3.90.50 \(\int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} (1+3 e^x x-12 x \log (3)) \, dx\)

Optimal. Leaf size=17 \[ e^{e^{3 \left (e^x-4 x \log (3)\right )} x} \]

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Rubi [F]  time = 1.16, 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 (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) \left (1+3 e^x x-12 x \log (3)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(3*E^x + E^(3*E^x - 12*x*Log[3])*x - 12*x*Log[3])*(1 + 3*E^x*x - 12*x*Log[3]),x]

[Out]

Defer[Int][E^(3*E^x + E^(3*E^x - 12*x*Log[3])*x - 12*x*Log[3]), x] + 3*Defer[Int][E^(3*E^x + E^(3*E^x - 12*x*L
og[3])*x + x*(1 - 12*Log[3]))*x, x] - 12*Log[3]*Defer[Int][E^(3*E^x + E^(3*E^x - 12*x*Log[3])*x - 12*x*Log[3])
*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right )+3 \exp \left (3 e^x+x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) x-12 \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) x \log (3)\right ) \, dx\\ &=3 \int \exp \left (3 e^x+x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) x \, dx-(12 \log (3)) \int \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) x \, dx+\int \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) \, dx\\ &=3 \int \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x+x (1-12 \log (3))\right ) x \, dx-(12 \log (3)) \int \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) x \, dx+\int \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.58, size = 16, normalized size = 0.94 \begin {gather*} e^{3^{-12 x} e^{3 e^x} x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(3*E^x + E^(3*E^x - 12*x*Log[3])*x - 12*x*Log[3])*(1 + 3*E^x*x - 12*x*Log[3]),x]

[Out]

E^((E^(3*E^x)*x)/3^(12*x))

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fricas [A]  time = 0.52, size = 14, normalized size = 0.82 \begin {gather*} e^{\left (x e^{\left (-12 \, x \log \relax (3) + 3 \, e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(x)*x-12*x*log(3)+1)*exp(3*exp(x)-12*x*log(3))*exp(x*exp(3*exp(x)-12*x*log(3))),x, algorithm="
fricas")

[Out]

e^(x*e^(-12*x*log(3) + 3*e^x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (3 \, x e^{x} - 12 \, x \log \relax (3) + 1\right )} e^{\left (x e^{\left (-12 \, x \log \relax (3) + 3 \, e^{x}\right )} - 12 \, x \log \relax (3) + 3 \, e^{x}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(x)*x-12*x*log(3)+1)*exp(3*exp(x)-12*x*log(3))*exp(x*exp(3*exp(x)-12*x*log(3))),x, algorithm="
giac")

[Out]

integrate((3*x*e^x - 12*x*log(3) + 1)*e^(x*e^(-12*x*log(3) + 3*e^x) - 12*x*log(3) + 3*e^x), x)

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maple [A]  time = 0.09, size = 12, normalized size = 0.71

method	result	size
risch	\({\mathrm e}^{x \,{\mathrm e}^{3 \,{\mathrm e}^{x}} \left (\frac {1}{531441}\right )^{x}}\)	\(12\)
norman	\({\mathrm e}^{x \,{\mathrm e}^{3 \,{\mathrm e}^{x}-12 x \ln \relax (3)}}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*exp(x)*x-12*x*ln(3)+1)*exp(3*exp(x)-12*x*ln(3))*exp(x*exp(3*exp(x)-12*x*ln(3))),x,method=_RETURNVERBOSE
)

[Out]

exp(x*exp(3*exp(x))*(1/531441)^x)

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maxima [A]  time = 0.56, size = 14, normalized size = 0.82 \begin {gather*} e^{\left (x e^{\left (-12 \, x \log \relax (3) + 3 \, e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(x)*x-12*x*log(3)+1)*exp(3*exp(x)-12*x*log(3))*exp(x*exp(3*exp(x)-12*x*log(3))),x, algorithm="
maxima")

[Out]

e^(x*e^(-12*x*log(3) + 3*e^x))

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mupad [B]  time = 0.30, size = 15, normalized size = 0.88 \begin {gather*} {\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{3\,{\mathrm {e}}^x}}{3^{12\,x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(3*exp(x) - 12*x*log(3))*exp(x*exp(3*exp(x) - 12*x*log(3)))*(3*x*exp(x) - 12*x*log(3) + 1),x)

[Out]

exp((x*exp(3*exp(x)))/3^(12*x))

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sympy [A]  time = 0.38, size = 15, normalized size = 0.88 \begin {gather*} e^{x e^{- 12 x \log {\relax (3 )} + 3 e^{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((3*exp(x)*x-12*x*ln(3)+1)*exp(3*exp(x)-12*x*ln(3))*exp(x*exp(3*exp(x)-12*x*ln(3))),x)

[Out]

exp(x*exp(-12*x*log(3) + 3*exp(x)))

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