\(\int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} (-5 x+10 x^2)+e^{e^{x-x^2}} \log (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))})}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))})+e^{e^{x-x^2}} \log ^2(\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))})} \, dx\) [49]

Optimal result

Integrand size = 176, antiderivative size = 34 \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=\frac {x}{x+\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \]

[Out]

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

Rubi [A] (verified)

Time = 1.80 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6820, 6843, 32} \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=-\frac {1}{\frac {x}{\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}+1} \]

[In]

Int[(-2*E^E^(x - x^2) + E^(x - x^2)*(-5*x + 10*x^2) + E^E^(x - x^2)*Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2
]])])/(E^E^(x - x^2)*x^2 + 2*E^E^(x - x^2)*x*Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2]])] + E^E^(x - x^2)*Lo
g[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2]])]^2),x]

[Out]

-(1 + x/Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2]])])^(-1)

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rule 6820

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6843

Int[(u_)*((a_.)*(v_)^(p_.) + (b_.)*(w_)^(q_.))^(m_.), x_Symbol] :> With[{c = Simplify[u/(p*w*D[v, x] - q*v*D[w
, x])]}, Dist[c*p, Subst[Int[(b + a*x^p)^m, x], x, v*w^(m*q + 1)], x] /; FreeQ[c, x]] /; FreeQ[{a, b, m, p, q}
, x] && EqQ[p + q*(m*p + 1), 0] && IntegerQ[p] && IntegerQ[m]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{-e^{x-x^2}-x^2} \left (-2 e^{e^{x-x^2}+x^2}+5 e^x x (-1+2 x)+e^{e^{x-x^2}+x^2} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )\right )}{\left (x+\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )\right )^2} \, dx \\ & = \text {Subst}\left (\int \frac {1}{(1+x)^2} \, dx,x,\frac {x}{\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}\right ) \\ & = -\frac {1}{1+\frac {x}{\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00 \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=\frac {x}{x+\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \]

[In]

Integrate[(-2*E^E^(x - x^2) + E^(x - x^2)*(-5*x + 10*x^2) + E^E^(x - x^2)*Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log
[Log[2]])])/(E^E^(x - x^2)*x^2 + 2*E^E^(x - x^2)*x*Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2]])] + E^E^(x - x
^2)*Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2]])]^2),x]

[Out]

x/(x + Log[(2*x^2)/(E^(5/E^E^(x - x^2))*Log[Log[2]])])

Maple [A] (verified)

Time = 1.68 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00

method	result	size
parallelrisch	\(\frac {x}{\ln \left (\frac {2 x^{2} {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x^{2}+x}}}}{\ln \left (\ln \left (2\right )\right )}\right )+x}\)	\(34\)
risch	\(\frac {2 x}{-i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right ) \operatorname {csgn}\left (i x^{2} {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right )^{2}+i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x^{2} {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right )^{2}-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+2 i \pi -2 i \pi \operatorname {csgn}\left (i x^{2} {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right )^{2}+2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right ) \operatorname {csgn}\left (i x^{2} {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right )+i \pi \operatorname {csgn}\left (i x^{2} {\mathrm e}^{-5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right )^{3}+2 \ln \left (2\right )-2 \ln \left (-\ln \left (\ln \left (2\right )\right )\right )+2 x +4 \ln \left (x \right )-2 \ln \left ({\mathrm e}^{5 \,{\mathrm e}^{-{\mathrm e}^{-x \left (-1+x \right )}}}\right )}\)	\(271\)

[In]

int((exp(exp(-x^2+x))*ln(2*x^2/ln(ln(2))/exp(5/exp(exp(-x^2+x))))-2*exp(exp(-x^2+x))+(10*x^2-5*x)*exp(-x^2+x))
/(exp(exp(-x^2+x))*ln(2*x^2/ln(ln(2))/exp(5/exp(exp(-x^2+x))))^2+2*x*exp(exp(-x^2+x))*ln(2*x^2/ln(ln(2))/exp(5
/exp(exp(-x^2+x))))+x^2*exp(exp(-x^2+x))),x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.91 \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=\frac {x}{x + \log \left (\frac {2 \, x^{2} e^{\left (-5 \, e^{\left (-e^{\left (-x^{2} + x\right )}\right )}\right )}}{\log \left (\log \left (2\right )\right )}\right )} \]

[In]

integrate((exp(exp(-x^2+x))*log(2*x^2/log(log(2))/exp(5/exp(exp(-x^2+x))))-2*exp(exp(-x^2+x))+(10*x^2-5*x)*exp
(-x^2+x))/(exp(exp(-x^2+x))*log(2*x^2/log(log(2))/exp(5/exp(exp(-x^2+x))))^2+2*x*exp(exp(-x^2+x))*log(2*x^2/lo
g(log(2))/exp(5/exp(exp(-x^2+x))))+x^2*exp(exp(-x^2+x))),x, algorithm="fricas")

[Out]

x/(x + log(2*x^2*e^(-5*e^(-e^(-x^2 + x)))/log(log(2))))

Sympy [A] (verification not implemented)

Time = 0.65 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.76 \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=\frac {x}{x + \log {\left (\frac {2 x^{2} e^{- 5 e^{- e^{- x^{2} + x}}}}{\log {\left (\log {\left (2 \right )} \right )}} \right )}} \]

[In]

integrate((exp(exp(-x**2+x))*ln(2*x**2/ln(ln(2))/exp(5/exp(exp(-x**2+x))))-2*exp(exp(-x**2+x))+(10*x**2-5*x)*e
xp(-x**2+x))/(exp(exp(-x**2+x))*ln(2*x**2/ln(ln(2))/exp(5/exp(exp(-x**2+x))))**2+2*x*exp(exp(-x**2+x))*ln(2*x*
*2/ln(ln(2))/exp(5/exp(exp(-x**2+x))))+x**2*exp(exp(-x**2+x))),x)

[Out]

x/(x + log(2*x**2*exp(-5*exp(-exp(-x**2 + x)))/log(log(2))))

Maxima [A] (verification not implemented)

none

Time = 0.46 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.15 \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=\frac {x e^{\left (e^{\left (-x^{2} + x\right )}\right )}}{{\left (x + \log \left (2\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (\log \left (2\right )\right )\right )\right )} e^{\left (e^{\left (-x^{2} + x\right )}\right )} - 5} \]

[In]

integrate((exp(exp(-x^2+x))*log(2*x^2/log(log(2))/exp(5/exp(exp(-x^2+x))))-2*exp(exp(-x^2+x))+(10*x^2-5*x)*exp
(-x^2+x))/(exp(exp(-x^2+x))*log(2*x^2/log(log(2))/exp(5/exp(exp(-x^2+x))))^2+2*x*exp(exp(-x^2+x))*log(2*x^2/lo
g(log(2))/exp(5/exp(exp(-x^2+x))))+x^2*exp(exp(-x^2+x))),x, algorithm="maxima")

[Out]

x*e^(e^(-x^2 + x))/((x + log(2) + 2*log(x) - log(log(log(2))))*e^(e^(-x^2 + x)) - 5)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 2943 vs. \(2 (31) = 62\).

Time = 0.82 (sec) , antiderivative size = 2943, normalized size of antiderivative = 86.56 \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=\text {Too large to display} \]

[In]

integrate((exp(exp(-x^2+x))*log(2*x^2/log(log(2))/exp(5/exp(exp(-x^2+x))))-2*exp(exp(-x^2+x))+(10*x^2-5*x)*exp
(-x^2+x))/(exp(exp(-x^2+x))*log(2*x^2/log(log(2))/exp(5/exp(exp(-x^2+x))))^2+2*x*exp(exp(-x^2+x))*log(2*x^2/lo
g(log(2))/exp(5/exp(exp(-x^2+x))))+x^2*exp(exp(-x^2+x))),x, algorithm="giac")

[Out]

(2*x^5*e^(-2*x^2 + 2*x) + 4*x^4*e^(-2*x^2 + 2*x)*log(2) + 2*x^3*e^(-2*x^2 + 2*x)*log(2)^2 + 4*x^4*e^(-2*x^2 +
2*x)*log(x^2) + 4*x^3*e^(-2*x^2 + 2*x)*log(2)*log(x^2) + 2*x^3*e^(-2*x^2 + 2*x)*log(x^2)^2 - 4*x^4*e^(-2*x^2 +
2*x)*log(log(log(2))) - 4*x^3*e^(-2*x^2 + 2*x)*log(2)*log(log(log(2))) - 4*x^3*e^(-2*x^2 + 2*x)*log(x^2)*log(
log(log(2))) + 2*x^3*e^(-2*x^2 + 2*x)*log(log(log(2)))^2 - 10*x^4*e^(-2*x^2 + 2*x - e^(-x^2 + x)) - x^4*e^(-2*
x^2 + 2*x) - 10*x^3*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(2) - 2*x^3*e^(-2*x^2 + 2*x)*log(2) - x^2*e^(-2*x^2 + 2
*x)*log(2)^2 - 10*x^3*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2) - 2*x^3*e^(-2*x^2 + 2*x)*log(x^2) - 2*x^2*e^(-2
*x^2 + 2*x)*log(2)*log(x^2) - x^2*e^(-2*x^2 + 2*x)*log(x^2)^2 + 10*x^3*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(log
(log(2))) + 2*x^3*e^(-2*x^2 + 2*x)*log(log(log(2))) + 2*x^2*e^(-2*x^2 + 2*x)*log(2)*log(log(log(2))) + 2*x^2*e
^(-2*x^2 + 2*x)*log(x^2)*log(log(log(2))) - x^2*e^(-2*x^2 + 2*x)*log(log(log(2)))^2 - x^3*e^(-x^2 + x) + 5*x^3
*e^(-2*x^2 + 2*x - e^(-x^2 + x)) - x^2*e^(-x^2 + x)*log(2) + 5*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(2) - x^
2*e^(-x^2 + x)*log(x^2) + 5*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2) + x^2*e^(-x^2 + x)*log(log(log(2))) -
5*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(log(log(2))) + 5*x^2*e^(-x^2 + x - e^(-x^2 + x)) - 2*x^2*e^(-x^2 +
x) - 2*x*e^(-x^2 + x)*log(2) - 2*x*e^(-x^2 + x)*log(x^2) + 2*x*e^(-x^2 + x)*log(log(log(2))) + 10*x*e^(-x^2 +
x - e^(-x^2 + x)))/(2*x^5*e^(-2*x^2 + 2*x) + 6*x^4*e^(-2*x^2 + 2*x)*log(2) + 6*x^3*e^(-2*x^2 + 2*x)*log(2)^2 +
2*x^2*e^(-2*x^2 + 2*x)*log(2)^3 + 6*x^4*e^(-2*x^2 + 2*x)*log(x^2) + 12*x^3*e^(-2*x^2 + 2*x)*log(2)*log(x^2) +
6*x^2*e^(-2*x^2 + 2*x)*log(2)^2*log(x^2) + 6*x^3*e^(-2*x^2 + 2*x)*log(x^2)^2 + 6*x^2*e^(-2*x^2 + 2*x)*log(2)*
log(x^2)^2 + 2*x^2*e^(-2*x^2 + 2*x)*log(x^2)^3 - 6*x^4*e^(-2*x^2 + 2*x)*log(log(log(2))) - 12*x^3*e^(-2*x^2 +
2*x)*log(2)*log(log(log(2))) - 6*x^2*e^(-2*x^2 + 2*x)*log(2)^2*log(log(log(2))) - 12*x^3*e^(-2*x^2 + 2*x)*log(
x^2)*log(log(log(2))) - 12*x^2*e^(-2*x^2 + 2*x)*log(2)*log(x^2)*log(log(log(2))) - 6*x^2*e^(-2*x^2 + 2*x)*log(
x^2)^2*log(log(log(2))) + 6*x^3*e^(-2*x^2 + 2*x)*log(log(log(2)))^2 + 6*x^2*e^(-2*x^2 + 2*x)*log(2)*log(log(lo
g(2)))^2 + 6*x^2*e^(-2*x^2 + 2*x)*log(x^2)*log(log(log(2)))^2 - 2*x^2*e^(-2*x^2 + 2*x)*log(log(log(2)))^3 - 20
*x^4*e^(-2*x^2 + 2*x - e^(-x^2 + x)) - x^4*e^(-2*x^2 + 2*x) - 40*x^3*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(2) -
3*x^3*e^(-2*x^2 + 2*x)*log(2) - 20*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(2)^2 - 3*x^2*e^(-2*x^2 + 2*x)*log(2
)^2 - x*e^(-2*x^2 + 2*x)*log(2)^3 - 40*x^3*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2) - 3*x^3*e^(-2*x^2 + 2*x)*l
og(x^2) - 40*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(2)*log(x^2) - 6*x^2*e^(-2*x^2 + 2*x)*log(2)*log(x^2) - 3*
x*e^(-2*x^2 + 2*x)*log(2)^2*log(x^2) - 20*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2)^2 - 3*x^2*e^(-2*x^2 + 2
*x)*log(x^2)^2 - 3*x*e^(-2*x^2 + 2*x)*log(2)*log(x^2)^2 - x*e^(-2*x^2 + 2*x)*log(x^2)^3 + 40*x^3*e^(-2*x^2 + 2
*x - e^(-x^2 + x))*log(log(log(2))) + 3*x^3*e^(-2*x^2 + 2*x)*log(log(log(2))) + 40*x^2*e^(-2*x^2 + 2*x - e^(-x
^2 + x))*log(2)*log(log(log(2))) + 6*x^2*e^(-2*x^2 + 2*x)*log(2)*log(log(log(2))) + 3*x*e^(-2*x^2 + 2*x)*log(2
)^2*log(log(log(2))) + 40*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2)*log(log(log(2))) + 6*x^2*e^(-2*x^2 + 2*
x)*log(x^2)*log(log(log(2))) + 6*x*e^(-2*x^2 + 2*x)*log(2)*log(x^2)*log(log(log(2))) + 3*x*e^(-2*x^2 + 2*x)*lo
g(x^2)^2*log(log(log(2))) - 20*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(log(log(2)))^2 - 3*x^2*e^(-2*x^2 + 2*x)
*log(log(log(2)))^2 - 3*x*e^(-2*x^2 + 2*x)*log(2)*log(log(log(2)))^2 - 3*x*e^(-2*x^2 + 2*x)*log(x^2)*log(log(l
og(2)))^2 + x*e^(-2*x^2 + 2*x)*log(log(log(2)))^3 - x^3*e^(-x^2 + x) + 10*x^3*e^(-2*x^2 + 2*x - e^(-x^2 + x))
+ 50*x^3*e^(-2*x^2 + 2*x - 2*e^(-x^2 + x)) - 2*x^2*e^(-x^2 + x)*log(2) + 20*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x)
)*log(2) + 50*x^2*e^(-2*x^2 + 2*x - 2*e^(-x^2 + x))*log(2) - x*e^(-x^2 + x)*log(2)^2 + 10*x*e^(-2*x^2 + 2*x -
e^(-x^2 + x))*log(2)^2 - 2*x^2*e^(-x^2 + x)*log(x^2) + 20*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2) + 50*x^
2*e^(-2*x^2 + 2*x - 2*e^(-x^2 + x))*log(x^2) - 2*x*e^(-x^2 + x)*log(2)*log(x^2) + 20*x*e^(-2*x^2 + 2*x - e^(-x
^2 + x))*log(2)*log(x^2) - x*e^(-x^2 + x)*log(x^2)^2 + 10*x*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(x^2)^2 + 2*x^2
*e^(-x^2 + x)*log(log(log(2))) - 20*x^2*e^(-2*x^2 + 2*x - e^(-x^2 + x))*log(log(log(2))) - 50*x^2*e^(-2*x^2 +
2*x - 2*e^(-x^2 + x))*log(log(log(2))) + 2*x*e^(-x^2 + x)*log(2)*log(log(log(2))) - 20*x*e^(-2*x^2 + 2*x - e^(
-x^2 + x))*log(2)*log(log(log(2))) + 2*x*e^(-x^2 + x)*log(x^2)*log(log(log(2))) - 20*x*e^(-2*x^2 + 2*x - e^(-x
^2 + x))*log(x^2)*log(log(log(2))) - x*e^(-x^2 + x)*log(log(log(2)))^2 + 10*x*e^(-2*x^2 + 2*x - e^(-x^2 + x))*
log(log(log(2)))^2 + 10*x^2*e^(-x^2 + x - e^(-x^2 + x)) - 2*x^2*e^(-x^2 + x) - 25*x^2*e^(-2*x^2 + 2*x - 2*e^(-
x^2 + x)) + 10*x*e^(-x^2 + x - e^(-x^2 + x))*log(2) - 4*x*e^(-x^2 + x)*log(2) - 25*x*e^(-2*x^2 + 2*x - 2*e^(-x
^2 + x))*log(2) - 2*e^(-x^2 + x)*log(2)^2 + 10*x*e^(-x^2 + x - e^(-x^2 + x))*log(x^2) - 4*x*e^(-x^2 + x)*log(x
^2) - 25*x*e^(-2*x^2 + 2*x - 2*e^(-x^2 + x))*log(x^2) - 4*e^(-x^2 + x)*log(2)*log(x^2) - 2*e^(-x^2 + x)*log(x^
2)^2 - 10*x*e^(-x^2 + x - e^(-x^2 + x))*log(log(log(2))) + 4*x*e^(-x^2 + x)*log(log(log(2))) + 25*x*e^(-2*x^2
+ 2*x - 2*e^(-x^2 + x))*log(log(log(2))) + 4*e^(-x^2 + x)*log(2)*log(log(log(2))) + 4*e^(-x^2 + x)*log(x^2)*lo
g(log(log(2))) - 2*e^(-x^2 + x)*log(log(log(2)))^2 + 20*x*e^(-x^2 + x - e^(-x^2 + x)) - 25*x*e^(-x^2 + x - 2*e
^(-x^2 + x)) + 20*e^(-x^2 + x - e^(-x^2 + x))*log(2) + 20*e^(-x^2 + x - e^(-x^2 + x))*log(x^2) - 20*e^(-x^2 +
x - e^(-x^2 + x))*log(log(log(2))) - 50*e^(-x^2 + x - 2*e^(-x^2 + x)))

Mupad [F(-1)]

Timed out. \[ \int \frac {-2 e^{e^{x-x^2}}+e^{x-x^2} \left (-5 x+10 x^2\right )+e^{e^{x-x^2}} \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}{e^{e^{x-x^2}} x^2+2 e^{e^{x-x^2}} x \log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )+e^{e^{x-x^2}} \log ^2\left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \, dx=-\int \frac {2\,{\mathrm {e}}^{{\mathrm {e}}^{x-x^2}}-{\mathrm {e}}^{{\mathrm {e}}^{x-x^2}}\,\ln \left (\frac {2\,x^2\,{\mathrm {e}}^{-5\,{\mathrm {e}}^{-{\mathrm {e}}^{x-x^2}}}}{\ln \left (\ln \left (2\right )\right )}\right )+{\mathrm {e}}^{x-x^2}\,\left (5\,x-10\,x^2\right )}{x^2\,{\mathrm {e}}^{{\mathrm {e}}^{x-x^2}}+{\mathrm {e}}^{{\mathrm {e}}^{x-x^2}}\,{\ln \left (\frac {2\,x^2\,{\mathrm {e}}^{-5\,{\mathrm {e}}^{-{\mathrm {e}}^{x-x^2}}}}{\ln \left (\ln \left (2\right )\right )}\right )}^2+2\,x\,{\mathrm {e}}^{{\mathrm {e}}^{x-x^2}}\,\ln \left (\frac {2\,x^2\,{\mathrm {e}}^{-5\,{\mathrm {e}}^{-{\mathrm {e}}^{x-x^2}}}}{\ln \left (\ln \left (2\right )\right )}\right )} \,d x \]

[In]

int(-(2*exp(exp(x - x^2)) - exp(exp(x - x^2))*log((2*x^2*exp(-5*exp(-exp(x - x^2))))/log(log(2))) + exp(x - x^
2)*(5*x - 10*x^2))/(x^2*exp(exp(x - x^2)) + exp(exp(x - x^2))*log((2*x^2*exp(-5*exp(-exp(x - x^2))))/log(log(2
)))^2 + 2*x*exp(exp(x - x^2))*log((2*x^2*exp(-5*exp(-exp(x - x^2))))/log(log(2)))),x)

[Out]

-int((2*exp(exp(x - x^2)) - exp(exp(x - x^2))*log((2*x^2*exp(-5*exp(-exp(x - x^2))))/log(log(2))) + exp(x - x^
2)*(5*x - 10*x^2))/(x^2*exp(exp(x - x^2)) + exp(exp(x - x^2))*log((2*x^2*exp(-5*exp(-exp(x - x^2))))/log(log(2
)))^2 + 2*x*exp(exp(x - x^2))*log((2*x^2*exp(-5*exp(-exp(x - x^2))))/log(log(2)))), x)