Integrand size = 308, antiderivative size = 35 \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx=e^{\frac {1}{\log \left (x-\frac {x^2}{\left (-e^2+2 e^{-e^{e^x}-x}\right )^2}\right )}} \]
Time = 0.45 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.74 \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx=e^{\frac {1}{\log \left (\frac {x \left (4-4 e^{2+e^{e^x}+x}+e^{2 \left (2+e^{e^x}+x\right )}-e^{2 \left (e^{e^x}+x\right )} x\right )}{\left (-2+e^{2+e^{e^x}+x}\right )^2}\right )}} \]
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]
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)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {\left (e^{2 x+2 e^{e^x}} \left (-4 e^{x+e^x} x^2-4 x^2-4 x+6 e^4\right )+e^{3 x+3 e^{e^x}} \left (2 e^2 x-e^6\right )-12 e^{x+e^{e^x}+2}+8\right ) \exp \left (\frac {1}{\log \left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4}\right )}\right )}{\left (e^{2 x+2 e^{e^x}} \left (2 x^2-6 e^4 x\right )+e^{3 x+3 e^{e^x}} \left (e^6 x-e^2 x^2\right )+12 e^{x+e^{e^x}+2} x-8 x\right ) \log ^2\left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4}\right )} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {\left (-e^{2 x+2 e^{e^x}} \left (-4 e^{x+e^x} x^2-4 x^2-4 x+6 e^4\right )-e^{3 x+3 e^{e^x}} \left (2 e^2 x-e^6\right )+12 e^{x+e^{e^x}+2}-8\right ) \exp \left (\frac {1}{\log \left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (\frac {1}{\log \left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (\frac {1}{\log \left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {e^{2 x+2 e^{e^x}} \left (e^4 x-x^2\right )-4 e^{x+e^{e^x}+2} x+4 x}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {\left (4 e^{3 x+2 e^{e^x}+e^x} x^2-2 e^{3 x+3 e^{e^x}+2} x+4 e^{2 \left (x+e^{e^x}\right )} (x+1) x+12 e^{x+e^{e^x}+2}-6 e^{2 \left (x+e^{e^x}+2\right )}+e^{3 \left (x+e^{e^x}+2\right )}-8\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )}{\left (2-e^{x+e^{e^x}+2}\right ) x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {\left (4 e^{e^x} x^2-2 e^{e^{e^x}+2} x+e^{e^{e^x}+6}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^4-x\right ) x \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (2 e^{e^x}+e^{e^{e^x}+2}\right ) \exp \left (-e^{e^x}+\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-2\right )}{\left (e^{x+e^{e^x}+2}-2\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}+\frac {4 \left (-2 e^{e^{e^x}} x+e^{x+2 e^{e^x}+2} x-2 e^{x+e^{e^x}+e^x} x+4 e^{e^x+2}-2 e^{x+e^{e^x}+e^x+4}+\left (1-e^4\right ) e^{x+2 e^{e^x}+2}-\left (1-2 e^4\right ) e^{e^{e^x}}\right ) \exp \left (\frac {1}{\log \left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}-e^{e^x}\right )}{\left (e^4-x\right ) \left (-e^{2 x+2 e^{e^x}} x-4 e^{x+e^{e^x}+2}+e^{2 x+2 e^{e^x}+4}+4\right ) \log ^2\left (\frac {x \left (-e^{2 \left (x+e^{e^x}\right )} x-4 e^{x+e^{e^x}+2}+e^{2 \left (x+e^{e^x}+2\right )}+4\right )}{\left (e^{x+e^{e^x}+2}-2\right )^2}\right )}\right )dx\) |
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))*Lo g[(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]
3.7.29.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.14 (sec) , antiderivative size = 828, normalized size of antiderivative = 23.66
\[\text {Expression too large to display}\]
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(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*exp(2)*exp(x+exp(ex p(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+ex p(exp(x)))^2-4*exp(2)*exp(x+exp(exp(x)))+4))^2,x)
exp(2/(I*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*Pi+I*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*csgn(I*x)*Pi-I*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*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)-I*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)*Pi*csgn(I*(exp(2*x+2*exp(exp(x)))*x+4*exp(2+x+ex p(exp(x)))-exp(4+2*x+2*exp(exp(x)))-4)/(exp(2+x+exp(exp(x)))-2)^2)-I*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))*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-I*csgn(I*(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))*Pi*csgn(I*(e xp(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/(exp(2+x+exp(exp(x)))-2)^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+exp(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))...
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.26 \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx=e^{\left (\frac {1}{\log \left (\frac {4 \, x e^{4} - {\left (x^{2} - x e^{4}\right )} e^{\left (2 \, {\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )} - 4 \, x e^{\left ({\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + 4\right )}}{4 \, e^{4} + e^{\left (2 \, {\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + 4\right )} - 4 \, e^{\left ({\left ({\left (x + 2\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + 4\right )}}\right )}\right )} \]
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*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, algorithm=\
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))))
Timed out. \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx=\text {Timed out} \]
integrate(((-exp(2)**3+2*exp(2)*x)*exp(x+exp(exp(x)))**3+(-4*x**2*exp(x)*e xp(exp(x))+6*exp(2)**2-4*x**2-4*x)*exp(x+exp(exp(x)))**2-12*exp(2)*exp(x+e xp(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+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)
Leaf count of result is larger than twice the leaf count of optimal. 1058 vs. \(2 (28) = 56\).
Time = 3.74 (sec) , antiderivative size = 1058, normalized size of antiderivative = 30.23 \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx=\text {Too large to display} \]
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*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, algorithm=\
-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*log(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)...
Timed out. \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx=\text {Timed out} \]
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*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, algorithm=\
Time = 10.53 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.17 \[ \int \frac {e^{\frac {1}{\log \left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )}} \left (8-12 e^{2+e^{e^x}+x}+e^{3 e^{e^x}+3 x} \left (-e^6+2 e^2 x\right )+e^{2 e^{e^x}+2 x} \left (6 e^4-4 x-4 x^2-4 e^{e^x+x} x^2\right )\right )}{\left (-8 x+12 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (-6 e^4 x+2 x^2\right )+e^{3 e^{e^x}+3 x} \left (e^6 x-e^2 x^2\right )\right ) \log ^2\left (\frac {4 x-4 e^{2+e^{e^x}+x} x+e^{2 e^{e^x}+2 x} \left (e^4 x-x^2\right )}{4-4 e^{2+e^{e^x}+x}+e^{4+2 e^{e^x}+2 x}}\right )} \, dx={\mathrm {e}}^{\frac {1}{\ln \left (\frac {4\,x-x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{2\,x}+x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4-4\,x\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x}{{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x+4}\right )}} \]
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*exp(e xp(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)