∫ e−x3 ((12−4x) log(3−x)+(4x+(−36x3+12x4) log(3−x)) log(x)+(ex3 (3−x) log(3−x)+ex3 x log(x)) log(log(4)))____________________________________________________________________________

Optimal. Leaf size=28 \[ -4+\frac {\log (x) \left (-4 e^{-x^3}-\log (\log (4))\right )}{\log (3-x)} \]

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Rubi [F] time = 3.00, 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 {e^{-x^3} \left ((12-4 x) \log (3-x)+\left (4 x+\left (-36 x^3+12 x^4\right ) \log (3-x)\right ) \log (x)+\left (e^{x^3} (3-x) \log (3-x)+e^{x^3} x \log (x)\right ) \log (\log (4))\right )}{\left (-3 x+x^2\right ) \log ^2(3-x)} \, dx \end {gather*}

Int[((12 - 4*x)*Log[3 - x] + (4*x + (-36*x^3 + 12*x^4)*Log[3 - x])*Log[x] + (E^x^3*(3 - x)*Log[3 - x] + E^x^3*

x*Log[x])*Log[Log[4]])/(E^x^3*(-3*x + x^2)*Log[3 - x]^2),x]

(-4*(3*x^3*Log[3 - x]*Log[x] - x^4*Log[3 - x]*Log[x]))/(E^x^3*(3 - x)*x^3*Log[3 - x]^2) - Log[Log[4]]*Defer[In

t][1/(x*Log[3 - x]), x] + Log[Log[4]]*Defer[Subst][Defer[Int][Log[3 - x]/(x*Log[x]^2), x], x, 3 - x]

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-x^3} \left ((12-4 x) \log (3-x)+\left (4 x+\left (-36 x^3+12 x^4\right ) \log (3-x)\right ) \log (x)+\left (e^{x^3} (3-x) \log (3-x)+e^{x^3} x \log (x)\right ) \log (\log (4))\right )}{(-3+x) x \log ^2(3-x)} \, dx\\ &=\int \frac {e^{-x^3} \left (-\left ((-3+x) \log (3-x) \left (-4+12 x^3 \log (x)-e^{x^3} \log (\log (4))\right )\right )-x \log (x) \left (4+e^{x^3} \log (\log (4))\right )\right )}{(3-x) x \log ^2(3-x)} \, dx\\ &=\int \left (\frac {4 e^{-x^3} \left (3 \log (3-x)-x \log (3-x)+x \log (x)-9 x^3 \log (3-x) \log (x)+3 x^4 \log (3-x) \log (x)\right )}{(-3+x) x \log ^2(3-x)}-\frac {(-3 \log (3-x)+x \log (3-x)-x \log (x)) \log (\log (4))}{(-3+x) x \log ^2(3-x)}\right ) \, dx\\ &=4 \int \frac {e^{-x^3} \left (3 \log (3-x)-x \log (3-x)+x \log (x)-9 x^3 \log (3-x) \log (x)+3 x^4 \log (3-x) \log (x)\right )}{(-3+x) x \log ^2(3-x)} \, dx-\log (\log (4)) \int \frac {-3 \log (3-x)+x \log (3-x)-x \log (x)}{(-3+x) x \log ^2(3-x)} \, dx\\ &=-\frac {4 e^{-x^3} \left (3 x^3 \log (3-x) \log (x)-x^4 \log (3-x) \log (x)\right )}{(3-x) x^3 \log ^2(3-x)}-\log (\log (4)) \int \frac {\frac {\log (3-x)}{x}-\frac {\log (x)}{-3+x}}{\log ^2(3-x)} \, dx\\ &=-\frac {4 e^{-x^3} \left (3 x^3 \log (3-x) \log (x)-x^4 \log (3-x) \log (x)\right )}{(3-x) x^3 \log ^2(3-x)}-\log (\log (4)) \int \left (\frac {1}{x \log (3-x)}-\frac {\log (x)}{(-3+x) \log ^2(3-x)}\right ) \, dx\\ &=-\frac {4 e^{-x^3} \left (3 x^3 \log (3-x) \log (x)-x^4 \log (3-x) \log (x)\right )}{(3-x) x^3 \log ^2(3-x)}-\log (\log (4)) \int \frac {1}{x \log (3-x)} \, dx+\log (\log (4)) \int \frac {\log (x)}{(-3+x) \log ^2(3-x)} \, dx\\ &=-\frac {4 e^{-x^3} \left (3 x^3 \log (3-x) \log (x)-x^4 \log (3-x) \log (x)\right )}{(3-x) x^3 \log ^2(3-x)}-\log (\log (4)) \int \frac {1}{x \log (3-x)} \, dx+\log (\log (4)) \operatorname {Subst}\left (\int \frac {\log (3-x)}{x \log ^2(x)} \, dx,x,3-x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.34, size = 25, normalized size = 0.89 \begin {gather*} -\frac {\log (x) \left (4 e^{-x^3}+\log (\log (4))\right )}{\log (3-x)} \end {gather*}

Integrate[((12 - 4*x)*Log[3 - x] + (4*x + (-36*x^3 + 12*x^4)*Log[3 - x])*Log[x] + (E^x^3*(3 - x)*Log[3 - x] +

E^x^3*x*Log[x])*Log[Log[4]])/(E^x^3*(-3*x + x^2)*Log[3 - x]^2),x]

-((Log[x]*(4/E^x^3 + Log[Log[4]]))/Log[3 - x])

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fricas [A] time = 0.75, size = 33, normalized size = 1.18 \begin {gather*} -\frac {{\left (e^{\left (x^{3}\right )} \log \relax (x) \log \left (2 \, \log \relax (2)\right ) + 4 \, \log \relax (x)\right )} e^{\left (-x^{3}\right )}}{\log \left (-x + 3\right )} \end {gather*}

integrate(((x*exp(x^3)*log(x)+(3-x)*exp(x^3)*log(3-x))*log(2*log(2))+((12*x^4-36*x^3)*log(3-x)+4*x)*log(x)+(-4

*x+12)*log(3-x))/(x^2-3*x)/exp(x^3)/log(3-x)^2,x, algorithm="fricas")

-(e^(x^3)*log(x)*log(2*log(2)) + 4*log(x))*e^(-x^3)/log(-x + 3)

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giac [A] time = 0.22, size = 32, normalized size = 1.14 \begin {gather*} -\frac {4 \, e^{\left (-x^{3}\right )} \log \relax (x) + \log \relax (2) \log \relax (x) + \log \relax (x) \log \left (\log \relax (2)\right )}{\log \left (-x + 3\right )} \end {gather*}

integrate(((x*exp(x^3)*log(x)+(3-x)*exp(x^3)*log(3-x))*log(2*log(2))+((12*x^4-36*x^3)*log(3-x)+4*x)*log(x)+(-4

*x+12)*log(3-x))/(x^2-3*x)/exp(x^3)/log(3-x)^2,x, algorithm="giac")

-(4*e^(-x^3)*log(x) + log(2)*log(x) + log(x)*log(log(2)))/log(-x + 3)

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method	result	size

risch	\(-\frac {\ln \relax (x ) \left ({\mathrm e}^{x^{3}} \ln \relax (2)+{\mathrm e}^{x^{3}} \ln \left (\ln \relax (2)\right )+4\right ) {\mathrm e}^{-x^{3}}}{\ln \left (3-x \right )}\)	\(36\)

int(((x*exp(x^3)*ln(x)+(3-x)*exp(x^3)*ln(3-x))*ln(2*ln(2))+((12*x^4-36*x^3)*ln(3-x)+4*x)*ln(x)+(-4*x+12)*ln(3-

x))/(x^2-3*x)/exp(x^3)/ln(3-x)^2,x,method=_RETURNVERBOSE)

-ln(x)*(exp(x^3)*ln(2)+exp(x^3)*ln(ln(2))+4)*exp(-x^3)/ln(3-x)

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maxima [A] time = 0.52, size = 34, normalized size = 1.21 \begin {gather*} -\frac {{\left ({\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} e^{\left (x^{3}\right )} \log \relax (x) + 4 \, \log \relax (x)\right )} e^{\left (-x^{3}\right )}}{\log \left (-x + 3\right )} \end {gather*}

integrate(((x*exp(x^3)*log(x)+(3-x)*exp(x^3)*log(3-x))*log(2*log(2))+((12*x^4-36*x^3)*log(3-x)+4*x)*log(x)+(-4

*x+12)*log(3-x))/(x^2-3*x)/exp(x^3)/log(3-x)^2,x, algorithm="maxima")

-((log(2) + log(log(2)))*e^(x^3)*log(x) + 4*log(x))*e^(-x^3)/log(-x + 3)

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int -\frac {{\mathrm {e}}^{-x^3}\,\left (\ln \left (2\,\ln \relax (2)\right )\,\left ({\mathrm {e}}^{x^3}\,\ln \left (3-x\right )\,\left (x-3\right )-x\,{\mathrm {e}}^{x^3}\,\ln \relax (x)\right )+\ln \left (3-x\right )\,\left (4\,x-12\right )-\ln \relax (x)\,\left (4\,x-\ln \left (3-x\right )\,\left (36\,x^3-12\,x^4\right )\right )\right )}{{\ln \left (3-x\right )}^2\,\left (3\,x-x^2\right )} \,d x \end {gather*}

int((exp(-x^3)*(log(2*log(2))*(exp(x^3)*log(3 - x)*(x - 3) - x*exp(x^3)*log(x)) + log(3 - x)*(4*x - 12) - log(

x)*(4*x - log(3 - x)*(36*x^3 - 12*x^4))))/(log(3 - x)^2*(3*x - x^2)),x)

-int(-(exp(-x^3)*(log(2*log(2))*(exp(x^3)*log(3 - x)*(x - 3) - x*exp(x^3)*log(x)) + log(3 - x)*(4*x - 12) - lo

g(x)*(4*x - log(3 - x)*(36*x^3 - 12*x^4))))/(log(3 - x)^2*(3*x - x^2)), x)

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sympy [A] time = 0.43, size = 36, normalized size = 1.29 \begin {gather*} \frac {- \log {\relax (2 )} \log {\relax (x )} - \log {\relax (x )} \log {\left (\log {\relax (2 )} \right )}}{\log {\left (3 - x \right )}} - \frac {4 e^{- x^{3}} \log {\relax (x )}}{\log {\left (3 - x \right )}} \end {gather*}

integrate(((x*exp(x**3)*ln(x)+(3-x)*exp(x**3)*ln(3-x))*ln(2*ln(2))+((12*x**4-36*x**3)*ln(3-x)+4*x)*ln(x)+(-4*x

+12)*ln(3-x))/(x**2-3*x)/exp(x**3)/ln(3-x)**2,x)

(-log(2)*log(x) - log(x)*log(log(2)))/log(3 - x) - 4*exp(-x**3)*log(x)/log(3 - x)

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3.41.79 \(\int \frac {e^{-x^3} ((12-4 x) \log (3-x)+(4 x+(-36 x^3+12 x^4) \log (3-x)) \log (x)+(e^{x^3} (3-x) \log (3-x)+e^{x^3} x \log (x)) \log (\log (4)))}{(-3 x+x^2) \log ^2(3-x)} \, dx\)