),x, algorithm="maxima")

[Out]

e^(24*e^(-x) + 2*e^(-x + 256))

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mupad [B]  time = 0.13, size = 16, normalized size = 1.14 \begin {gather*} {\mathrm {e}}^{24\,{\mathrm {e}}^{-x}+2\,{\mathrm {e}}^{256-x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(-x)*(2*exp(256) + 24))*exp(-x)*(2*exp(256) + 24),x)

[Out]

exp(24*exp(-x) + 2*exp(256 - x))

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sympy [A]  time = 0.16, size = 10, normalized size = 0.71 \begin {gather*} e^{\left (24 + 2 e^{256}\right ) e^{- x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*exp(256)-24)*exp((2*exp(256)+24)/exp(x))/exp(x),x)

[Out]

exp((24 + 2*exp(256))*exp(-x))

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