3.7.29 \(\int \frac {e^{\frac {1}{\log (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} (e^4 x-x^2)}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}})}} (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} (-e^6+2 e^2 x)+e^{2 e^{e^x}+2 x} (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2))}{(-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} (-6 e^4 x+2 x^2)+e^{3 e^{e^x}+3 x} (e^6 x-e^2 x^2)) \log ^2(\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} (e^4 x-x^2)}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}})} \, dx\)

Optimal. Leaf size=35 \[ e^{\frac {1}{\log \left (x-\frac {x^2}{\left (-e^2+2 e^{-e^{e^x}-x}\right )^2}\right )}} \]

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Rubi [F]  time = 180.00, 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*}

Verification is not applicable to the result.

[In]

Int[(E^Log[(4*x - 4*E^(2 + E^E^x + x)*x + E^(2*E^E^x + 2*x)*(E^4*x - x^2))/(4 - 4*E^(2 + E^E^x + x) + E^(4 + 2
*E^E^x + 2*x))]^(-1)*(8 - 12*E^(2 + E^E^x + x) + E^(3*E^E^x + 3*x)*(-E^6 + 2*E^2*x) + E^(2*E^E^x + 2*x)*(6*E^4
- 4*x - 4*x^2 - 4*E^(E^x + x)*x^2)))/((-8*x + 12*E^(2 + E^E^x + x)*x + E^(2*E^E^x + 2*x)*(-6*E^4*x + 2*x^2) +
E^(3*E^E^x + 3*x)*(E^6*x - E^2*x^2))*Log[(4*x - 4*E^(2 + E^E^x + x)*x + E^(2*E^E^x + 2*x)*(E^4*x - x^2))/(4 -
4*E^(2 + E^E^x + x) + E^(4 + 2*E^E^x + 2*x))]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.39, size = 61, normalized size = 1.74 \begin {gather*} e^{\frac {1}{\log \left (\frac {x \left (4-4 e^{2+e^{e^x}+x}+e^{2 \left (2+e^{e^x}+x\right )}-e^{2 \left (e^{e^x}+x\right )} x\right )}{\left (-2+e^{2+e^{e^x}+x}\right )^2}\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^Log[(4*x - 4*E^(2 + E^E^x + x)*x + E^(2*E^E^x + 2*x)*(E^4*x - x^2))/(4 - 4*E^(2 + E^E^x + x) + E^
(4 + 2*E^E^x + 2*x))]^(-1)*(8 - 12*E^(2 + E^E^x + x) + E^(3*E^E^x + 3*x)*(-E^6 + 2*E^2*x) + E^(2*E^E^x + 2*x)*
(6*E^4 - 4*x - 4*x^2 - 4*E^(E^x + x)*x^2)))/((-8*x + 12*E^(2 + E^E^x + x)*x + E^(2*E^E^x + 2*x)*(-6*E^4*x + 2*
x^2) + E^(3*E^E^x + 3*x)*(E^6*x - E^2*x^2))*Log[(4*x - 4*E^(2 + E^E^x + x)*x + E^(2*E^E^x + 2*x)*(E^4*x - x^2)
)/(4 - 4*E^(2 + E^E^x + x) + E^(4 + 2*E^E^x + 2*x))]^2),x]

[Out]

E^Log[(x*(4 - 4*E^(2 + E^E^x + x) + E^(2*(2 + E^E^x + x)) - E^(2*(E^E^x + x))*x))/(-2 + E^(2 + E^E^x + x))^2]^
(-1)

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fricas [B]  time = 0.81, size = 114, normalized size = 3.26 \begin {gather*} e^{\left (\frac {1}{\log \left (\frac {4 \, x e^{4} - {\left (x^{2} - x e^{4}\right )} e^{\left (2 \, {\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )} - 4 \, x e^{\left ({\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + 4\right )}}{4 \, e^{4} + e^{\left (2 \, {\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + 4\right )} - 4 \, e^{\left ({\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + 4\right )}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(2)^3+2*exp(2)*x)*exp(x+exp(exp(x)))^3+(-4*x^2*exp(x)*exp(exp(x))+6*exp(2)^2-4*x^2-4*x)*exp(x+
exp(exp(x)))^2-12*exp(2)*exp(x+exp(exp(x)))+8)*exp(1/log(((x*exp(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp
(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*exp(x+exp(exp(x)))+4)))/((x*exp(2)^3-x^2*exp(2))*
exp(x+exp(exp(x)))^3+(-6*x*exp(2)^2+2*x^2)*exp(x+exp(exp(x)))^2+12*x*exp(2)*exp(x+exp(exp(x)))-8*x)/log(((x*ex
p(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*ex
p(x+exp(exp(x)))+4))^2,x, algorithm="fricas")

[Out]

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

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(2)^3+2*exp(2)*x)*exp(x+exp(exp(x)))^3+(-4*x^2*exp(x)*exp(exp(x))+6*exp(2)^2-4*x^2-4*x)*exp(x+
exp(exp(x)))^2-12*exp(2)*exp(x+exp(exp(x)))+8)*exp(1/log(((x*exp(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp
(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*exp(x+exp(exp(x)))+4)))/((x*exp(2)^3-x^2*exp(2))*
exp(x+exp(exp(x)))^3+(-6*x*exp(2)^2+2*x^2)*exp(x+exp(exp(x)))^2+12*x*exp(2)*exp(x+exp(exp(x)))-8*x)/log(((x*ex
p(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*ex
p(x+exp(exp(x)))+4))^2,x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 47.70, size = 828, normalized size = 23.66

method	result	size
risch	\({\mathrm e}^{\frac {2}{i \pi \mathrm {csgn}\left (i \left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}\right )^{3}-2 i \pi \mathrm {csgn}\left (i \left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )\right )+i \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )\right )^{2}+i \pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )^{3}+i \pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )-i \pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )\right )-i \pi \,\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right ) \mathrm {csgn}\left (\frac {i}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )\right )-i \pi \,\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right ) \mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )^{2}-i \pi \,\mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right ) \mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right ) \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )^{3}+i \pi \mathrm {csgn}\left (\frac {i x \left ({\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x +4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-4\right )}{\left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )^{2}}\right )^{2} \mathrm {csgn}\left (i x \right )+2 \ln \relax (x )-4 \ln \left ({\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}-2\right )+2 \ln \left ({\mathrm e}^{4+2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}}-{\mathrm e}^{2 x +2 \,{\mathrm e}^{{\mathrm e}^{x}}} x -4 \,{\mathrm e}^{2+x +{\mathrm e}^{{\mathrm e}^{x}}}+4\right )}}\)	\(828\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-exp(2)^3+2*exp(2)*x)*exp(x+exp(exp(x)))^3+(-4*x^2*exp(x)*exp(exp(x))+6*exp(2)^2-4*x^2-4*x)*exp(x+exp(ex
p(x)))^2-12*exp(2)*exp(x+exp(exp(x)))+8)*exp(1/ln(((x*exp(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp(x+exp(
exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*exp(x+exp(exp(x)))+4)))/((x*exp(2)^3-x^2*exp(2))*exp(x+e
xp(exp(x)))^3+(-6*x*exp(2)^2+2*x^2)*exp(x+exp(exp(x)))^2+12*x*exp(2)*exp(x+exp(exp(x)))-8*x)/ln(((x*exp(2)^2-x
^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*exp(x+exp(
exp(x)))+4))^2,x,method=_RETURNVERBOSE)

[Out]

exp(2/(I*Pi*csgn(I*(exp(2+x+exp(exp(x)))-2)^2)^3-2*I*Pi*csgn(I*(exp(2+x+exp(exp(x)))-2)^2)^2*csgn(I*(exp(2+x+e
xp(exp(x)))-2))+I*Pi*csgn(I*(exp(2+x+exp(exp(x)))-2)^2)*csgn(I*(exp(2+x+exp(exp(x)))-2))^2+I*Pi*csgn(I*(exp(2*
x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)^3+I*Pi*csgn(
I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)^2*c
sgn(I/(exp(2+x+exp(exp(x)))-2)^2)-I*Pi*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2*exp
(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)^2*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2
*exp(exp(x)))-4))-I*Pi*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2*exp(exp(x)))-4)/(ex
p(2+x+exp(exp(x)))-2)^2)*csgn(I/(exp(2+x+exp(exp(x)))-2)^2)*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp
(x)))-exp(4+2*x+2*exp(exp(x)))-4))-I*Pi*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2*ex
p(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)*csgn(I*x*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+
2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)^2-I*Pi*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)))-e
xp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)*csgn(I*x*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+exp(exp(x)
))-exp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)*csgn(I*x)+I*Pi*csgn(I*x*(exp(2*x+2*exp(exp(x)))*x+4
*exp(2+x+exp(exp(x)))-exp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)^3+I*Pi*csgn(I*x*(exp(2*x+2*exp(e
xp(x)))*x+4*exp(2+x+exp(exp(x)))-exp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)^2*csgn(I*x)+2*ln(x)-4
*ln(exp(2+x+exp(exp(x)))-2)+2*ln(exp(4+2*x+2*exp(exp(x)))-exp(2*x+2*exp(exp(x)))*x-4*exp(2+x+exp(exp(x)))+4)))

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maxima [B]  time = 8.35, size = 1058, normalized size = 30.23 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(2)^3+2*exp(2)*x)*exp(x+exp(exp(x)))^3+(-4*x^2*exp(x)*exp(exp(x))+6*exp(2)^2-4*x^2-4*x)*exp(x+
exp(exp(x)))^2-12*exp(2)*exp(x+exp(exp(x)))+8)*exp(1/log(((x*exp(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp
(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*exp(x+exp(exp(x)))+4)))/((x*exp(2)^3-x^2*exp(2))*
exp(x+exp(exp(x)))^3+(-6*x*exp(2)^2+2*x^2)*exp(x+exp(exp(x)))^2+12*x*exp(2)*exp(x+exp(exp(x)))-8*x)/log(((x*ex
p(2)^2-x^2)*exp(x+exp(exp(x)))^2-4*x*exp(2)*exp(x+exp(exp(x)))+4*x)/(exp(2)^2*exp(x+exp(exp(x)))^2-4*exp(2)*ex
p(x+exp(exp(x)))+4))^2,x, algorithm="maxima")

[Out]

-4*x^2*e^(3*x + 1/(log(-(x - e^4)*e^(2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) - 2*log(e^(x + e^(
e^x) + 2) - 2)) + e^x + 2*e^(e^x))/((2*x*e^2 - e^6)*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x) + (2*x^2 + 2*
x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x + e^(e^x) + 2) + 8) - 4*x^2*e^(2*x + 1/(log(-(x - e^4)*e^(2*x + 2*
e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) - 2*log(e^(x + e^(e^x) + 2) - 2)) + 2*e^(e^x))/((2*x*e^2 - e^6)
*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x) + (2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x + e^(e^
x) + 2) + 8) + 2*x*e^(3*x + 1/(log(-(x - e^4)*e^(2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) - 2*lo
g(e^(x + e^(e^x) + 2) - 2)) + 3*e^(e^x) + 2)/((2*x*e^2 - e^6)*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x) + (
2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x + e^(e^x) + 2) + 8) - 4*x*e^(2*x + 1/(log(-(x - e^4)*e^(
2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) - 2*log(e^(x + e^(e^x) + 2) - 2)) + 2*e^(e^x))/((2*x*e^
2 - e^6)*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x) + (2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x
+ e^(e^x) + 2) + 8) - e^(3*x + 1/(log(-(x - e^4)*e^(2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) -
2*log(e^(x + e^(e^x) + 2) - 2)) + 3*e^(e^x) + 6)/((2*x*e^2 - e^6)*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x)
+ (2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x + e^(e^x) + 2) + 8) + 6*e^(2*x + 1/(log(-(x - e^4)*e
^(2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) - 2*log(e^(x + e^(e^x) + 2) - 2)) + 2*e^(e^x) + 4)/((
2*x*e^2 - e^6)*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x) + (2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 1
2*e^(x + e^(e^x) + 2) + 8) - 12*e^(x + 1/(log(-(x - e^4)*e^(2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + lo
g(x) - 2*log(e^(x + e^(e^x) + 2) - 2)) + e^(e^x) + 2)/((2*x*e^2 - e^6)*e^(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x +
e^x) + (2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x + e^(e^x) + 2) + 8) + 8*e^(1/(log(-(x - e^4)*e^
(2*x + 2*e^(e^x)) - 4*e^(x + e^(e^x) + 2) + 4) + log(x) - 2*log(e^(x + e^(e^x) + 2) - 2)))/((2*x*e^2 - e^6)*e^
(3*x + 3*e^(e^x)) - 2*(2*x^2*e^(3*x + e^x) + (2*x^2 + 2*x - 3*e^4)*e^(2*x))*e^(2*e^(e^x)) - 12*e^(x + e^(e^x)
+ 2) + 8)

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mupad [B]  time = 2.30, size = 76, normalized size = 2.17 \begin {gather*} {\mathrm {e}}^{\frac {1}{\ln \left (\frac {4\,x-x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{2\,x}+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4-4\,x\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x}{{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x+4}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1/log((4*x + exp(2*x + 2*exp(exp(x)))*(x*exp(4) - x^2) - 4*x*exp(2)*exp(x + exp(exp(x))))/(exp(2*x +
2*exp(exp(x)))*exp(4) - 4*exp(2)*exp(x + exp(exp(x))) + 4)))*(exp(2*x + 2*exp(exp(x)))*(4*x - 6*exp(4) + 4*x^2
+ 4*x^2*exp(exp(x))*exp(x)) + 12*exp(2)*exp(x + exp(exp(x))) + exp(3*x + 3*exp(exp(x)))*(exp(6) - 2*x*exp(2))
- 8))/(log((4*x + exp(2*x + 2*exp(exp(x)))*(x*exp(4) - x^2) - 4*x*exp(2)*exp(x + exp(exp(x))))/(exp(2*x + 2*e
xp(exp(x)))*exp(4) - 4*exp(2)*exp(x + exp(exp(x))) + 4))^2*(8*x + exp(2*x + 2*exp(exp(x)))*(6*x*exp(4) - 2*x^2
) - exp(3*x + 3*exp(exp(x)))*(x*exp(6) - x^2*exp(2)) - 12*x*exp(2)*exp(x + exp(exp(x))))),x)

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(2)**3+2*exp(2)*x)*exp(x+exp(exp(x)))**3+(-4*x**2*exp(x)*exp(exp(x))+6*exp(2)**2-4*x**2-4*x)*e
xp(x+exp(exp(x)))**2-12*exp(2)*exp(x+exp(exp(x)))+8)*exp(1/ln(((x*exp(2)**2-x**2)*exp(x+exp(exp(x)))**2-4*x*ex
p(2)*exp(x+exp(exp(x)))+4*x)/(exp(2)**2*exp(x+exp(exp(x)))**2-4*exp(2)*exp(x+exp(exp(x)))+4)))/((x*exp(2)**3-x
**2*exp(2))*exp(x+exp(exp(x)))**3+(-6*x*exp(2)**2+2*x**2)*exp(x+exp(exp(x)))**2+12*x*exp(2)*exp(x+exp(exp(x)))
-8*x)/ln(((x*exp(2)**2-x**2)*exp(x+exp(exp(x)))**2-4*x*exp(2)*exp(x+exp(exp(x)))+4*x)/(exp(2)**2*exp(x+exp(exp
(x)))**2-4*exp(2)*exp(x+exp(exp(x)))+4))**2,x)

[Out]

Timed out

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