\(\int \frac {-1+e^{1+e^x-x+e^2 (2 x-x^2)} (-x+e^x x+e^2 (2 x-2 x^2))}{e^{2+2 e^x-2 x+2 e^2 (2 x-x^2)} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 (2 x-x^2)} (2 x \log (2)-2 x \log (x))} \, dx\) [1082]

Optimal result

Integrand size = 134, antiderivative size = 30 \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=\frac {1}{-e^{-1+e^x-(-2+x) \left (1+e^2 x\right )}-\log (2)+\log (x)} \]

[Out]

1/(ln(x)-exp(exp(x)-(-2+x)*(1+exp(2)*x)-1)-ln(2))

Rubi [F]

\[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=\int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx \]

[In]

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

[Out]

-E^(-1 - E^x + x - E^2*(2 - x)*x) - (E^(-2*(1 + E^x) + 2*(1 - 2*E^2)*x + 2*E^2*x^2)*(E^x*x*Log[4] - (4*(1 - 2*
E^2)*x*Log[2]*Log[4])/Log[16] - E^2*x^2*Log[16] - 2*E^x*x*Log[x] + 2*(1 - 2*E^2)*x*Log[x] + 4*E^2*x^2*Log[x]))
/(2*x*(1 - 2*E^2 - E^x + 2*E^2*x)) + (1 - 2*E^2)*Log[2]*Defer[Int][(E^(-2 - 2*E^x + 4*x + 4*E^2*(-2 + x)*x)*Lo
g[x/2]^2)/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x])^2, x] - Log[2]*Defer[I
nt][(E^(-2 - 2*E^x + 5*x + 4*E^2*(-2 + x)*x)*Log[x/2]^2)/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x +
E^2*(-2 + x)*x)*Log[x])^2, x] - Defer[Int][(E^(-2 - 2*E^x + 4*x + 4*E^2*(-2 + x)*x)*Log[x/2]^2)/(x*(E^(1 + E^
x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x])^2), x] + Log[4]*Defer[Int][(E^(-2*E^x + 4*
x + 4*E^2*(-2 + x)*x)*x*Log[x/2]^2)/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[
x])^2, x] + (2 - E^(-2))*Defer[Int][(E^(-2*E^x + 4*x + 4*E^2*(-2 + x)*x)*Log[x/2]^2*Log[x])/(E^(1 + E^x) + E^(
x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x])^2, x] - 2*Defer[Int][(E^(-2*E^x + 4*x + 4*E^2*(-2
+ x)*x)*x*Log[x/2]^2*Log[x])/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x])^2,
x] - (1 - 2*E^2)*Log[2]*Log[8]*Defer[Int][E^(-2 - 2*E^x + 3*x + 3*E^2*(-2 + x)*x)/(E^(1 + E^x) + E^(x + E^2*(-
2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x] + Log[2]*Log[8]*Defer[Int][E^(-2 - 2*E^x + 4*x + 3*E^2*(
-2 + x)*x)/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x] + Log[4]*Defer[In
t][E^(-2 - 2*E^x + 3*x + 3*E^2*(-2 + x)*x)/(x*(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 +
x)*x)*Log[x])), x] - Log[2]*Log[64]*Defer[Int][(E^(-2*E^x + 3*x + 3*E^2*(-2 + x)*x)*x)/(E^(1 + E^x) + E^(x + E
^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x] - 6*(2 - E^(-2))*Log[2]*Defer[Int][(E^(-2*E^x + 3*x
+ 3*E^2*(-2 + x)*x)*Log[x])/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x]
- 6*Log[2]*Defer[Int][(E^(-2 - 2*E^x + 4*x + 3*E^2*(-2 + x)*x)*Log[x])/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*
Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x] + 12*Log[2]*Defer[Int][(E^(-2*E^x + 3*x + 3*E^2*(-2 + x)*x)*x*Log[
x])/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x] + 3*(2 - E^(-2))*Defer[I
nt][(E^(-2*E^x + 3*x + 3*E^2*(-2 + x)*x)*Log[x]^2)/(E^(1 + E^x) + E^(x + E^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(
-2 + x)*x)*Log[x]), x] - 6*Defer[Int][(E^(-2*E^x + 3*x + 3*E^2*(-2 + x)*x)*x*Log[x]^2)/(E^(1 + E^x) + E^(x + E
^2*(-2 + x)*x)*Log[2] - E^(x + E^2*(-2 + x)*x)*Log[x]), x] + Defer[Int][(E^(-2 - 2*E^x + 5*x + 4*E^2*(-2 + x)*
x)*Log[x/2]^2*Log[x])/(-E^(1 + E^x) - E^(x + E^2*(-2 + x)*x)*Log[2] + E^(x + E^2*(-2 + x)*x)*Log[x])^2, x] + 2
*Defer[Int][(E^(-2 - 2*E^x + 3*x + 3*E^2*(-2 + x)*x)*Log[x])/(x*(-E^(1 + E^x) - E^(x + E^2*(-2 + x)*x)*Log[2]
+ E^(x + E^2*(-2 + x)*x)*Log[x])), x] - 3*Defer[Int][(E^(-2 - 2*E^x + 4*x + 3*E^2*(-2 + x)*x)*Log[x]^2)/(-E^(1
+ E^x) - E^(x + E^2*(-2 + x)*x)*Log[2] + E^(x + E^2*(-2 + x)*x)*Log[x]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{2 \left (1-2 e^2\right ) x+2 e^2 x^2} \left (-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )^2} \, dx \\ & = \int \left (\exp \left (-1-e^x-x+2 \left (1-2 e^2\right ) x-e^2 (-2+x) x+2 e^2 x^2\right ) \left (-1+2 e^2+e^x-2 e^2 x\right )+\frac {\exp \left (-2 \left (1+e^x\right )+2 \left (1-2 e^2\right ) x+2 e^2 x^2\right ) \left (-1-e^x x \log (4)-4 e^2 x \log (2) \left (1-\frac {\log (4)}{e^2 \log (16)}\right )+e^2 x^2 \log (16)+2 e^x x \log (x)-2 \left (1-2 e^2\right ) x \log (x)-4 e^2 x^2 \log (x)\right )}{x}+\frac {\exp \left (-2-2 e^x+2 x+2 \left (1-2 e^2\right ) x+2 e^2 (-2+x) x+2 e^2 x^2\right ) \log ^2\left (\frac {x}{2}\right ) \left (-1-e^x x \log (2)+e^2 x^2 \log (4)+x \log (2) \left (1-\frac {e^2 \log (4)}{\log (2)}\right )+e^x x \log (x)-\left (1-2 e^2\right ) x \log (x)-2 e^2 x^2 \log (x)\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )^2}+\frac {\exp \left (-2-2 e^x+x+2 \left (1-2 e^2\right ) x+e^2 (-2+x) x+2 e^2 x^2\right ) (\log (2)-\log (x)) \left (2+e^x x \log (8)-e^2 x^2 \log (64)-x \log (8) \left (1-\frac {e^2 \log (64)}{\log (8)}\right )-3 e^x x \log (x)+3 \left (1-2 e^2\right ) x \log (x)+6 e^2 x^2 \log (x)\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )}\right ) \, dx \\ & = \int \exp \left (-1-e^x-x+2 \left (1-2 e^2\right ) x-e^2 (-2+x) x+2 e^2 x^2\right ) \left (-1+2 e^2+e^x-2 e^2 x\right ) \, dx+\int \frac {\exp \left (-2 \left (1+e^x\right )+2 \left (1-2 e^2\right ) x+2 e^2 x^2\right ) \left (-1-e^x x \log (4)-4 e^2 x \log (2) \left (1-\frac {\log (4)}{e^2 \log (16)}\right )+e^2 x^2 \log (16)+2 e^x x \log (x)-2 \left (1-2 e^2\right ) x \log (x)-4 e^2 x^2 \log (x)\right )}{x} \, dx+\int \frac {\exp \left (-2-2 e^x+2 x+2 \left (1-2 e^2\right ) x+2 e^2 (-2+x) x+2 e^2 x^2\right ) \log ^2\left (\frac {x}{2}\right ) \left (-1-e^x x \log (2)+e^2 x^2 \log (4)+x \log (2) \left (1-\frac {e^2 \log (4)}{\log (2)}\right )+e^x x \log (x)-\left (1-2 e^2\right ) x \log (x)-2 e^2 x^2 \log (x)\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )^2} \, dx+\int \frac {\exp \left (-2-2 e^x+x+2 \left (1-2 e^2\right ) x+e^2 (-2+x) x+2 e^2 x^2\right ) (\log (2)-\log (x)) \left (2+e^x x \log (8)-e^2 x^2 \log (64)-x \log (8) \left (1-\frac {e^2 \log (64)}{\log (8)}\right )-3 e^x x \log (x)+3 \left (1-2 e^2\right ) x \log (x)+6 e^2 x^2 \log (x)\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )} \, dx \\ & = -\frac {\exp \left (-2 \left (1+e^x\right )+2 \left (1-2 e^2\right ) x+2 e^2 x^2\right ) \left (e^x x \log (4)-e^2 x^2 \log (16)-\frac {4 x \log (2) \left (\log (4)-e^2 \log (16)\right )}{\log (16)}-2 e^x x \log (x)+2 \left (1-2 e^2\right ) x \log (x)+4 e^2 x^2 \log (x)\right )}{2 x \left (1-2 e^2-e^x+2 e^2 x\right )}+\int e^{-1-e^x+x+e^2 (-2+x) x} \left (-1+e^x-2 e^2 (-1+x)\right ) \, dx+\int \frac {e^{-2-2 e^x+4 x+4 e^2 (-2+x) x} \log ^2\left (\frac {x}{2}\right ) \left (-1+e^2 x^2 \log (4)+x \left (\log (2)-e^x \log (2)-e^2 \log (4)\right )-\left (1-e^x+2 e^2 (-1+x)\right ) x \log (x)\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )^2} \, dx+\int \frac {e^{-2-2 e^x+3 x+3 e^2 (-2+x) x} (\log (2)-\log (x)) \left (2-e^2 x^2 \log (64)+x \left (-\log (8)+e^x \log (8)+e^2 \log (64)\right )+3 \left (1-e^x+2 e^2 (-1+x)\right ) x \log (x)\right )}{x \left (e^{1+e^x}+e^{x+e^2 (-2+x) x} \log (2)-e^{x+e^2 (-2+x) x} \log (x)\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.39 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.83 \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=-\frac {e^{e^2 x^2}}{e^{1+e^x-x+2 e^2 x}+e^{e^2 x^2} \log (2)-e^{e^2 x^2} \log (x)} \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.63 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07

method	result	size
risch	\(-\frac {1}{\ln \left (2\right )-\ln \left (x \right )+{\mathrm e}^{-x^{2} {\mathrm e}^{2}+2 \,{\mathrm e}^{2} x +{\mathrm e}^{x}-x +1}}\)	\(32\)
parallelrisch	\(-\frac {1}{\ln \left (2\right )-\ln \left (x \right )+{\mathrm e}^{{\mathrm e}^{x}+\left (-x^{2}+2 x \right ) {\mathrm e}^{2}-x +1}}\)	\(32\)

[In]

int(((exp(x)*x+(-2*x^2+2*x)*exp(2)-x)*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)-1)/(x*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1
)^2+(-2*x*ln(x)+2*x*ln(2))*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)+x*ln(x)^2-2*x*ln(2)*ln(x)+x*ln(2)^2),x,method=_RE
TURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=-\frac {1}{e^{\left (-{\left (x^{2} - 2 \, x\right )} e^{2} - x + e^{x} + 1\right )} + \log \left (2\right ) - \log \left (x\right )} \]

[In]

integrate(((exp(x)*x+(-2*x^2+2*x)*exp(2)-x)*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)-1)/(x*exp(exp(x)+(-x^2+2*x)*exp(
2)-x+1)^2+(-2*x*log(x)+2*x*log(2))*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)+x*log(x)^2-2*x*log(2)*log(x)+x*log(2)^2),
x, algorithm="fricas")

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.14 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=- \frac {1}{e^{- x + \left (- x^{2} + 2 x\right ) e^{2} + e^{x} + 1} - \log {\left (x \right )} + \log {\left (2 \right )}} \]

[In]

integrate(((exp(x)*x+(-2*x**2+2*x)*exp(2)-x)*exp(exp(x)+(-x**2+2*x)*exp(2)-x+1)-1)/(x*exp(exp(x)+(-x**2+2*x)*e
xp(2)-x+1)**2+(-2*x*ln(x)+2*x*ln(2))*exp(exp(x)+(-x**2+2*x)*exp(2)-x+1)+x*ln(x)**2-2*x*ln(2)*ln(x)+x*ln(2)**2)
,x)

[Out]

-1/(exp(-x + (-x**2 + 2*x)*exp(2) + exp(x) + 1) - log(x) + log(2))

Maxima [A] (verification not implemented)

none

Time = 0.44 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.37 \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=-\frac {e^{\left (x^{2} e^{2} + x\right )}}{{\left (\log \left (2\right ) - \log \left (x\right )\right )} e^{\left (x^{2} e^{2} + x\right )} + e^{\left (2 \, x e^{2} + e^{x} + 1\right )}} \]

[In]

integrate(((exp(x)*x+(-2*x^2+2*x)*exp(2)-x)*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)-1)/(x*exp(exp(x)+(-x^2+2*x)*exp(
2)-x+1)^2+(-2*x*log(x)+2*x*log(2))*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)+x*log(x)^2-2*x*log(2)*log(x)+x*log(2)^2),
x, algorithm="maxima")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1135 vs. \(2 (27) = 54\).

Time = 0.56 (sec) , antiderivative size = 1135, normalized size of antiderivative = 37.83 \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=\text {Too large to display} \]

[In]

integrate(((exp(x)*x+(-2*x^2+2*x)*exp(2)-x)*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)-1)/(x*exp(exp(x)+(-x^2+2*x)*exp(
2)-x+1)^2+(-2*x*log(x)+2*x*log(2))*exp(exp(x)+(-x^2+2*x)*exp(2)-x+1)+x*log(x)^2-2*x*log(2)*log(x)+x*log(2)^2),
x, algorithm="giac")

[Out]

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

Mupad [F(-1)]

Timed out. \[ \int \frac {-1+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} \left (-x+e^x x+e^2 \left (2 x-2 x^2\right )\right )}{e^{2+2 e^x-2 x+2 e^2 \left (2 x-x^2\right )} x+x \log ^2(2)-2 x \log (2) \log (x)+x \log ^2(x)+e^{1+e^x-x+e^2 \left (2 x-x^2\right )} (2 x \log (2)-2 x \log (x))} \, dx=\int \frac {{\mathrm {e}}^{{\mathrm {e}}^x-x+{\mathrm {e}}^2\,\left (2\,x-x^2\right )+1}\,\left ({\mathrm {e}}^2\,\left (2\,x-2\,x^2\right )-x+x\,{\mathrm {e}}^x\right )-1}{x\,{\ln \left (x\right )}^2+{\mathrm {e}}^{{\mathrm {e}}^x-x+{\mathrm {e}}^2\,\left (2\,x-x^2\right )+1}\,\left (2\,x\,\ln \left (2\right )-2\,x\,\ln \left (x\right )\right )+x\,{\ln \left (2\right )}^2+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^x-2\,x+2\,{\mathrm {e}}^2\,\left (2\,x-x^2\right )+2}-2\,x\,\ln \left (2\right )\,\ln \left (x\right )} \,d x \]

[In]

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

[Out]

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