3.90.68 \(\int \frac {1}{3} e^{-\frac {1}{3} e^{e^5} (e^{4-e^3 x}+x)} (3+3 e^{\frac {1}{3} e^{e^5} (e^{4-e^3 x}+x)}+e^{e^5} (3+e^{7-e^3 x} (-3+x)-x)) \, dx\)

Optimal. Leaf size=30 \[ 1+e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} (-3+x)+x \]

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Rubi [F]  time = 2.95, 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 {1}{3} e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \left (3+3 e^{\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )}+e^{e^5} \left (3+e^{7-e^3 x} (-3+x)-x\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3 + 3*E^((E^E^5*(E^(4 - E^3*x) + x))/3) + E^E^5*(3 + E^(7 - E^3*x)*(-3 + x) - x))/(3*E^((E^E^5*(E^(4 - E^
3*x) + x))/3)),x]

[Out]

x + Defer[Int][E^(-1/3*(E^E^5*(E^(4 - E^3*x) + x))), x] + Defer[Int][E^(E^5 - (E^E^5*(E^(4 - E^3*x) + x))/3),
x] - Defer[Int][E^(7*(1 + E^5/7) - E^3*x - (E^E^5*(E^(4 - E^3*x) + x))/3), x] - Defer[Int][E^(E^5 - (E^E^5*(E^
(4 - E^3*x) + x))/3)*x, x]/3 + Defer[Int][E^(7*(1 + E^5/7) - E^3*x - (E^E^5*(E^(4 - E^3*x) + x))/3)*x, x]/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \left (3+3 e^{\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )}+e^{e^5} \left (3+e^{7-e^3 x} (-3+x)-x\right )\right ) \, dx\\ &=\frac {1}{3} \int \left (3+3 e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )}-e^{e^5-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \left (-e^7+e^{e^3 x}\right ) (-3+x)\right ) \, dx\\ &=x-\frac {1}{3} \int e^{e^5-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \left (-e^7+e^{e^3 x}\right ) (-3+x) \, dx+\int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx\\ &=x-\frac {1}{3} \int \left (e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} (-3+x)-e^{7+e^5-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} (-3+x)\right ) \, dx+\int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx\\ &=x-\frac {1}{3} \int e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} (-3+x) \, dx+\frac {1}{3} \int e^{7+e^5-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} (-3+x) \, dx+\int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx\\ &=x+\frac {1}{3} \int \exp \left (7 \left (1+\frac {e^5}{7}\right )-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )\right ) (-3+x) \, dx-\frac {1}{3} \int \left (-3 e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )}+e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} x\right ) \, dx+\int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx\\ &=x-\frac {1}{3} \int e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} x \, dx+\frac {1}{3} \int \left (-3 \exp \left (7 \left (1+\frac {e^5}{7}\right )-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )\right )+\exp \left (7 \left (1+\frac {e^5}{7}\right )-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )\right ) x\right ) \, dx+\int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx+\int e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx\\ &=x-\frac {1}{3} \int e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} x \, dx+\frac {1}{3} \int \exp \left (7 \left (1+\frac {e^5}{7}\right )-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )\right ) x \, dx+\int e^{-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx+\int e^{e^5-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )} \, dx-\int \exp \left (7 \left (1+\frac {e^5}{7}\right )-e^3 x-\frac {1}{3} e^{e^5} \left (e^{4-e^3 x}+x\right )\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.28, size = 33, normalized size = 1.10 \begin {gather*} e^{\frac {1}{3} e^{e^5} \left (-e^{4-e^3 x}-x\right )} (-3+x)+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3 + 3*E^((E^E^5*(E^(4 - E^3*x) + x))/3) + E^E^5*(3 + E^(7 - E^3*x)*(-3 + x) - x))/(3*E^((E^E^5*(E^(
4 - E^3*x) + x))/3)),x]

[Out]

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

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fricas [B]  time = 0.45, size = 48, normalized size = 1.60 \begin {gather*} {\left (x e^{\left (\frac {1}{3} \, {\left (x e^{3} + e^{\left (-x e^{3} + 7\right )}\right )} e^{\left (e^{5} - 3\right )}\right )} + x - 3\right )} e^{\left (-\frac {1}{3} \, {\left (x e^{3} + e^{\left (-x e^{3} + 7\right )}\right )} e^{\left (e^{5} - 3\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(3*exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5)))+((x-3)*exp(3)*exp(-x*exp(3)+4)+3-x)*exp(exp(5))+3)/
exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5))),x, algorithm="fricas")

[Out]

(x*e^(1/3*(x*e^3 + e^(-x*e^3 + 7))*e^(e^5 - 3)) + x - 3)*e^(-1/3*(x*e^3 + e^(-x*e^3 + 7))*e^(e^5 - 3))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{3} \, {\left ({\left ({\left (x - 3\right )} e^{\left (-x e^{3} + 7\right )} - x + 3\right )} e^{\left (e^{5}\right )} + 3 \, e^{\left (\frac {1}{3} \, {\left (x + e^{\left (-x e^{3} + 4\right )}\right )} e^{\left (e^{5}\right )}\right )} + 3\right )} e^{\left (-\frac {1}{3} \, {\left (x + e^{\left (-x e^{3} + 4\right )}\right )} e^{\left (e^{5}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(3*exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5)))+((x-3)*exp(3)*exp(-x*exp(3)+4)+3-x)*exp(exp(5))+3)/
exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5))),x, algorithm="giac")

[Out]

integrate(1/3*(((x - 3)*e^(-x*e^3 + 7) - x + 3)*e^(e^5) + 3*e^(1/3*(x + e^(-x*e^3 + 4))*e^(e^5)) + 3)*e^(-1/3*
(x + e^(-x*e^3 + 4))*e^(e^5)), x)

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maple [A]  time = 0.14, size = 26, normalized size = 0.87

method	result	size
risch	\(x +\frac {\left (3 x -9\right ) {\mathrm e}^{-\frac {\left ({\mathrm e}^{-x \,{\mathrm e}^{3}+4}+x \right ) {\mathrm e}^{{\mathrm e}^{5}}}{3}}}{3}\)	\(26\)
norman	\(\left (-3+x +x \,{\mathrm e}^{\frac {\left ({\mathrm e}^{-x \,{\mathrm e}^{3}+4}+x \right ) {\mathrm e}^{{\mathrm e}^{5}}}{3}}\right ) {\mathrm e}^{-\frac {\left ({\mathrm e}^{-x \,{\mathrm e}^{3}+4}+x \right ) {\mathrm e}^{{\mathrm e}^{5}}}{3}}\)	\(41\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*(3*exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5)))+((x-3)*exp(3)*exp(-x*exp(3)+4)+3-x)*exp(exp(5))+3)/exp(1/
3*(exp(-x*exp(3)+4)+x)*exp(exp(5))),x,method=_RETURNVERBOSE)

[Out]

x+1/3*(3*x-9)*exp(-1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5)))

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maxima [A]  time = 0.49, size = 26, normalized size = 0.87 \begin {gather*} {\left (x - 3\right )} e^{\left (-\frac {1}{3} \, x e^{\left (e^{5}\right )} - \frac {1}{3} \, e^{\left (-x e^{3} + e^{5} + 4\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(3*exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5)))+((x-3)*exp(3)*exp(-x*exp(3)+4)+3-x)*exp(exp(5))+3)/
exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5))),x, algorithm="maxima")

[Out]

(x - 3)*e^(-1/3*x*e^(e^5) - 1/3*e^(-x*e^3 + e^5 + 4)) + x

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mupad [B]  time = 0.28, size = 48, normalized size = 1.60 \begin {gather*} x-3\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^5}}{3}-\frac {{\mathrm {e}}^4\,{\mathrm {e}}^{-x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{{\mathrm {e}}^5}}{3}}+x\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^5}}{3}-\frac {{\mathrm {e}}^4\,{\mathrm {e}}^{-x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{{\mathrm {e}}^5}}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-(exp(exp(5))*(x + exp(4 - x*exp(3))))/3)*(exp((exp(exp(5))*(x + exp(4 - x*exp(3))))/3) + (exp(exp(5))
*(exp(4 - x*exp(3))*exp(3)*(x - 3) - x + 3))/3 + 1),x)

[Out]

x - 3*exp(- (x*exp(exp(5)))/3 - (exp(4)*exp(-x*exp(3))*exp(exp(5)))/3) + x*exp(- (x*exp(exp(5)))/3 - (exp(4)*e
xp(-x*exp(3))*exp(exp(5)))/3)

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sympy [A]  time = 0.29, size = 24, normalized size = 0.80 \begin {gather*} x + \left (x - 3\right ) e^{- \left (\frac {x}{3} + \frac {e^{- x e^{3} + 4}}{3}\right ) e^{e^{5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(3*exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5)))+((x-3)*exp(3)*exp(-x*exp(3)+4)+3-x)*exp(exp(5))+3)/
exp(1/3*(exp(-x*exp(3)+4)+x)*exp(exp(5))),x)

[Out]

x + (x - 3)*exp(-(x/3 + exp(-x*exp(3) + 4)/3)*exp(exp(5)))

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