Integrand size = 201, antiderivative size = 30 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{e^{\left (1+x-\log ^2(2)\right ) \left (\frac {18}{(1-x)^2}+\log \left (\frac {x}{2}\right )\right )}} \] Output:
exp(exp((x+1-ln(2)^2)*(18/(1-x)^2+ln(1/2*x))))
\[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=\int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx \] Input:
Integrate[(E^(E^((18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2)) + (18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2)) *(-1 - 52*x - 18*x^2 - 2*x^3 + x^4 + (1 + 33*x + 3*x^2 - x^3)*Log[2]^2 + ( -x + 3*x^2 - 3*x^3 + x^4)*Log[x/2]))/(-x + 3*x^2 - 3*x^3 + x^4),x]
Output:
Integrate[(E^(E^((18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2)) + (18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2)) *(-1 - 52*x - 18*x^2 - 2*x^3 + x^4 + (1 + 33*x + 3*x^2 - x^3)*Log[2]^2 + ( -x + 3*x^2 - 3*x^3 + x^4)*Log[x/2]))/(-x + 3*x^2 - 3*x^3 + x^4), x]
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.
| \(\displaystyle \int \frac {\left (x^4-2 x^3-18 x^2+\left (-x^3+3 x^2+33 x+1\right ) \log ^2(2)+\left (x^4-3 x^3+3 x^2-x\right ) \log \left (\frac {x}{2}\right )-52 x-1\right ) \exp \left (\exp \left (\frac {\left (x^3-x^2+\left (-x^2+2 x-1\right ) \log ^2(2)-x+1\right ) \log \left (\frac {x}{2}\right )+18 x+18-18 \log ^2(2)}{x^2-2 x+1}\right )+\frac {\left (x^3-x^2+\left (-x^2+2 x-1\right ) \log ^2(2)-x+1\right ) \log \left (\frac {x}{2}\right )+18 x+18-18 \log ^2(2)}{x^2-2 x+1}\right )}{x^4-3 x^3+3 x^2-x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (x^4-2 x^3-18 x^2+\left (-x^3+3 x^2+33 x+1\right ) \log ^2(2)+\left (x^4-3 x^3+3 x^2-x\right ) \log \left (\frac {x}{2}\right )-52 x-1\right ) \exp \left (\exp \left (\frac {\left (x^3-x^2+\left (-x^2+2 x-1\right ) \log ^2(2)-x+1\right ) \log \left (\frac {x}{2}\right )+18 x+18-18 \log ^2(2)}{x^2-2 x+1}\right )+\frac {\left (x^3-x^2+\left (-x^2+2 x-1\right ) \log ^2(2)-x+1\right ) \log \left (\frac {x}{2}\right )+18 x+18-18 \log ^2(2)}{x^2-2 x+1}\right )}{x \left (x^3-3 x^2+3 x-1\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {\left (x^4-2 x^3-18 x^2+\left (-x^3+3 x^2+33 x+1\right ) \log ^2(2)+\left (x^4-3 x^3+3 x^2-x\right ) \log \left (\frac {x}{2}\right )-52 x-1\right ) \exp \left (\exp \left (\frac {\left (x^3-x^2+\left (-x^2+2 x-1\right ) \log ^2(2)-x+1\right ) \log \left (\frac {x}{2}\right )+18 x+18-18 \log ^2(2)}{x^2-2 x+1}\right )+\frac {\left (x^3-x^2+\left (-x^2+2 x-1\right ) \log ^2(2)-x+1\right ) \log \left (\frac {x}{2}\right )+18 x+18-18 \log ^2(2)}{x^2-2 x+1}\right )}{(x-1)^3 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}} x^3}{(x-1)^3}-\frac {2 e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}} x^2}{(x-1)^3}-\frac {18 e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}} x}{(x-1)^3}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}} \log \left (\frac {x}{2}\right )-\frac {52 e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}}}{(x-1)^3}-\frac {e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}}}{(x-1)^3 x}-\frac {e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}+e^{\frac {18 x+\left (x^3-x^2-x+\left (-x^2+2 x-1\right ) \log ^2(2)+1\right ) \log \left (\frac {x}{2}\right )-18 \log ^2(2)+18}{x^2-2 x+1}}} \left (x^3-3 x^2-33 x-1\right ) \log ^2(2)}{(x-1)^3 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1+\log ^2(2)} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {\left (1-\log ^2(2)\right ) 2^{-x-1+\log ^2(2)} x^{x-\log ^2(2)} \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )}{(x-1)^3}+2^{-x-1+\log ^2(2)} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )+\frac {\left (33 \log ^2(2)-52\right ) 2^{-x-1+\log ^2(2)} x^{x+1-\log ^2(2)} \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )}{(x-1)^3}+\frac {3 \left (\log ^2(2)-6\right ) 2^{-x-1+\log ^2(2)} x^{x+2-\log ^2(2)} \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )}{(x-1)^3}-\frac {\left (2+\log ^2(2)\right ) 2^{-x-1+\log ^2(2)} x^{x+3-\log ^2(2)} \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )}{(x-1)^3}+\frac {2^{-x-1+\log ^2(2)} x^{x+4-\log ^2(2)} \exp \left (\frac {(x-1)^2 2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+18 x+18 \left (1-\log ^2(2)\right )}{(x-1)^2}\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{-x-1} \left (1-\log ^2(2)\right ) x^{x-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+2^{-x-1} \log \left (\frac {x}{2}\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )+\frac {2^{-x-1} \left (33 \log ^2(2)-52\right ) x^{x+1-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {3\ 2^{-x-1} \left (\log ^2(2)-6\right ) x^{x+2-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}-\frac {2^{-x-1} \left (2+\log ^2(2)\right ) x^{x+3-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}+\frac {2^{-x-1} x^{x+4-\log ^2(2)} \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(x-1)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-x-1} x^{x-\log ^2(2)} \left (-x^4+x^3 \left (2+\log ^2(2)\right )-3 x^2 \left (\log ^2(2)-6\right )-x \left (33 \log ^2(2)-52\right )-(x-1)^3 x \log \left (\frac {x}{2}\right )+1-\log ^2(2)\right ) \exp \left (2^{-x-1+\log ^2(2)} e^{\frac {18 \left (x+1-\log ^2(2)\right )}{(x-1)^2}} x^{x+1-\log ^2(2)}+\frac {18 x}{(x-1)^2}+\frac {18 \left (1-\log ^2(2)\right )}{(x-1)^2}+\log ^3(2)\right )}{(1-x)^3}dx\) |
Input:
Int[(E^(E^((18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2 )*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2)) + (18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2))*(-1 - 52*x - 18*x^2 - 2*x^3 + x^4 + (1 + 33*x + 3*x^2 - x^3)*Log[2]^2 + (-x + 3 *x^2 - 3*x^3 + x^4)*Log[x/2]))/(-x + 3*x^2 - 3*x^3 + x^4),x]
Output:
$Aborted
Time = 123.53 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.33
| method | result | size |
| risch | \({\mathrm e}^{{\mathrm e}^{-\frac {\left (\ln \left (2\right )^{2}-x -1\right ) \left (\ln \left (\frac {x}{2}\right ) x^{2}-2 x \ln \left (\frac {x}{2}\right )+\ln \left (\frac {x}{2}\right )+18\right )}{\left (-1+x \right )^{2}}}}\) | \(40\) |
| parallelrisch | \({\mathrm e}^{{\mathrm e}^{\frac {\left (\left (-x^{2}+2 x -1\right ) \ln \left (2\right )^{2}+x^{3}-x^{2}-x +1\right ) \ln \left (\frac {x}{2}\right )-18 \ln \left (2\right )^{2}+18 x +18}{x^{2}-2 x +1}}}\) | \(58\) |
Input:
int(((x^4-3*x^3+3*x^2-x)*ln(1/2*x)+(-x^3+3*x^2+33*x+1)*ln(2)^2+x^4-2*x^3-1 8*x^2-52*x-1)*exp((((-x^2+2*x-1)*ln(2)^2+x^3-x^2-x+1)*ln(1/2*x)-18*ln(2)^2 +18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*ln(2)^2+x^3-x^2-x+1)*ln(1/2* x)-18*ln(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x,method=_RETURNV ERBOSE)
Output:
exp(exp(-(ln(2)^2-x-1)*(ln(1/2*x)*x^2-2*x*ln(1/2*x)+ln(1/2*x)+18)/(-1+x)^2 ))
Leaf count of result is larger than twice the leaf count of optimal. 177 vs. \(2 (25) = 50\).
Time = 0.10 (sec) , antiderivative size = 177, normalized size of antiderivative = 5.90 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{\left (\frac {{\left (x^{2} - 2 \, x + 1\right )} e^{\left (-\frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1}\right )} - 18 \, \log \left (2\right )^{2} + {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) + 18 \, x + 18}{x^{2} - 2 \, x + 1} + \frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1}\right )} \] Input:
integrate(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4 -2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)- 18*log(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2- x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x, algorithm="fricas")
Output:
e^(((x^2 - 2*x + 1)*e^(-(18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x ^2 - x + 1)*log(1/2*x) - 18*x - 18)/(x^2 - 2*x + 1)) - 18*log(2)^2 + (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) + 18*x + 18)/(x^2 - 2 *x + 1) + (18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*lo g(1/2*x) - 18*x - 18)/(x^2 - 2*x + 1))
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (22) = 44\).
Time = 2.59 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.70 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{e^{\frac {18 x + \left (x^{3} - x^{2} - x + \left (- x^{2} + 2 x - 1\right ) \log {\left (2 \right )}^{2} + 1\right ) \log {\left (\frac {x}{2} \right )} - 18 \log {\left (2 \right )}^{2} + 18}{x^{2} - 2 x + 1}}} \] Input:
integrate(((x**4-3*x**3+3*x**2-x)*ln(1/2*x)+(-x**3+3*x**2+33*x+1)*ln(2)**2 +x**4-2*x**3-18*x**2-52*x-1)*exp((((-x**2+2*x-1)*ln(2)**2+x**3-x**2-x+1)*l n(1/2*x)-18*ln(2)**2+18*x+18)/(x**2-2*x+1))*exp(exp((((-x**2+2*x-1)*ln(2)* *2+x**3-x**2-x+1)*ln(1/2*x)-18*ln(2)**2+18*x+18)/(x**2-2*x+1)))/(x**4-3*x* *3+3*x**2-x),x)
Output:
exp(exp((18*x + (x**3 - x**2 - x + (-x**2 + 2*x - 1)*log(2)**2 + 1)*log(x/ 2) - 18*log(2)**2 + 18)/(x**2 - 2*x + 1)))
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (25) = 50\).
Time = 2.28 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.07 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{\left (\frac {1}{2} \, x e^{\left (\log \left (2\right )^{3} - \log \left (2\right )^{2} \log \left (x\right ) - x \log \left (2\right ) + x \log \left (x\right ) - \frac {18 \, \log \left (2\right )^{2}}{x^{2} - 2 \, x + 1} + \frac {36}{x^{2} - 2 \, x + 1} + \frac {18}{x - 1}\right )}\right )} \] Input:
integrate(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4 -2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)- 18*log(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2- x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x, algorithm="maxima")
Output:
e^(1/2*x*e^(log(2)^3 - log(2)^2*log(x) - x*log(2) + x*log(x) - 18*log(2)^2 /(x^2 - 2*x + 1) + 36/(x^2 - 2*x + 1) + 18/(x - 1)))
\[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=\int { \frac {{\left (x^{4} - 2 \, x^{3} - {\left (x^{3} - 3 \, x^{2} - 33 \, x - 1\right )} \log \left (2\right )^{2} - 18 \, x^{2} + {\left (x^{4} - 3 \, x^{3} + 3 \, x^{2} - x\right )} \log \left (\frac {1}{2} \, x\right ) - 52 \, x - 1\right )} e^{\left (-\frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1} + e^{\left (-\frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1}\right )}\right )}}{x^{4} - 3 \, x^{3} + 3 \, x^{2} - x} \,d x } \] Input:
integrate(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4 -2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)- 18*log(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2- x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x, algorithm="giac")
Output:
integrate((x^4 - 2*x^3 - (x^3 - 3*x^2 - 33*x - 1)*log(2)^2 - 18*x^2 + (x^4 - 3*x^3 + 3*x^2 - x)*log(1/2*x) - 52*x - 1)*e^(-(18*log(2)^2 - (x^3 - (x^ 2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) - 18*x - 18)/(x^2 - 2*x + 1) + e^(-(18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log (1/2*x) - 18*x - 18)/(x^2 - 2*x + 1)))/(x^4 - 3*x^3 + 3*x^2 - x), x)
Time = 3.61 (sec) , antiderivative size = 159, normalized size of antiderivative = 5.30 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx={\mathrm {e}}^{{\left (\frac {1}{2}\right )}^{x+1}\,x^{\frac {x^2}{x-1}-\frac {x+x^2\,{\ln \left (2\right )}^2-2\,x\,{\ln \left (2\right )}^2+{\ln \left (2\right )}^2}{x^2-2\,x+1}+\frac {1}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {18}{x^2-2\,x+1}}\,{\mathrm {e}}^{-\frac {2\,x\,{\ln \left (2\right )}^3}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {18\,x}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {x^2\,{\ln \left (2\right )}^3}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {{\ln \left (2\right )}^3}{x^2-2\,x+1}}\,{\mathrm {e}}^{-\frac {18\,{\ln \left (2\right )}^2}{x^2-2\,x+1}}} \] Input:
int((exp((18*x - log(x/2)*(x + log(2)^2*(x^2 - 2*x + 1) + x^2 - x^3 - 1) - 18*log(2)^2 + 18)/(x^2 - 2*x + 1))*exp(exp((18*x - log(x/2)*(x + log(2)^2 *(x^2 - 2*x + 1) + x^2 - x^3 - 1) - 18*log(2)^2 + 18)/(x^2 - 2*x + 1)))*(5 2*x + log(x/2)*(x - 3*x^2 + 3*x^3 - x^4) - log(2)^2*(33*x + 3*x^2 - x^3 + 1) + 18*x^2 + 2*x^3 - x^4 + 1))/(x - 3*x^2 + 3*x^3 - x^4),x)
Output:
exp((1/2)^(x + 1)*x^(x^2/(x - 1) - (x + x^2*log(2)^2 - 2*x*log(2)^2 + log( 2)^2)/(x^2 - 2*x + 1) + 1/(x^2 - 2*x + 1))*exp(18/(x^2 - 2*x + 1))*exp(-(2 *x*log(2)^3)/(x^2 - 2*x + 1))*exp((18*x)/(x^2 - 2*x + 1))*exp((x^2*log(2)^ 3)/(x^2 - 2*x + 1))*exp(log(2)^3/(x^2 - 2*x + 1))*exp(-(18*log(2)^2)/(x^2 - 2*x + 1)))
\[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=\text {too large to display} \] Input:
int(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4-2*x^3 -18*x^2-52*x-1)*exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)-18*log (2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^2-x+1)*l og(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x)
Output:
(2**(log(2)**2)*(int((x**x*e**((36*x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x + 36*x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1 ))*2**x + x**x*e**((18*x + 18)/(x**2 - 2*x + 1))*2**(log(2)**2)*x**3 + x** x*e**((18*x + 18)/(x**2 - 2*x + 1))*2**(log(2)**2)*x)/(2*x**(log(2)**2)*e* *((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x**2 - 4*x**(log(2)**2)*e**((18*lo g(2)**2)/(x**2 - 2*x + 1))*2**x*x + 2*x**(log(2)**2)*e**((18*log(2)**2)/(x **2 - 2*x + 1))*2**x))*x**4)/(x**(log(2)**2)*e**((18*x**(log(2)**2)*e**((1 8*log(2)**2)/(x**2 - 2*x + 1))*2**x*log(2)**2 + x**x*e**((18*x + 18)/(x**2 - 2*x + 1))*2**(log(2)**2)*x**2)/(x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x**2 - 2*x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x + x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x))*2 **x*x**3 - 3*x**(log(2)**2)*e**((18*x**(log(2)**2)*e**((18*log(2)**2)/(x** 2 - 2*x + 1))*2**x*log(2)**2 + x**x*e**((18*x + 18)/(x**2 - 2*x + 1))*2**( log(2)**2)*x**2)/(x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x *x**2 - 2*x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x + x** (log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x))*2**x*x**2 + 3*x**( log(2)**2)*e**((18*x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2** x*log(2)**2 + x**x*e**((18*x + 18)/(x**2 - 2*x + 1))*2**(log(2)**2)*x**2)/ (x**(log(2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x**2 - 2*x**(log (2)**2)*e**((18*log(2)**2)/(x**2 - 2*x + 1))*2**x*x + x**(log(2)**2)*e*...