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

Optimal. Leaf size=7 \[ e^{e^{e^x}} \]

[Out]

exp(exp(exp(x)))

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Rubi [A]  time = 0.01, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2282, 2194} \[ e^{e^{e^x}} \]

Antiderivative was successfully verified.

[In]

Int[E^(E^E^x + E^x + x),x]

[Out]

E^E^E^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 {align*} \int e^{e^{e^x}+e^x+x} \, dx &=\operatorname {Subst}\left (\int e^{e^x+x} \, dx,x,e^x\right )\\ &=\operatorname {Subst}\left (\int e^x \, dx,x,e^{e^x}\right )\\ &=e^{e^{e^x}}\\ \end {align*}

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Mathematica [A]  time = 0.01, size = 7, normalized size = 1.00 \[ e^{e^{e^x}} \]

Antiderivative was successfully verified.

[In]

Integrate[E^(E^E^x + E^x + x),x]

[Out]

E^E^E^x

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fricas [A]  time = 0.40, size = 4, normalized size = 0.57 \[ e^{\left (e^{\left (e^{x}\right )}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(exp(x))+exp(x)+x),x, algorithm="fricas")

[Out]

e^(e^(e^x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(exp(x))+exp(x)+x),x, algorithm="giac")

[Out]

integrate(e^(x + e^x + e^(e^x)), x)

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maple [A]  time = 0.03, size = 5, normalized size = 0.71 \[ {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(exp(x))+exp(x)+x),x)

[Out]

exp(exp(exp(x)))

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maxima [A]  time = 0.66, size = 4, normalized size = 0.57 \[ e^{\left (e^{\left (e^{x}\right )}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(exp(x))+exp(x)+x),x, algorithm="maxima")

[Out]

e^(e^(e^x))

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mupad [B]  time = 3.46, size = 4, normalized size = 0.57 \[ {\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x + exp(exp(x)) + exp(x)),x)

[Out]

exp(exp(exp(x)))

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sympy [A]  time = 0.92, size = 5, normalized size = 0.71 \[ e^{e^{e^{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(exp(exp(x))+exp(x)+x),x)

[Out]

exp(exp(exp(x)))

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