3.97.75 \(\int \frac {1}{36} e^{1+e^{\frac {1}{36} (-108-36 e^x+x)}+e^{1+e^{\frac {1}{36} (-108-36 e^x+x)}} x} (-36+e^{\frac {1}{36} (-108-36 e^x+x)} (-x+36 e^x x)) \, dx\)

Optimal. Leaf size=26 \[ -4-e^{e^{1+e^{-3-e^x+\frac {x}{36}}} x} \]

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Rubi [F]  time = 1.95, 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}{36} \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \left (-36+e^{\frac {1}{36} \left (-108-36 e^x+x\right )} \left (-x+36 e^x x\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(1 + E^((-108 - 36*E^x + x)/36) + E^(1 + E^((-108 - 36*E^x + x)/36))*x)*(-36 + E^((-108 - 36*E^x + x)/3
6)*(-x + 36*E^x*x)))/36,x]

[Out]

-Defer[Int][E^(1 + E^((-108 - 36*E^x + x)/36) + E^(1 + E^((-108 - 36*E^x + x)/36))*x), x] - Defer[Int][E^(1 +
E^((-108 - 36*E^x + x)/36) + E^(1 + E^((-108 - 36*E^x + x)/36))*x + (-108 - 36*E^x + x)/36)*x, x]/36 + Defer[I
nt][E^(1 + E^((-108 - 36*E^x + x)/36) + x + E^(1 + E^((-108 - 36*E^x + x)/36))*x + (-108 - 36*E^x + x)/36)*x,
x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{36} \int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \left (-36+e^{\frac {1}{36} \left (-108-36 e^x+x\right )} \left (-x+36 e^x x\right )\right ) \, dx\\ &=\frac {1}{36} \int \left (-36 \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right )+\exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) \left (-1+36 e^x\right ) x\right ) \, dx\\ &=\frac {1}{36} \int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) \left (-1+36 e^x\right ) x \, dx-\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \, dx\\ &=\frac {1}{36} \int \left (-\exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x+36 \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+x+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x\right ) \, dx-\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \, dx\\ &=-\left (\frac {1}{36} \int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x \, dx\right )-\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \, dx+\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+x+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.36, size = 24, normalized size = 0.92 \begin {gather*} -e^{e^{1+e^{-3-e^x+\frac {x}{36}}} x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(1 + E^((-108 - 36*E^x + x)/36) + E^(1 + E^((-108 - 36*E^x + x)/36))*x)*(-36 + E^((-108 - 36*E^x
+ x)/36)*(-x + 36*E^x*x)))/36,x]

[Out]

-E^(E^(1 + E^(-3 - E^x + x/36))*x)

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fricas [A]  time = 0.51, size = 18, normalized size = 0.69 \begin {gather*} -e^{\left (x e^{\left (e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*((36*exp(x)*x-x)*exp(-exp(x)+1/36*x-3)-36)*exp(exp(-exp(x)+1/36*x-3)+1)*exp(x*exp(exp(-exp(x)+1
/36*x-3)+1)),x, algorithm="fricas")

[Out]

-e^(x*e^(e^(1/36*x - e^x - 3) + 1))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{36} \, {\left ({\left (36 \, x e^{x} - x\right )} e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} - 36\right )} e^{\left (x e^{\left (e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )} + e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*((36*exp(x)*x-x)*exp(-exp(x)+1/36*x-3)-36)*exp(exp(-exp(x)+1/36*x-3)+1)*exp(x*exp(exp(-exp(x)+1
/36*x-3)+1)),x, algorithm="giac")

[Out]

integrate(1/36*((36*x*e^x - x)*e^(1/36*x - e^x - 3) - 36)*e^(x*e^(e^(1/36*x - e^x - 3) + 1) + e^(1/36*x - e^x
- 3) + 1), x)

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maple [A]  time = 0.14, size = 19, normalized size = 0.73

method	result	size
risch	\(-{\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x}+\frac {x}{36}-3}+1}}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/36*((36*exp(x)*x-x)*exp(-exp(x)+1/36*x-3)-36)*exp(exp(-exp(x)+1/36*x-3)+1)*exp(x*exp(exp(-exp(x)+1/36*x-
3)+1)),x,method=_RETURNVERBOSE)

[Out]

-exp(x*exp(exp(-exp(x)+1/36*x-3)+1))

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maxima [A]  time = 0.64, size = 18, normalized size = 0.69 \begin {gather*} -e^{\left (x e^{\left (e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*((36*exp(x)*x-x)*exp(-exp(x)+1/36*x-3)-36)*exp(exp(-exp(x)+1/36*x-3)+1)*exp(x*exp(exp(-exp(x)+1
/36*x-3)+1)),x, algorithm="maxima")

[Out]

-e^(x*e^(e^(1/36*x - e^x - 3) + 1))

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mupad [B]  time = 6.32, size = 20, normalized size = 0.77 \begin {gather*} -{\mathrm {e}}^{x\,{\mathrm {e}}^{{\mathrm {e}}^{x/36}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{-{\mathrm {e}}^x}}\,\mathrm {e}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(x/36 - exp(x) - 3) + 1)*exp(x*exp(exp(x/36 - exp(x) - 3) + 1))*(exp(x/36 - exp(x) - 3)*(x - 36*x
*exp(x)) + 36))/36,x)

[Out]

-exp(x*exp(exp(x/36)*exp(-3)*exp(-exp(x)))*exp(1))

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sympy [A]  time = 4.10, size = 17, normalized size = 0.65 \begin {gather*} - e^{x e^{e^{\frac {x}{36} - e^{x} - 3} + 1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/36*((36*exp(x)*x-x)*exp(-exp(x)+1/36*x-3)-36)*exp(exp(-exp(x)+1/36*x-3)+1)*exp(x*exp(exp(-exp(x)+1
/36*x-3)+1)),x)

[Out]

-exp(x*exp(exp(x/36 - exp(x) - 3) + 1))

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