\(\int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} (1+3 e^x x-12 x \log (3)) \, dx\) [8950]

Optimal result

Integrand size = 42, antiderivative size = 17 \[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=e^{e^{3 \left (e^x-4 x \log (3)\right )} x} \]

[Out]

exp(x*exp(3*exp(x)-12*x*ln(3)))

Rubi [F]

\[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=\int \exp \left (3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)\right ) \left (1+3 e^x x-12 x \log (3)\right ) \, dx \]

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.56 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=e^{3^{-12 x} e^{3 e^x} x} \]

[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))

Maple [A] (verified)

Time = 0.52 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71

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

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

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=e^{\left (x e^{\left (-12 \, x \log \left (3\right ) + 3 \, e^{x}\right )}\right )} \]

[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))

Sympy [A] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=e^{x e^{- 12 x \log {\left (3 \right )} + 3 e^{x}}} \]

[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)))

Maxima [A] (verification not implemented)

none

Time = 0.38 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=e^{\left (x e^{\left (-12 \, x \log \left (3\right ) + 3 \, e^{x}\right )}\right )} \]

[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))

Giac [F]

\[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx=\int { {\left (3 \, x e^{x} - 12 \, x \log \left (3\right ) + 1\right )} e^{\left (x e^{\left (-12 \, x \log \left (3\right ) + 3 \, e^{x}\right )} - 12 \, x \log \left (3\right ) + 3 \, e^{x}\right )} \,d x } \]

[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)

Mupad [B] (verification not implemented)

Time = 12.43 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int e^{3 e^x+e^{3 e^x-12 x \log (3)} x-12 x \log (3)} \left (1+3 e^x x-12 x \log (3)\right ) \, dx={\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{3\,{\mathrm {e}}^x}}{3^{12\,x}}} \]

[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))