∫ 400+100e2+100x2+e e2−eex ___________________ 10+e2−eex (1+x) (e4−2eex x2+10e2−eex+ex+x x2)+e2−eex (80+80x+20x2+20x3+e2(20+20x))+e4−2eex (4+8x+5x2+2x3+x4+e2(1+2x+x2))__________________________________________________________________________________________________________________ 100x2+e2−eex (20x2+20x3)+e4−2eex (x2+2x3+x4) dx

Optimal. Leaf size=32 \[ -e^{\frac {1}{1+10 e^{-2+e^{e^x}}+x}}-\frac {4+e^2}{x}+x \]

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Rubi [F] time = 0.00, 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*} \text {\$Aborted} \end {gather*}

Int[(400 + 100*E^2 + 100*x^2 + E^(E^(2 - E^E^x)/(10 + E^(2 - E^E^x)*(1 + x)))*(E^(4 - 2*E^E^x)*x^2 + 10*E^(2 -

E^E^x + E^x + x)*x^2) + E^(2 - E^E^x)*(80 + 80*x + 20*x^2 + 20*x^3 + E^2*(20 + 20*x)) + E^(4 - 2*E^E^x)*(4 +

8*x + 5*x^2 + 2*x^3 + x^4 + E^2*(1 + 2*x + x^2)))/(100*x^2 + E^(2 - E^E^x)*(20*x^2 + 20*x^3) + E^(4 - 2*E^E^x)

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Mathematica [A] time = 0.88, size = 41, normalized size = 1.28 \begin {gather*} -e^{\frac {e^2}{e^2+10 e^{e^{e^x}}+e^2 x}}+\frac {-4-e^2}{x}+x \end {gather*}

Integrate[(400 + 100*E^2 + 100*x^2 + E^(E^(2 - E^E^x)/(10 + E^(2 - E^E^x)*(1 + x)))*(E^(4 - 2*E^E^x)*x^2 + 10*

E^(2 - E^E^x + E^x + x)*x^2) + E^(2 - E^E^x)*(80 + 80*x + 20*x^2 + 20*x^3 + E^2*(20 + 20*x)) + E^(4 - 2*E^E^x)

*(4 + 8*x + 5*x^2 + 2*x^3 + x^4 + E^2*(1 + 2*x + x^2)))/(100*x^2 + E^(2 - E^E^x)*(20*x^2 + 20*x^3) + E^(4 - 2*

-E^(E^2/(E^2 + 10*E^E^E^x + E^2*x)) + (-4 - E^2)/x + x

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fricas [A] time = 0.81, size = 54, normalized size = 1.69 \begin {gather*} \frac {x^{2} - x e^{\left (\frac {e^{\left (x + e^{x} - e^{\left (e^{x}\right )} + 2\right )}}{{\left (x + 1\right )} e^{\left (x + e^{x} - e^{\left (e^{x}\right )} + 2\right )} + 10 \, e^{\left (x + e^{x}\right )}}\right )} - e^{2} - 4}{x} \end {gather*}

integrate(((x^2*exp(-exp(exp(x))+2)^2+10*x^2*exp(x)*exp(exp(x))*exp(-exp(exp(x))+2))*exp(exp(-exp(exp(x))+2)/(

(x+1)*exp(-exp(exp(x))+2)+10))+((x^2+2*x+1)*exp(2)+x^4+2*x^3+5*x^2+8*x+4)*exp(-exp(exp(x))+2)^2+((20*x+20)*exp

(2)+20*x^3+20*x^2+80*x+80)*exp(-exp(exp(x))+2)+100*exp(2)+100*x^2+400)/((x^4+2*x^3+x^2)*exp(-exp(exp(x))+2)^2+

(20*x^3+20*x^2)*exp(-exp(exp(x))+2)+100*x^2),x, algorithm="fricas")

(x^2 - x*e^(e^(x + e^x - e^(e^x) + 2)/((x + 1)*e^(x + e^x - e^(e^x) + 2) + 10*e^(x + e^x))) - e^2 - 4)/x

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {100 \, x^{2} + {\left (10 \, x^{2} e^{\left (x + e^{x} - e^{\left (e^{x}\right )} + 2\right )} + x^{2} e^{\left (-2 \, e^{\left (e^{x}\right )} + 4\right )}\right )} e^{\left (\frac {e^{\left (-e^{\left (e^{x}\right )} + 2\right )}}{{\left (x + 1\right )} e^{\left (-e^{\left (e^{x}\right )} + 2\right )} + 10}\right )} + 20 \, {\left (x^{3} + x^{2} + {\left (x + 1\right )} e^{2} + 4 \, x + 4\right )} e^{\left (-e^{\left (e^{x}\right )} + 2\right )} + {\left (x^{4} + 2 \, x^{3} + 5 \, x^{2} + {\left (x^{2} + 2 \, x + 1\right )} e^{2} + 8 \, x + 4\right )} e^{\left (-2 \, e^{\left (e^{x}\right )} + 4\right )} + 100 \, e^{2} + 400}{100 \, x^{2} + 20 \, {\left (x^{3} + x^{2}\right )} e^{\left (-e^{\left (e^{x}\right )} + 2\right )} + {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} e^{\left (-2 \, e^{\left (e^{x}\right )} + 4\right )}}\,{d x} \end {gather*}

integrate(((x^2*exp(-exp(exp(x))+2)^2+10*x^2*exp(x)*exp(exp(x))*exp(-exp(exp(x))+2))*exp(exp(-exp(exp(x))+2)/(

(x+1)*exp(-exp(exp(x))+2)+10))+((x^2+2*x+1)*exp(2)+x^4+2*x^3+5*x^2+8*x+4)*exp(-exp(exp(x))+2)^2+((20*x+20)*exp

(2)+20*x^3+20*x^2+80*x+80)*exp(-exp(exp(x))+2)+100*exp(2)+100*x^2+400)/((x^4+2*x^3+x^2)*exp(-exp(exp(x))+2)^2+

(20*x^3+20*x^2)*exp(-exp(exp(x))+2)+100*x^2),x, algorithm="giac")

integrate((100*x^2 + (10*x^2*e^(x + e^x - e^(e^x) + 2) + x^2*e^(-2*e^(e^x) + 4))*e^(e^(-e^(e^x) + 2)/((x + 1)*

e^(-e^(e^x) + 2) + 10)) + 20*(x^3 + x^2 + (x + 1)*e^2 + 4*x + 4)*e^(-e^(e^x) + 2) + (x^4 + 2*x^3 + 5*x^2 + (x^

2 + 2*x + 1)*e^2 + 8*x + 4)*e^(-2*e^(e^x) + 4) + 100*e^2 + 400)/(100*x^2 + 20*(x^3 + x^2)*e^(-e^(e^x) + 2) + (

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method	result	size

risch	$x -\frac {{\mathrm e}^{2}}{x}-\frac {4}{x}-{\mathrm e}^{\frac {{\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+2}}{{\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+2} x +{\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+2}+10}}$	$49$

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

exp(-exp(exp(x))+2)+10))+((x^2+2*x+1)*exp(2)+x^4+2*x^3+5*x^2+8*x+4)*exp(-exp(exp(x))+2)^2+((20*x+20)*exp(2)+20

*x^3+20*x^2+80*x+80)*exp(-exp(exp(x))+2)+100*exp(2)+100*x^2+400)/((x^4+2*x^3+x^2)*exp(-exp(exp(x))+2)^2+(20*x^

3+20*x^2)*exp(-exp(exp(x))+2)+100*x^2),x,method=_RETURNVERBOSE)

x-exp(2)/x-4/x-exp(exp(-exp(exp(x))+2)/(exp(-exp(exp(x))+2)*x+exp(-exp(exp(x))+2)+10))

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maxima [A] time = 0.50, size = 35, normalized size = 1.09 \begin {gather*} \frac {x^{2} - x e^{\left (\frac {e^{2}}{x e^{2} + e^{2} + 10 \, e^{\left (e^{\left (e^{x}\right )}\right )}}\right )} - e^{2} - 4}{x} \end {gather*}

integrate(((x^2*exp(-exp(exp(x))+2)^2+10*x^2*exp(x)*exp(exp(x))*exp(-exp(exp(x))+2))*exp(exp(-exp(exp(x))+2)/(

(x+1)*exp(-exp(exp(x))+2)+10))+((x^2+2*x+1)*exp(2)+x^4+2*x^3+5*x^2+8*x+4)*exp(-exp(exp(x))+2)^2+((20*x+20)*exp

(2)+20*x^3+20*x^2+80*x+80)*exp(-exp(exp(x))+2)+100*exp(2)+100*x^2+400)/((x^4+2*x^3+x^2)*exp(-exp(exp(x))+2)^2+

(20*x^3+20*x^2)*exp(-exp(exp(x))+2)+100*x^2),x, algorithm="maxima")

(x^2 - x*e^(e^2/(x*e^2 + e^2 + 10*e^(e^(e^x)))) - e^2 - 4)/x

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mupad [B] time = 3.77, size = 46, normalized size = 1.44 \begin {gather*} x-{\mathrm {e}}^{\frac {{\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^2}{{\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^2+x\,{\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^2+10}}-\frac {{\mathrm {e}}^2+4}{x} \end {gather*}

int((100*exp(2) + exp(4 - 2*exp(exp(x)))*(8*x + exp(2)*(2*x + x^2 + 1) + 5*x^2 + 2*x^3 + x^4 + 4) + exp(2 - ex

p(exp(x)))*(80*x + 20*x^2 + 20*x^3 + exp(2)*(20*x + 20) + 80) + exp(exp(2 - exp(exp(x)))/(exp(2 - exp(exp(x)))

*(x + 1) + 10))*(x^2*exp(4 - 2*exp(exp(x))) + 10*x^2*exp(exp(x))*exp(2 - exp(exp(x)))*exp(x)) + 100*x^2 + 400)

/(exp(4 - 2*exp(exp(x)))*(x^2 + 2*x^3 + x^4) + exp(2 - exp(exp(x)))*(20*x^2 + 20*x^3) + 100*x^2),x)

x - exp((exp(-exp(exp(x)))*exp(2))/(exp(-exp(exp(x)))*exp(2) + x*exp(-exp(exp(x)))*exp(2) + 10)) - (exp(2) + 4

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sympy [A] time = 3.38, size = 32, normalized size = 1.00 \begin {gather*} x - e^{\frac {e^{2 - e^{e^{x}}}}{\left (x + 1\right ) e^{2 - e^{e^{x}}} + 10}} + \frac {- e^{2} - 4}{x} \end {gather*}

integrate(((x**2*exp(-exp(exp(x))+2)**2+10*x**2*exp(x)*exp(exp(x))*exp(-exp(exp(x))+2))*exp(exp(-exp(exp(x))+2

)/((x+1)*exp(-exp(exp(x))+2)+10))+((x**2+2*x+1)*exp(2)+x**4+2*x**3+5*x**2+8*x+4)*exp(-exp(exp(x))+2)**2+((20*x

+20)*exp(2)+20*x**3+20*x**2+80*x+80)*exp(-exp(exp(x))+2)+100*exp(2)+100*x**2+400)/((x**4+2*x**3+x**2)*exp(-exp

(exp(x))+2)**2+(20*x**3+20*x**2)*exp(-exp(exp(x))+2)+100*x**2),x)

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

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