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

Optimal. Leaf size=29 \[ \frac {e^{e^2}-x}{x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 11.39, 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*} \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{e^2}-\frac {3 e^{x^2} \left (e^{e^2}-x\right ) \left (1+2 x^2\right )}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )}-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\\ &=\int \left (\frac {\left (-1+e^4\right ) \left (e^{e^2}-x\right ) \left (1+2 x^2\right )}{x \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}+\frac {-e^{e^2}+x-2 e^{e^2} x^2+2 x^3-e^{e^2} x \log \left (-1+e^4-3 e^{x^2} x\right )-x \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}\right ) \, dx\\ &=\left (-1+e^4\right ) \int \frac {\left (e^{e^2}-x\right ) \left (1+2 x^2\right )}{x \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {-e^{e^2}+x-2 e^{e^2} x^2+2 x^3-e^{e^2} x \log \left (-1+e^4-3 e^{x^2} x\right )-x \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\\ &=\left (-1+e^4\right ) \int \left (-\frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}-\frac {e^{e^2}}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}-\frac {2 e^{e^2} x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}+\frac {2 x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}\right ) \, dx+\int \frac {-\left (\left (e^{e^2}-x\right ) \left (1+2 x^2\right )\right )-x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (e^{e^2}+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\\ &=\left (1-e^4\right ) \int \frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 \left (1-e^4\right )\right ) \int \frac {x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (e^{e^2} \left (1-e^4\right )\right ) \int \frac {1}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (2 e^{e^2} \left (1-e^4\right )\right ) \int \frac {x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \left (\frac {1}{-x-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}+\frac {\left (-e^{e^2}+x\right ) \left (1+2 x^2+x \log \left (-1+e^4-3 e^{x^2} x\right )\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}\right ) \, dx\\ &=\left (1-e^4\right ) \int \frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 \left (1-e^4\right )\right ) \int \frac {x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (e^{e^2} \left (1-e^4\right )\right ) \int \frac {1}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (2 e^{e^2} \left (1-e^4\right )\right ) \int \frac {x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {1}{-x-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx+\int \frac {\left (-e^{e^2}+x\right ) \left (1+2 x^2+x \log \left (-1+e^4-3 e^{x^2} x\right )\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\\ &=\left (1-e^4\right ) \int \frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 \left (1-e^4\right )\right ) \int \frac {x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (e^{e^2} \left (1-e^4\right )\right ) \int \frac {1}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (2 e^{e^2} \left (1-e^4\right )\right ) \int \frac {x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {1}{-x-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx+\int \left (\frac {1+2 x^2+x \log \left (-1+e^4-3 e^{x^2} x\right )}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}-\frac {e^{e^2} \left (1+2 x^2+x \log \left (-1+e^4-3 e^{x^2} x\right )\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}\right ) \, dx\\ &=-\left (e^{e^2} \int \frac {1+2 x^2+x \log \left (-1+e^4-3 e^{x^2} x\right )}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\right )+\left (1-e^4\right ) \int \frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 \left (1-e^4\right )\right ) \int \frac {x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (e^{e^2} \left (1-e^4\right )\right ) \int \frac {1}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (2 e^{e^2} \left (1-e^4\right )\right ) \int \frac {x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {1}{-x-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx+\int \frac {1+2 x^2+x \log \left (-1+e^4-3 e^{x^2} x\right )}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\\ &=-\left (e^{e^2} \int \left (\frac {1}{\left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}+\frac {1}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}+\frac {2 x}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}\right ) \, dx\right )+\left (1-e^4\right ) \int \frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 \left (1-e^4\right )\right ) \int \frac {x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (e^{e^2} \left (1-e^4\right )\right ) \int \frac {1}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (2 e^{e^2} \left (1-e^4\right )\right ) \int \frac {x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {1}{-x-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx+\int \left (\frac {x}{\left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}+\frac {1}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}+\frac {2 x^2}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {x^2}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-e^{e^2} \int \frac {1}{\left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-e^{e^2} \int \frac {1}{x \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 e^{e^2}\right ) \int \frac {x}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (1-e^4\right ) \int \frac {1}{\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx-\left (2 \left (1-e^4\right )\right ) \int \frac {x^2}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (e^{e^2} \left (1-e^4\right )\right ) \int \frac {1}{x \left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\left (2 e^{e^2} \left (1-e^4\right )\right ) \int \frac {x}{\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {1}{-x-\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx+\int \frac {x}{\left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx+\int \frac {1}{\log \left (-1+e^4-3 e^{x^2} x\right ) \left (x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.20, size = 29, normalized size = 1.00 \begin {gather*} \frac {e^{e^2}-x}{x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(E^E^2 - x)/(x + Log[Log[-1 + E^4 - 3*E^x^2*x]])

________________________________________________________________________________________

fricas [A]  time = 1.23, size = 42, normalized size = 1.45 \begin {gather*} -\frac {x - e^{\left (e^{2}\right )}}{x + \log \left (\log \left (-{\left (3 \, x e^{\left (x^{2} + e^{2}\right )} - {\left (e^{4} - 1\right )} e^{\left (e^{2}\right )}\right )} e^{\left (-e^{2}\right )}\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x - e^(e^2))/(x + log(log(-(3*x*e^(x^2 + e^2) - (e^4 - 1)*e^(e^2))*e^(-e^2))))

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(-((3*x*e^(x^2) - e^4 + 1)*e^(e^2)*log(-3*x*e^(x^2) + e^4 - 1) + (3*x*e^(x^2) - e^4 + 1)*log(-3*x*e^(
x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1)) + 3*(2*x^2 + 1)*e^(x^2 + e^2) - 3*(2*x^3 + x)*e^(x^2))/((3*x*
e^(x^2) - e^4 + 1)*log(-3*x*e^(x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1))^2 + 2*(3*x^2*e^(x^2) - x*e^4 +
x)*log(-3*x*e^(x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1)) + (3*x^3*e^(x^2) - x^2*e^4 + x^2)*log(-3*x*e^
(x^2) + e^4 - 1)), x)

________________________________________________________________________________________

maple [A]  time = 0.07, size = 26, normalized size = 0.90

method	result	size
risch	\(\frac {{\mathrm e}^{{\mathrm e}^{2}}-x}{\ln \left (\ln \left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )\right )+x}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(exp(exp(2))-x)/(ln(ln(-3*exp(x^2)*x+exp(4)-1))+x)

________________________________________________________________________________________

maxima [A]  time = 0.47, size = 26, normalized size = 0.90 \begin {gather*} -\frac {x - e^{\left (e^{2}\right )}}{x + \log \left (\log \left (-3 \, x e^{\left (x^{2}\right )} + e^{4} - 1\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x - e^(e^2))/(x + log(log(-3*x*e^(x^2) + e^4 - 1)))

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\ln \left (\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\right )\,\left (3\,x\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^4+1\right )-{\mathrm {e}}^{x^2}\,\left (6\,x^3+3\,x\right )+\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (3\,x\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^4+1\right )+{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (6\,x^2+3\right )}{\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\left (3\,x\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^4+1\right )\,{\ln \left (\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\right )}^2+\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\left (2\,x-2\,x\,{\mathrm {e}}^4+6\,x^2\,{\mathrm {e}}^{x^2}\right )\,\ln \left (\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\right )+\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\left (3\,x^3\,{\mathrm {e}}^{x^2}-x^2\,{\mathrm {e}}^4+x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 1.54, size = 24, normalized size = 0.83 \begin {gather*} \frac {- x + e^{e^{2}}}{x + \log {\left (\log {\left (- 3 x e^{x^{2}} - 1 + e^{4} \right )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3*exp(x**2)*x+exp(4)-1)*ln(-3*exp(x**2)*x+exp(4)-1)*ln(ln(-3*exp(x**2)*x+exp(4)-1))+(-3*exp(x**2)
*x+exp(4)-1)*exp(exp(2))*ln(-3*exp(x**2)*x+exp(4)-1)+(-6*x**2-3)*exp(x**2)*exp(exp(2))+(6*x**3+3*x)*exp(x**2))
/((3*exp(x**2)*x+1-exp(4))*ln(-3*exp(x**2)*x+exp(4)-1)*ln(ln(-3*exp(x**2)*x+exp(4)-1))**2+(6*x**2*exp(x**2)-2*
x*exp(4)+2*x)*ln(-3*exp(x**2)*x+exp(4)-1)*ln(ln(-3*exp(x**2)*x+exp(4)-1))+(3*x**3*exp(x**2)-x**2*exp(4)+x**2)*
ln(-3*exp(x**2)*x+exp(4)-1)),x)

[Out]

(-x + exp(exp(2)))/(x + log(log(-3*x*exp(x**2) - 1 + exp(4))))

________________________________________________________________________________________