3.91.21 \(\int 2 e^{e^e+2 x} \, dx\)

Optimal. Leaf size=17 \[ e^{26+e^{32}}+e^{e^e+2 x} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.53, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} e^{2 x+e^e} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*E^(E^E + 2*x),x]

[Out]

E^(E^E + 2*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} &=2 \int e^{e^e+2 x} \, dx\\ &=e^{e^e+2 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.53 \begin {gather*} e^{e^e+2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*E^(E^E + 2*x),x]

[Out]

E^(E^E + 2*x)

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fricas [A]  time = 0.52, size = 8, normalized size = 0.47 \begin {gather*} e^{\left (2 \, x + e^{e}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(2*x+exp(exp(1))),x, algorithm="fricas")

[Out]

e^(2*x + e^e)

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giac [A]  time = 0.18, size = 8, normalized size = 0.47 \begin {gather*} e^{\left (2 \, x + e^{e}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(2*x+exp(exp(1))),x, algorithm="giac")

[Out]

e^(2*x + e^e)

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maple [A]  time = 0.03, size = 9, normalized size = 0.53

method	result	size
gosper	\({\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}}}\)	\(9\)
derivativedivides	\({\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}}}\)	\(9\)
default	\({\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}}}\)	\(9\)
norman	\({\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}}}\)	\(9\)
risch	\({\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}}}\)	\(9\)
meijerg	\(-{\mathrm e}^{{\mathrm e}^{{\mathrm e}}} \left (1-{\mathrm e}^{2 x}\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(2*x+exp(exp(1))),x,method=_RETURNVERBOSE)

[Out]

exp(2*x+exp(exp(1)))

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maxima [A]  time = 0.35, size = 8, normalized size = 0.47 \begin {gather*} e^{\left (2 \, x + e^{e}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(2*x+exp(exp(1))),x, algorithm="maxima")

[Out]

e^(2*x + e^e)

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mupad [B]  time = 7.84, size = 9, normalized size = 0.53 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\mathrm {e}}}\,{\mathrm {e}}^{2\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(2*x + exp(exp(1))),x)

[Out]

exp(exp(exp(1)))*exp(2*x)

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sympy [A]  time = 0.08, size = 8, normalized size = 0.47 \begin {gather*} e^{2 x + e^{e}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*exp(2*x+exp(exp(1))),x)

[Out]

exp(2*x + exp(E))

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