3.46.85 \(\int 6 e^{11+e-2 e^{11-3 x}-3 x} \, dx\)

Optimal. Leaf size=13 \[ e^{e-2 e^{11-3 x}} \]

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Rubi [A]  time = 0.02, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2282, 2194} \begin {gather*} e^{e-2 e^{11-3 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[6*E^(11 + E - 2*E^(11 - 3*x) - 3*x),x]

[Out]

E^(E - 2*E^(11 - 3*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} &=6 \int e^{11+e-2 e^{11-3 x}-3 x} \, dx\\ &=-\left (2 \operatorname {Subst}\left (\int e^{11+e-2 e^{11} x} \, dx,x,e^{-3 x}\right )\right )\\ &=e^{e-2 e^{11-3 x}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} e^{e-2 e^{11-3 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[6*E^(11 + E - 2*E^(11 - 3*x) - 3*x),x]

[Out]

E^(E - 2*E^(11 - 3*x))

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fricas [A]  time = 0.65, size = 16, normalized size = 1.23 \begin {gather*} e^{\left (e - \frac {1}{2} \, e^{\left (-3 \, x + 2 \, \log \relax (2) + 11\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*exp(exp(1))*exp(2*log(2)+11-3*x)/exp(1/2*exp(2*log(2)+11-3*x)),x, algorithm="fricas")

[Out]

e^(e - 1/2*e^(-3*x + 2*log(2) + 11))

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giac [A]  time = 0.15, size = 12, normalized size = 0.92 \begin {gather*} e^{\left (e - 2 \, e^{\left (-3 \, x + 11\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*exp(exp(1))*exp(2*log(2)+11-3*x)/exp(1/2*exp(2*log(2)+11-3*x)),x, algorithm="giac")

[Out]

e^(e - 2*e^(-3*x + 11))

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maple [A]  time = 0.03, size = 13, normalized size = 1.00

method	result	size
risch	\({\mathrm e}^{{\mathrm e}-2 \,{\mathrm e}^{11-3 x}}\)	\(13\)
derivativedivides	\({\mathrm e}^{{\mathrm e}} {\mathrm e}^{-2 \,{\mathrm e}^{11-3 x}}\)	\(20\)
default	\({\mathrm e}^{{\mathrm e}} {\mathrm e}^{-2 \,{\mathrm e}^{11-3 x}}\)	\(20\)
norman	\({\mathrm e}^{{\mathrm e}} {\mathrm e}^{-2 \,{\mathrm e}^{11-3 x}}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3/2*exp(exp(1))*exp(2*ln(2)+11-3*x)/exp(1/2*exp(2*ln(2)+11-3*x)),x,method=_RETURNVERBOSE)

[Out]

exp(exp(1)-2*exp(11-3*x))

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maxima [A]  time = 0.36, size = 12, normalized size = 0.92 \begin {gather*} e^{\left (e - 2 \, e^{\left (-3 \, x + 11\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*exp(exp(1))*exp(2*log(2)+11-3*x)/exp(1/2*exp(2*log(2)+11-3*x)),x, algorithm="maxima")

[Out]

e^(e - 2*e^(-3*x + 11))

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mupad [B]  time = 0.09, size = 13, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{-2\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{11}}\,{\mathrm {e}}^{\mathrm {e}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*exp(-exp(2*log(2) - 3*x + 11)/2)*exp(2*log(2) - 3*x + 11)*exp(exp(1)))/2,x)

[Out]

exp(-2*exp(-3*x)*exp(11))*exp(exp(1))

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sympy [A]  time = 0.14, size = 14, normalized size = 1.08 \begin {gather*} e^{e} e^{- 2 e^{11 - 3 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3/2*exp(exp(1))*exp(2*ln(2)+11-3*x)/exp(1/2*exp(2*ln(2)+11-3*x)),x)

[Out]

exp(E)*exp(-2*exp(11 - 3*x))

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