∫ x+(−2ex+2ee10 x+2x log(x 4 )) log(−e+ee10 +log(x 4 )) ___________________________________________________________________

Optimal. Leaf size=20 \[ x^2 \log \left (-e+e^{e^{10}}+\log \left (\frac {x}{4}\right )\right ) \]

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Rubi [F] time = 0.22, 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 {x+\left (-2 e x+2 e^{e^{10}} x+2 x \log \left (\frac {x}{4}\right )\right ) \log \left (-e+e^{e^{10}}+\log \left (\frac {x}{4}\right )\right )}{-e+e^{e^{10}}+\log \left (\frac {x}{4}\right )} \, dx \end {gather*}

Int[(x + (-2*E*x + 2*E^E^10*x + 2*x*Log[x/4])*Log[-E + E^E^10 + Log[x/4]])/(-E + E^E^10 + Log[x/4]),x]

16*E^(2*E - 2*E^E^10)*ExpIntegralEi[-2*(E - E^E^10 - Log[x/4])] + 2*Defer[Int][x*Log[-(E*(1 - E^(-1 + E^10)))

\begin {gather*} \begin {aligned} \text {integral} &=\int x \left (\frac {1}{-e+e^{e^{10}}+\log \left (\frac {x}{4}\right )}+2 \log \left (-e+e^{e^{10}}+\log \left (\frac {x}{4}\right )\right )\right ) \, dx\\ &=\int \left (\frac {x}{-e \left (1-e^{-1+e^{10}}\right )+\log \left (\frac {x}{4}\right )}+2 x \log \left (-e \left (1-e^{-1+e^{10}}\right )+\log \left (\frac {x}{4}\right )\right )\right ) \, dx\\ &=2 \int x \log \left (-e \left (1-e^{-1+e^{10}}\right )+\log \left (\frac {x}{4}\right )\right ) \, dx+\int \frac {x}{-e \left (1-e^{-1+e^{10}}\right )+\log \left (\frac {x}{4}\right )} \, dx\\ &=2 \int x \log \left (-e \left (1-e^{-1+e^{10}}\right )+\log \left (\frac {x}{4}\right )\right ) \, dx+16 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-e \left (1-e^{-1+e^{10}}\right )+x} \, dx,x,\log \left (\frac {x}{4}\right )\right )\\ &=16 e^{2 e-2 e^{e^{10}}} \text {Ei}\left (-2 \left (e-e^{e^{10}}-\log \left (\frac {x}{4}\right )\right )\right )+2 \int x \log \left (-e \left (1-e^{-1+e^{10}}\right )+\log \left (\frac {x}{4}\right )\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.11, size = 20, normalized size = 1.00 \begin {gather*} x^2 \log \left (-e+e^{e^{10}}+\log \left (\frac {x}{4}\right )\right ) \end {gather*}

Integrate[(x + (-2*E*x + 2*E^E^10*x + 2*x*Log[x/4])*Log[-E + E^E^10 + Log[x/4]])/(-E + E^E^10 + Log[x/4]),x]

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fricas [A] time = 0.56, size = 17, normalized size = 0.85 \begin {gather*} x^{2} \log \left (-e + e^{\left (e^{10}\right )} + \log \left (\frac {1}{4} \, x\right )\right ) \end {gather*}

integrate(((2*x*log(1/4*x)+2*x*exp(exp(5)^2)-2*x*exp(1))*log(log(1/4*x)+exp(exp(5)^2)-exp(1))+x)/(log(1/4*x)+e

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giac [B] time = 0.21, size = 35, normalized size = 1.75 \begin {gather*} \frac {1}{2} \, x^{2} \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\relax (x) - 1\right )}^{2} + {\left (e - e^{\left (e^{10}\right )} - \log \left (\frac {1}{4} \, {\left | x \right |}\right )\right )}^{2}\right ) \end {gather*}

integrate(((2*x*log(1/4*x)+2*x*exp(exp(5)^2)-2*x*exp(1))*log(log(1/4*x)+exp(exp(5)^2)-exp(1))+x)/(log(1/4*x)+e

1/2*x^2*log(1/4*pi^2*(sgn(x) - 1)^2 + (e - e^(e^10) - log(1/4*abs(x)))^2)

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method	result	size

risch	\(x^{2} \ln \left (\ln \left (\frac {x}{4}\right )+{\mathrm e}^{{\mathrm e}^{10}}-{\mathrm e}\right )\)	\(18\)
norman	\(x^{2} \ln \left (\ln \left (\frac {x}{4}\right )+{\mathrm e}^{{\mathrm e}^{10}}-{\mathrm e}\right )\)	\(20\)

int(((2*x*ln(1/4*x)+2*x*exp(exp(5)^2)-2*x*exp(1))*ln(ln(1/4*x)+exp(exp(5)^2)-exp(1))+x)/(ln(1/4*x)+exp(exp(5)^

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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x^{2} \log \left (-e + e^{\left (e^{10}\right )} - 2 \, \log \relax (2) + \log \relax (x)\right ) - 16 \, e^{\left (2 \, e - 2 \, e^{\left (e^{10}\right )}\right )} E_{1}\left (2 \, e - 2 \, e^{\left (e^{10}\right )} - 2 \, \log \left (\frac {1}{4} \, x\right )\right ) - \int -\frac {x}{e - e^{\left (e^{10}\right )} + 2 \, \log \relax (2) - \log \relax (x)}\,{d x} \end {gather*}

integrate(((2*x*log(1/4*x)+2*x*exp(exp(5)^2)-2*x*exp(1))*log(log(1/4*x)+exp(exp(5)^2)-exp(1))+x)/(log(1/4*x)+e

x^2*log(-e + e^(e^10) - 2*log(2) + log(x)) - 16*e^(2*e - 2*e^(e^10))*exp_integral_e(1, 2*e - 2*e^(e^10) - 2*lo

g(1/4*x)) - integrate(-x/(e - e^(e^10) + 2*log(2) - log(x)), x)

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mupad [B] time = 6.72, size = 17, normalized size = 0.85 \begin {gather*} x^2\,\ln \left (\ln \left (\frac {x}{4}\right )-\mathrm {e}+{\mathrm {e}}^{{\mathrm {e}}^{10}}\right ) \end {gather*}

int((x + log(log(x/4) - exp(1) + exp(exp(10)))*(2*x*log(x/4) - 2*x*exp(1) + 2*x*exp(exp(10))))/(log(x/4) - exp

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sympy [A] time = 0.50, size = 17, normalized size = 0.85 \begin {gather*} x^{2} \log {\left (\log {\left (\frac {x}{4} \right )} - e + e^{e^{10}} \right )} \end {gather*}

integrate(((2*x*ln(1/4*x)+2*x*exp(exp(5)**2)-2*x*exp(1))*ln(ln(1/4*x)+exp(exp(5)**2)-exp(1))+x)/(ln(1/4*x)+exp

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3.93.12 \(\int \frac {x+(-2 e x+2 e^{e^{10}} x+2 x \log (\frac {x}{4})) \log (-e+e^{e^{10}}+\log (\frac {x}{4}))}{-e+e^{e^{10}}+\log (\frac {x}{4})} \, dx\)