3.20.65 \(\int \frac {e^{4+e^{\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}}+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}} (-3-e-e^{e^3}+e^x)}{3+e+e^{e^3}} \, dx\)

Optimal. Leaf size=34 \[ e^{4+e^{\frac {-x+\left (\frac {e^x}{3+e+e^{e^3}}-x\right ) x}{x}}} \]

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Rubi [F]  time = 36.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right ) \left (-3-e-e^{e^3}+e^x\right )}{3+e+e^{e^3}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(4 + E^((-3 + E^x + E*(-1 - x) + E^E^3*(-1 - x) - 3*x)/(3 + E + E^E^3)) + (-3 + E^x + E*(-1 - x) + E^E^
3*(-1 - x) - 3*x)/(3 + E + E^E^3))*(-3 - E - E^E^3 + E^x))/(3 + E + E^E^3),x]

[Out]

-Defer[Int][E^(4 + E^((-3 + E^x + E*(-1 - x) + E^E^3*(-1 - x) - 3*x)/(3 + E + E^E^3)) + (-3 + E^x + E*(-1 - x)
+ E^E^3*(-1 - x) - 3*x)/(3 + E + E^E^3)), x] + Defer[Int][E^(4 + E^((-3 + E^x + E*(-1 - x) + E^E^3*(-1 - x) -
3*x)/(3 + E + E^E^3)) + (-3 + E^x + E*(-1 - x) + E^E^3*(-1 - x) - 3*x)/(3 + E + E^E^3) + x), x]/(3 + E + E^E^
3)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right ) \left (-3-e-e^{e^3}+e^x\right ) \, dx}{3+e+e^{e^3}}\\ &=\frac {\int \exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right ) \left (e^x-3 \left (1+\frac {1}{3} \left (e+e^{e^3}\right )\right )\right ) \, dx}{3+e+e^{e^3}}\\ &=\frac {\int \left (\exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}+x\right )-3 \exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right ) \left (1+\frac {1}{3} \left (e+e^{e^3}\right )\right )\right ) \, dx}{3+e+e^{e^3}}\\ &=\frac {\int \exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}+x\right ) \, dx}{3+e+e^{e^3}}-\int \exp \left (4+\exp \left (\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right )+\frac {-3+e^x+e (-1-x)+e^{e^3} (-1-x)-3 x}{3+e+e^{e^3}}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.30, size = 25, normalized size = 0.74 \begin {gather*} e^{4+e^{-1+\frac {e^x}{3+e+e^{e^3}}-x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(4 + E^((-3 + E^x + E*(-1 - x) + E^E^3*(-1 - x) - 3*x)/(3 + E + E^E^3)) + (-3 + E^x + E*(-1 - x)
+ E^E^3*(-1 - x) - 3*x)/(3 + E + E^E^3))*(-3 - E - E^E^3 + E^x))/(3 + E + E^E^3),x]

[Out]

E^(4 + E^(-1 + E^x/(3 + E + E^E^3) - x))

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fricas [B]  time = 0.65, size = 110, normalized size = 3.24 \begin {gather*} e^{\left (\frac {{\left (x + 1\right )} e + {\left (x + 1\right )} e^{\left (e^{3}\right )} + 3 \, x - e^{x} + 3}{e + e^{\left (e^{3}\right )} + 3} - \frac {{\left (x - 3\right )} e - {\left (e + e^{\left (e^{3}\right )} + 3\right )} e^{\left (-\frac {{\left (x + 1\right )} e + {\left (x + 1\right )} e^{\left (e^{3}\right )} + 3 \, x - e^{x} + 3}{e + e^{\left (e^{3}\right )} + 3}\right )} + {\left (x - 3\right )} e^{\left (e^{3}\right )} + 3 \, x - e^{x} - 9}{e + e^{\left (e^{3}\right )} + 3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(exp(3))+exp(x)-3-exp(1))*exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+ex
p(1)))*exp(exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))+4)/(exp(exp(3))+3+exp(1
)),x, algorithm="fricas")

[Out]

e^(((x + 1)*e + (x + 1)*e^(e^3) + 3*x - e^x + 3)/(e + e^(e^3) + 3) - ((x - 3)*e - (e + e^(e^3) + 3)*e^(-((x +
1)*e + (x + 1)*e^(e^3) + 3*x - e^x + 3)/(e + e^(e^3) + 3)) + (x - 3)*e^(e^3) + 3*x - e^x - 9)/(e + e^(e^3) + 3
))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (e - e^{x} + e^{\left (e^{3}\right )} + 3\right )} e^{\left (-\frac {{\left (x + 1\right )} e + {\left (x + 1\right )} e^{\left (e^{3}\right )} + 3 \, x - e^{x} + 3}{e + e^{\left (e^{3}\right )} + 3} + e^{\left (-\frac {{\left (x + 1\right )} e + {\left (x + 1\right )} e^{\left (e^{3}\right )} + 3 \, x - e^{x} + 3}{e + e^{\left (e^{3}\right )} + 3}\right )} + 4\right )}}{e + e^{\left (e^{3}\right )} + 3}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(exp(3))+exp(x)-3-exp(1))*exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+ex
p(1)))*exp(exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))+4)/(exp(exp(3))+3+exp(1
)),x, algorithm="giac")

[Out]

integrate(-(e - e^x + e^(e^3) + 3)*e^(-((x + 1)*e + (x + 1)*e^(e^3) + 3*x - e^x + 3)/(e + e^(e^3) + 3) + e^(-(
(x + 1)*e + (x + 1)*e^(e^3) + 3*x - e^x + 3)/(e + e^(e^3) + 3)) + 4)/(e + e^(e^3) + 3), x)

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maple [A]  time = 0.08, size = 39, normalized size = 1.15

method	result	size
derivativedivides	\({\mathrm e}^{{\mathrm e}^{\frac {\left (-x -1\right ) {\mathrm e}^{{\mathrm e}^{3}}+{\mathrm e}^{x}+\left (-x -1\right ) {\mathrm e}-3 x -3}{{\mathrm e}^{{\mathrm e}^{3}}+3+{\mathrm e}}}+4}\)	\(39\)
default	\({\mathrm e}^{{\mathrm e}^{\frac {\left (-x -1\right ) {\mathrm e}^{{\mathrm e}^{3}}+{\mathrm e}^{x}+\left (-x -1\right ) {\mathrm e}-3 x -3}{{\mathrm e}^{{\mathrm e}^{3}}+3+{\mathrm e}}}+4}\)	\(39\)
norman	\({\mathrm e}^{{\mathrm e}^{\frac {\left (-x -1\right ) {\mathrm e}^{{\mathrm e}^{3}}+{\mathrm e}^{x}+\left (-x -1\right ) {\mathrm e}-3 x -3}{{\mathrm e}^{{\mathrm e}^{3}}+3+{\mathrm e}}}+4}\)	\(39\)
risch	\({\mathrm e}^{{\mathrm e}^{-\frac {x \,{\mathrm e}+x \,{\mathrm e}^{{\mathrm e}^{3}}+{\mathrm e}-{\mathrm e}^{x}+{\mathrm e}^{{\mathrm e}^{3}}+3 x +3}{{\mathrm e}^{{\mathrm e}^{3}}+3+{\mathrm e}}}+4}\)	\(39\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(exp(3))+exp(x)-3-exp(1))*exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))
*exp(exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))+4)/(exp(exp(3))+3+exp(1)),x,m
ethod=_RETURNVERBOSE)

[Out]

exp(exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))+4)

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maxima [B]  time = 4.13, size = 115, normalized size = 3.38 \begin {gather*} \frac {{\left ({\left (e^{\left (e^{3}\right )} + 3\right )} e^{4} + e^{5}\right )} e^{\left (e^{\left (-\frac {x e}{e + e^{\left (e^{3}\right )} + 3} - \frac {x e^{\left (e^{3}\right )}}{e + e^{\left (e^{3}\right )} + 3} - \frac {3 \, x}{e + e^{\left (e^{3}\right )} + 3} - \frac {e}{e + e^{\left (e^{3}\right )} + 3} + \frac {e^{x}}{e + e^{\left (e^{3}\right )} + 3} - \frac {e^{\left (e^{3}\right )}}{e + e^{\left (e^{3}\right )} + 3} - \frac {3}{e + e^{\left (e^{3}\right )} + 3}\right )}\right )}}{e + e^{\left (e^{3}\right )} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(exp(3))+exp(x)-3-exp(1))*exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+ex
p(1)))*exp(exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))+4)/(exp(exp(3))+3+exp(1
)),x, algorithm="maxima")

[Out]

((e^(e^3) + 3)*e^4 + e^5)*e^(e^(-x*e/(e + e^(e^3) + 3) - x*e^(e^3)/(e + e^(e^3) + 3) - 3*x/(e + e^(e^3) + 3) -
e/(e + e^(e^3) + 3) + e^x/(e + e^(e^3) + 3) - e^(e^3)/(e + e^(e^3) + 3) - 3/(e + e^(e^3) + 3)))/(e + e^(e^3)
+ 3)

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mupad [B]  time = 0.42, size = 103, normalized size = 3.03 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-\frac {\mathrm {e}}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}\,{\mathrm {e}}^{-\frac {3\,x}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{{\mathrm {e}}^3}}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}\,{\mathrm {e}}^{-\frac {x\,\mathrm {e}}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}\,{\mathrm {e}}^{-\frac {3}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^3}}{\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^3}+3}}}\,{\mathrm {e}}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(-(3*x - exp(x) + exp(exp(3))*(x + 1) + exp(1)*(x + 1) + 3)/(exp(1) + exp(exp(3)) + 3)) + 4)*exp(
-(3*x - exp(x) + exp(exp(3))*(x + 1) + exp(1)*(x + 1) + 3)/(exp(1) + exp(exp(3)) + 3))*(exp(1) + exp(exp(3)) -
exp(x) + 3))/(exp(1) + exp(exp(3)) + 3),x)

[Out]

exp(exp(-exp(1)/(exp(1) + exp(exp(3)) + 3))*exp(-(3*x)/(exp(1) + exp(exp(3)) + 3))*exp(-exp(exp(3))/(exp(1) +
exp(exp(3)) + 3))*exp(exp(x)/(exp(1) + exp(exp(3)) + 3))*exp(-(x*exp(1))/(exp(1) + exp(exp(3)) + 3))*exp(-3/(e
xp(1) + exp(exp(3)) + 3))*exp(-(x*exp(exp(3)))/(exp(1) + exp(exp(3)) + 3)))*exp(4)

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sympy [A]  time = 0.79, size = 41, normalized size = 1.21 \begin {gather*} e^{e^{\frac {- 3 x + e \left (- x - 1\right ) + \left (- x - 1\right ) e^{e^{3}} + e^{x} - 3}{e + 3 + e^{e^{3}}}} + 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(exp(3))+exp(x)-3-exp(1))*exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+ex
p(1)))*exp(exp(((-x-1)*exp(exp(3))+exp(x)+(-x-1)*exp(1)-3*x-3)/(exp(exp(3))+3+exp(1)))+4)/(exp(exp(3))+3+exp(1
)),x)

[Out]

exp(exp((-3*x + E*(-x - 1) + (-x - 1)*exp(exp(3)) + exp(x) - 3)/(E + 3 + exp(exp(3)))) + 4)

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