3.45.85 \(\int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} (-30-15 x+e^{-4+x} (15+15 x))) \, dx\)

Optimal. Leaf size=32 \[ e^{e^{x-3 (1+x) \left (-e^5+5 e^{2-e^{-4+x}+x}+x\right )}} \]

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Rubi [F]  time = 25.10, 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 \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*(-15 - 1
5*x) - 2*x - 3*x^2 + E^5*(3 + 3*x))*(-2 + 3*E^5 - 6*x + E^(2 - E^(-4 + x) + x)*(-30 - 15*x + E^(-4 + x)*(15 +
15*x))),x]

[Out]

15*Defer[Int][E^(-2 - E^(-4 + x) + E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(
2 - E^(-4 + x) + x)*(-15 - 15*x) - 3*x^2 + E^5*(3 + 3*x)), x] - (2 - 3*E^5)*Defer[Int][E^(E^(E^(2 - E^(-4 + x)
+ x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3
+ 3*x)), x] - 30*Defer[Int][E^(2 - E^(-4 + x) + E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3
+ 3*x)) + E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - x - 3*x^2 + E^5*(3 + 3*x)), x] + 15*Defer[Int][E^(-2 - E^(-4
+ x) + E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*(-15 - 1
5*x) - 3*x^2 + E^5*(3 + 3*x))*x, x] - 6*Defer[Int][E^(E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E
^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x))*x, x] - 15*Defer[Int][E^(2
- E^(-4 + x) + E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*
(-15 - 15*x) - x - 3*x^2 + E^5*(3 + 3*x))*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) \left (-2 \left (1-\frac {3 e^5}{2}\right )-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx\\ &=\int \left (-2 \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) \left (1-\frac {3 e^5}{2}\right )-6 \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) x+15 \exp \left (-2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-x-3 x^2+e^5 (3+3 x)\right ) \left (-2 e^4+e^x-e^4 x+e^x x\right )\right ) \, dx\\ &=-\left (6 \int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) x \, dx\right )+15 \int \exp \left (-2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-x-3 x^2+e^5 (3+3 x)\right ) \left (-2 e^4+e^x-e^4 x+e^x x\right ) \, dx-\left (2-3 e^5\right ) \int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) \, dx\\ &=-\left (6 \int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) x \, dx\right )+15 \int \left (\exp \left (-2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-3 x^2+e^5 (3+3 x)\right )-2 \exp \left (2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-x-3 x^2+e^5 (3+3 x)\right )+\exp \left (-2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-3 x^2+e^5 (3+3 x)\right ) x-\exp \left (2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-x-3 x^2+e^5 (3+3 x)\right ) x\right ) \, dx-\left (2-3 e^5\right ) \int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) \, dx\\ &=-\left (6 \int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) x \, dx\right )+15 \int \exp \left (-2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-3 x^2+e^5 (3+3 x)\right ) \, dx+15 \int \exp \left (-2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-3 x^2+e^5 (3+3 x)\right ) x \, dx-15 \int \exp \left (2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-x-3 x^2+e^5 (3+3 x)\right ) x \, dx-30 \int \exp \left (2-e^{-4+x}+\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-x-3 x^2+e^5 (3+3 x)\right ) \, dx-\left (2-3 e^5\right ) \int \exp \left (\exp \left (e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right )+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.41, size = 38, normalized size = 1.19 \begin {gather*} e^{e^{3 e^5 (1+x)-15 e^{2-e^{-4+x}+x} (1+x)-x (2+3 x)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*(-
15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x))*(-2 + 3*E^5 - 6*x + E^(2 - E^(-4 + x) + x)*(-30 - 15*x + E^(-4 + x)*
(15 + 15*x))),x]

[Out]

E^E^(3*E^5*(1 + x) - 15*E^(2 - E^(-4 + x) + x)*(1 + x) - x*(2 + 3*x))

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fricas [A]  time = 0.66, size = 33, normalized size = 1.03 \begin {gather*} e^{\left (e^{\left (-3 \, x^{2} + 3 \, {\left (x + 1\right )} e^{5} - 15 \, {\left (x + 1\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((15*x+15)*exp(x-4)-15*x-30)*exp(-exp(x-4)+2+x)+3*exp(5)-6*x-2)*exp((-15*x-15)*exp(-exp(x-4)+2+x)+(
3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x, algorithm="fricas
")

[Out]

e^(e^(-3*x^2 + 3*(x + 1)*e^5 - 15*(x + 1)*e^(x - e^(x - 4) + 2) - 2*x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (15 \, {\left ({\left (x + 1\right )} e^{\left (x - 4\right )} - x - 2\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 6 \, x + 3 \, e^{5} - 2\right )} e^{\left (-3 \, x^{2} + 3 \, {\left (x + 1\right )} e^{5} - 15 \, {\left (x + 1\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x + e^{\left (-3 \, x^{2} + 3 \, {\left (x + 1\right )} e^{5} - 15 \, {\left (x + 1\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((15*x+15)*exp(x-4)-15*x-30)*exp(-exp(x-4)+2+x)+3*exp(5)-6*x-2)*exp((-15*x-15)*exp(-exp(x-4)+2+x)+(
3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x, algorithm="giac")

[Out]

integrate((15*((x + 1)*e^(x - 4) - x - 2)*e^(x - e^(x - 4) + 2) - 6*x + 3*e^5 - 2)*e^(-3*x^2 + 3*(x + 1)*e^5 -
15*(x + 1)*e^(x - e^(x - 4) + 2) - 2*x + e^(-3*x^2 + 3*(x + 1)*e^5 - 15*(x + 1)*e^(x - e^(x - 4) + 2) - 2*x))
, x)

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maple [A]  time = 0.15, size = 46, normalized size = 1.44

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{3 x \,{\mathrm e}^{5}-15 \,{\mathrm e}^{-{\mathrm e}^{x -4}+2+x} x -3 x^{2}+3 \,{\mathrm e}^{5}-15 \,{\mathrm e}^{-{\mathrm e}^{x -4}+2+x}-2 x}}\)	\(46\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((15*x+15)*exp(x-4)-15*x-30)*exp(-exp(x-4)+2+x)+3*exp(5)-6*x-2)*exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)
*exp(5)-3*x^2-2*x)*exp(exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x,method=_RETURNVERBOSE)

[Out]

exp(exp(3*x*exp(5)-15*exp(-exp(x-4)+2+x)*x-3*x^2+3*exp(5)-15*exp(-exp(x-4)+2+x)-2*x))

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maxima [A]  time = 1.26, size = 45, normalized size = 1.41 \begin {gather*} e^{\left (e^{\left (-3 \, x^{2} + 3 \, x e^{5} - 15 \, x e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x + 3 \, e^{5} - 15 \, e^{\left (x - e^{\left (x - 4\right )} + 2\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((15*x+15)*exp(x-4)-15*x-30)*exp(-exp(x-4)+2+x)+3*exp(5)-6*x-2)*exp((-15*x-15)*exp(-exp(x-4)+2+x)+(
3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x, algorithm="maxima
")

[Out]

e^(e^(-3*x^2 + 3*x*e^5 - 15*x*e^(x - e^(x - 4) + 2) - 2*x + 3*e^5 - 15*e^(x - e^(x - 4) + 2)))

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mupad [B]  time = 3.52, size = 52, normalized size = 1.62 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-15\,{\mathrm {e}}^{-{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{3\,{\mathrm {e}}^5}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-15\,x\,{\mathrm {e}}^{-{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-3\,x^2}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(5)*(3*x + 3) - exp(x - exp(x - 4) + 2)*(15*x + 15) - 3*x^2 - 2*x)*exp(exp(exp(5)*(3*x + 3) - exp(
x - exp(x - 4) + 2)*(15*x + 15) - 3*x^2 - 2*x))*(6*x - 3*exp(5) + exp(x - exp(x - 4) + 2)*(15*x - exp(x - 4)*(
15*x + 15) + 30) + 2),x)

[Out]

exp(exp(-15*exp(-exp(-4)*exp(x))*exp(2)*exp(x))*exp(3*exp(5))*exp(-2*x)*exp(-15*x*exp(-exp(-4)*exp(x))*exp(2)*
exp(x))*exp(-3*x^2)*exp(3*x*exp(5)))

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sympy [A]  time = 14.71, size = 36, normalized size = 1.12 \begin {gather*} e^{e^{- 3 x^{2} - 2 x + \left (- 15 x - 15\right ) e^{x - e^{x - 4} + 2} + \left (3 x + 3\right ) e^{5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((15*x+15)*exp(x-4)-15*x-30)*exp(-exp(x-4)+2+x)+3*exp(5)-6*x-2)*exp((-15*x-15)*exp(-exp(x-4)+2+x)+(
3*x+3)*exp(5)-3*x**2-2*x)*exp(exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x**2-2*x)),x)

[Out]

exp(exp(-3*x**2 - 2*x + (-15*x - 15)*exp(x - exp(x - 4) + 2) + (3*x + 3)*exp(5)))

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