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

Optimal. Leaf size=34 \[ \frac {x}{x+\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \]

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Rubi [A]  time = 1.75, antiderivative size = 38, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 3, integrand size = 176, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6688, 6711, 32} \begin {gather*} -\frac {1}{\frac {x}{\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )}+1} \end {gather*}

Antiderivative was successfully verified.

[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 6688

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

Rule 6711

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 {gather*} \begin {aligned} \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\\ &=\operatorname {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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 34, normalized size = 1.00 \begin {gather*} \frac {x}{x+\log \left (\frac {2 e^{-5 e^{-e^{x-x^2}}} x^2}{\log (\log (2))}\right )} \end {gather*}

Antiderivative was successfully verified.

[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]])])

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fricas [A]  time = 0.69, size = 31, normalized size = 0.91 \begin {gather*} \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 \relax (2)\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))))

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giac [B]  time = 3.31, size = 2943, normalized size = 86.56 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[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)))

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maple [C]  time = 0.73, size = 271, normalized size = 7.97

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

Verification of antiderivative is not currently implemented for this CAS.

[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]

2*x/(2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-2*I*Pi*csgn(I*x^2*exp(-5*exp(-exp(-x*(x-1)))))^2-I*Pi*csgn(I*x)^2*csgn(I*x
^2)+I*Pi*csgn(I*x^2*exp(-5*exp(-exp(-x*(x-1)))))^3+I*Pi*csgn(I*x^2)*csgn(I*x^2*exp(-5*exp(-exp(-x*(x-1)))))^2+
2*I*Pi-I*Pi*csgn(I*x^2)^3+I*Pi*csgn(I*exp(-5*exp(-exp(-x*(x-1)))))*csgn(I*x^2*exp(-5*exp(-exp(-x*(x-1)))))^2-I
*Pi*csgn(I*x^2)*csgn(I*exp(-5*exp(-exp(-x*(x-1)))))*csgn(I*x^2*exp(-5*exp(-exp(-x*(x-1)))))+2*ln(2)-2*ln(-ln(l
n(2)))+2*x+4*ln(x)-2*ln(exp(5*exp(-exp(-x*(x-1))))))

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maxima [A]  time = 2.62, size = 39, normalized size = 1.15 \begin {gather*} \frac {x e^{\left (e^{\left (-x^{2} + x\right )}\right )}}{{\left (x + \log \relax (2) + 2 \, \log \relax (x) - \log \left (\log \left (\log \relax (2)\right )\right )\right )} e^{\left (e^{\left (-x^{2} + x\right )}\right )} - 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\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 \relax (2)\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 \relax (2)\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 \relax (2)\right )}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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sympy [A]  time = 1.23, size = 26, normalized size = 0.76 \begin {gather*} \frac {x}{x + \log {\left (\frac {2 x^{2} e^{- 5 e^{- e^{- x^{2} + x}}}}{\log {\left (\log {\relax (2 )} \right )}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))))

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