3.2.93 \(\int (1-e^{29+e^{e^{25+x}}+e^{25+x}+x}) \, dx\)

Optimal. Leaf size=24 \[ -e^4-e^{4+e^{e^{25+x}}}+x-\log (5) \]

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Rubi [A]  time = 0.03, antiderivative size = 15, normalized size of antiderivative = 0.62, number of steps used = 4, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2282, 2194} \begin {gather*} x-e^{e^{e^{x+25}}+4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - E^(29 + E^E^(25 + x) + E^(25 + x) + x),x]

[Out]

-E^(4 + E^E^(25 + x)) + 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} &=x-\int e^{29+e^{e^{25+x}}+e^{25+x}+x} \, dx\\ &=x-\operatorname {Subst}\left (\int e^{29+e^{e^{25} x}+e^{25} x} \, dx,x,e^x\right )\\ &=x-\frac {\operatorname {Subst}\left (\int e^{29+x} \, dx,x,e^{e^{25+x}}\right )}{e^{25}}\\ &=-e^{4+e^{e^{25+x}}}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 15, normalized size = 0.62 \begin {gather*} -e^{4+e^{e^{25+x}}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - E^(29 + E^E^(25 + x) + E^(25 + x) + x),x]

[Out]

-E^(4 + E^E^(25 + x)) + x

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fricas [A]  time = 0.92, size = 39, normalized size = 1.62 \begin {gather*} {\left (x e^{\left (x + e^{\left (x + 25\right )} + 25\right )} - e^{\left (x + e^{\left (x + 25\right )} + e^{\left (e^{\left (x + 25\right )}\right )} + 29\right )}\right )} e^{\left (-x - e^{\left (x + 25\right )} - 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(4)*exp(x+25)*exp(exp(x+25))*exp(exp(exp(x+25)))+1,x, algorithm="fricas")

[Out]

(x*e^(x + e^(x + 25) + 25) - e^(x + e^(x + 25) + e^(e^(x + 25)) + 29))*e^(-x - e^(x + 25) - 25)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -e^{\left (x + e^{\left (x + 25\right )} + e^{\left (e^{\left (x + 25\right )}\right )} + 29\right )} + 1\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(4)*exp(x+25)*exp(exp(x+25))*exp(exp(exp(x+25)))+1,x, algorithm="giac")

[Out]

integrate(-e^(x + e^(x + 25) + e^(e^(x + 25)) + 29) + 1, x)

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maple [A]  time = 0.03, size = 13, normalized size = 0.54

method	result	size
default	\(x -{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x +25}}} {\mathrm e}^{4}\)	\(13\)
norman	\(x -{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x +25}}} {\mathrm e}^{4}\)	\(13\)
risch	\(x -{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x +25}}+4}\)	\(13\)
derivativedivides	\(\ln \left ({\mathrm e}^{x +25}\right )-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x +25}}} {\mathrm e}^{4}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(4)*exp(x+25)*exp(exp(x+25))*exp(exp(exp(x+25)))+1,x,method=_RETURNVERBOSE)

[Out]

x-exp(exp(exp(x+25)))*exp(4)

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maxima [A]  time = 0.69, size = 12, normalized size = 0.50 \begin {gather*} x - e^{\left (e^{\left (e^{\left (x + 25\right )}\right )} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(4)*exp(x+25)*exp(exp(x+25))*exp(exp(exp(x+25)))+1,x, algorithm="maxima")

[Out]

x - e^(e^(e^(x + 25)) + 4)

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mupad [B]  time = 0.09, size = 12, normalized size = 0.50 \begin {gather*} x-{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x+25}}}\,{\mathrm {e}}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - exp(exp(exp(x + 25)))*exp(x + 25)*exp(4)*exp(exp(x + 25)),x)

[Out]

x - exp(exp(exp(x + 25)))*exp(4)

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sympy [A]  time = 0.20, size = 12, normalized size = 0.50 \begin {gather*} x - e^{4} e^{e^{e^{x + 25}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(4)*exp(x+25)*exp(exp(x+25))*exp(exp(exp(x+25)))+1,x)

[Out]

x - exp(4)*exp(exp(exp(x + 25)))

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