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

Optimal. Leaf size=23 \[ 4+e^{3 e^{4+e^{e^4} (4-x)} x}+x \]

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Rubi [F]  time = 1.23, 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 \left (1+\exp \left (4+e^{e^4} (4-x)+3 e^{4+e^{e^4} (4-x)} x\right ) \left (3-3 e^{e^4} x\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.46, size = 26, normalized size = 1.13 \begin {gather*} e^{3 e^{4+4 e^{e^4}-e^{e^4} x} x}+x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^(3*E^(4 + 4*E^E^4 - E^E^4*x)*x) + x

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fricas [B]  time = 0.72, size = 50, normalized size = 2.17 \begin {gather*} {\left (x e^{\left (-{\left (x - 4\right )} e^{\left (e^{4}\right )} + 4\right )} + e^{\left (3 \, x e^{\left (-{\left (x - 4\right )} e^{\left (e^{4}\right )} + 4\right )} - {\left (x - 4\right )} e^{\left (e^{4}\right )} + 4\right )}\right )} e^{\left ({\left (x - 4\right )} e^{\left (e^{4}\right )} - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x*exp(exp(4))+3)*exp((-x+4)*exp(exp(4))+4)*exp(3*x*exp((-x+4)*exp(exp(4))+4))+1,x, algorithm="fr
icas")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x*exp(exp(4))+3)*exp((-x+4)*exp(exp(4))+4)*exp(3*x*exp((-x+4)*exp(exp(4))+4))+1,x, algorithm="gi
ac")

[Out]

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

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maple [A]  time = 0.11, size = 19, normalized size = 0.83

method	result	size
default	\(x +{\mathrm e}^{3 x \,{\mathrm e}^{\left (-x +4\right ) {\mathrm e}^{{\mathrm e}^{4}}+4}}\)	\(19\)
norman	\(x +{\mathrm e}^{3 x \,{\mathrm e}^{\left (-x +4\right ) {\mathrm e}^{{\mathrm e}^{4}}+4}}\)	\(19\)
risch	\(x +{\mathrm e}^{3 x \,{\mathrm e}^{-x \,{\mathrm e}^{{\mathrm e}^{4}}+4 \,{\mathrm e}^{{\mathrm e}^{4}}+4}}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-3*x*exp(exp(4))+3)*exp((-x+4)*exp(exp(4))+4)*exp(3*x*exp((-x+4)*exp(exp(4))+4))+1,x,method=_RETURNVERBOS
E)

[Out]

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

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maxima [A]  time = 0.88, size = 20, normalized size = 0.87 \begin {gather*} x + e^{\left (3 \, x e^{\left (-x e^{\left (e^{4}\right )} + 4 \, e^{\left (e^{4}\right )} + 4\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*x*exp(exp(4))+3)*exp((-x+4)*exp(exp(4))+4)*exp(3*x*exp((-x+4)*exp(exp(4))+4))+1,x, algorithm="ma
xima")

[Out]

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

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mupad [B]  time = 2.06, size = 21, normalized size = 0.91 \begin {gather*} x+{\mathrm {e}}^{3\,x\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{{\mathrm {e}}^4}}\,{\mathrm {e}}^4\,{\mathrm {e}}^{4\,{\mathrm {e}}^{{\mathrm {e}}^4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.19, size = 17, normalized size = 0.74 \begin {gather*} x + e^{3 x e^{\left (4 - x\right ) e^{e^{4}} + 4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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