Integrand size = 134, antiderivative size = 24 \begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=e^{\frac {\left (1+5 e^{-x}-e^x+\log (2)\right )^2}{x}} \end {dmath*}
\begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=\int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx \end {dmath*}
Integrate[(E^(-2*x + (25 + E^(4*x) + E^(3*x)*(-2 - 2*Log[2]) + E^x*(10 + 1 0*Log[2]) + E^(2*x)*(-9 + 2*Log[2] + Log[2]^2))/(E^(2*x)*x))*(-25 - 50*x + E^(4*x)*(-1 + 2*x) + E^x*(-10 - 10*x + (-10 - 10*x)*Log[2]) + E^(3*x)*(2 - 2*x + (2 - 2*x)*Log[2]) + E^(2*x)*(9 - 2*Log[2] - Log[2]^2)))/x^2,x]
Integrate[(E^(-2*x + (25 + E^(4*x) + E^(3*x)*(-2 - 2*Log[2]) + E^x*(10 + 1 0*Log[2]) + E^(2*x)*(-9 + 2*Log[2] + Log[2]^2))/(E^(2*x)*x))*(-25 - 50*x + E^(4*x)*(-1 + 2*x) + E^x*(-10 - 10*x + (-10 - 10*x)*Log[2]) + E^(3*x)*(2 - 2*x + (2 - 2*x)*Log[2]) + E^(2*x)*(9 - 2*Log[2] - Log[2]^2)))/x^2, 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.
| \(\displaystyle \int \frac {\left (-50 x+e^{4 x} (2 x-1)+e^{2 x} \left (9-\log ^2(2)-2 \log (2)\right )+e^x (-10 x+(-10 x-10) \log (2)-10)+e^{3 x} (-2 x+(2-2 x) \log (2)+2)-25\right ) \exp \left (\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}-2 x\right )}{x^2} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-2 e^{2 x} x-10 x+e^{2 x}-e^x (1+\log (2))-5\right ) \left (-e^{2 x}+e^x (1+\log (2))+5\right ) \exp \left (\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}-2 x\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2 (x-1) (1+\log (2)) \exp \left (x+\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}\right )}{x^2}+\frac {(2 x-1) \exp \left (2 x+\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}\right )}{x^2}-\frac {25 (2 x+1) \exp \left (\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}-2 x\right )}{x^2}-\frac {\left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}\right )}{x^2}-\frac {10 (x+1) (1+\log (2)) \exp \left (\frac {e^{-2 x} \left (e^{4 x}+e^{2 x} \left (-9+\log ^2(2)+2 \log (2)\right )+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+25\right )}{x}-x\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (e^{4 x} (2 x-1)-25 (2 x+1)-e^{2 x} \left (-9+\log ^2(2)+\log (4)\right )-e^{3 x} (x-1) (2+\log (4))-10 e^x (x+1) (1+\log (2))\right ) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (x-1) (2+\log (4)) \exp \left (x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}+\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x-1) \exp \left (2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {25\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} (2 x+1) \exp \left (-2 x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}} \left (-9+\log ^2(2)+\log (4)\right ) \exp \left (\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}-\frac {5\ 2^{\frac {2 e^{-x} \left (e^x+5\right )}{x}+1} (x+1) (1+\log (2)) \exp \left (-x+\frac {25 e^{-2 x}}{x}+\frac {10 e^{-x}}{x}+\frac {e^{2 x}}{x}-\frac {9 \left (1-\frac {\log ^2(2)}{9}\right )}{x}-\frac {e^x (2+\log (4))}{x}\right )}{x^2}\right )dx\) |
Int[(E^(-2*x + (25 + E^(4*x) + E^(3*x)*(-2 - 2*Log[2]) + E^x*(10 + 10*Log[ 2]) + E^(2*x)*(-9 + 2*Log[2] + Log[2]^2))/(E^(2*x)*x))*(-25 - 50*x + E^(4* x)*(-1 + 2*x) + E^x*(-10 - 10*x + (-10 - 10*x)*Log[2]) + E^(3*x)*(2 - 2*x + (2 - 2*x)*Log[2]) + E^(2*x)*(9 - 2*Log[2] - Log[2]^2)))/x^2,x]
3.3.14.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(50\) vs. \(2(21)=42\).
Time = 5.95 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left ({\mathrm e}^{4 x}+\left (-2 \ln \left (2\right )-2\right ) {\mathrm e}^{3 x}+\left (\ln \left (2\right )^{2}+2 \ln \left (2\right )-9\right ) {\mathrm e}^{2 x}+\left (10 \ln \left (2\right )+10\right ) {\mathrm e}^{x}+25\right ) {\mathrm e}^{-2 x}}{x}}\) | \(51\) |
| risch | \(4^{\frac {1}{x}} \left (\frac {1}{4}\right )^{\frac {{\mathrm e}^{x}}{x}} 1024^{\frac {{\mathrm e}^{-x}}{x}} {\mathrm e}^{\frac {10 \,{\mathrm e}^{-x}+\ln \left (2\right )^{2}+{\mathrm e}^{2 x}-2 \,{\mathrm e}^{x}-9+25 \,{\mathrm e}^{-2 x}}{x}}\) | \(56\) |
int(((-1+2*x)*exp(x)^4+((2-2*x)*ln(2)-2*x+2)*exp(x)^3+(-ln(2)^2-2*ln(2)+9) *exp(x)^2+((-10*x-10)*ln(2)-10*x-10)*exp(x)-50*x-25)*exp((exp(x)^4+(-2*ln( 2)-2)*exp(x)^3+(ln(2)^2+2*ln(2)-9)*exp(x)^2+(10*ln(2)+10)*exp(x)+25)/x/exp (x)^2)/exp(x)^2/x^2,x,method=_RETURNVERBOSE)
exp((exp(x)^4+(-2*ln(2)-2)*exp(x)^3+(ln(2)^2+2*ln(2)-9)*exp(x)^2+(10*ln(2) +10)*exp(x)+25)/x/exp(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (21) = 42\).
Time = 0.30 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.58 \begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=e^{\left (2 \, x - \frac {{\left (2 \, {\left (\log \left (2\right ) + 1\right )} e^{\left (3 \, x\right )} + {\left (2 \, x^{2} - \log \left (2\right )^{2} - 2 \, \log \left (2\right ) + 9\right )} e^{\left (2 \, x\right )} - 10 \, {\left (\log \left (2\right ) + 1\right )} e^{x} - e^{\left (4 \, x\right )} - 25\right )} e^{\left (-2 \, x\right )}}{x}\right )} \end {dmath*}
integrate(((-1+2*x)*exp(x)^4+((2-2*x)*log(2)-2*x+2)*exp(x)^3+(-log(2)^2-2* log(2)+9)*exp(x)^2+((-10*x-10)*log(2)-10*x-10)*exp(x)-50*x-25)*exp((exp(x) ^4+(-2*log(2)-2)*exp(x)^3+(log(2)^2+2*log(2)-9)*exp(x)^2+(10*log(2)+10)*ex p(x)+25)/x/exp(x)^2)/exp(x)^2/x^2,x, algorithm=\
e^(2*x - (2*(log(2) + 1)*e^(3*x) + (2*x^2 - log(2)^2 - 2*log(2) + 9)*e^(2* x) - 10*(log(2) + 1)*e^x - e^(4*x) - 25)*e^(-2*x)/x)
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (17) = 34\).
Time = 0.31 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.25 \begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=e^{\frac {\left (e^{4 x} + \left (-2 - 2 \log {\left (2 \right )}\right ) e^{3 x} + \left (-9 + \log {\left (2 \right )}^{2} + 2 \log {\left (2 \right )}\right ) e^{2 x} + \left (10 \log {\left (2 \right )} + 10\right ) e^{x} + 25\right ) e^{- 2 x}}{x}} \end {dmath*}
integrate(((-1+2*x)*exp(x)**4+((2-2*x)*ln(2)-2*x+2)*exp(x)**3+(-ln(2)**2-2 *ln(2)+9)*exp(x)**2+((-10*x-10)*ln(2)-10*x-10)*exp(x)-50*x-25)*exp((exp(x) **4+(-2*ln(2)-2)*exp(x)**3+(ln(2)**2+2*ln(2)-9)*exp(x)**2+(10*ln(2)+10)*ex p(x)+25)/x/exp(x)**2)/exp(x)**2/x**2,x)
exp((exp(4*x) + (-2 - 2*log(2))*exp(3*x) + (-9 + log(2)**2 + 2*log(2))*exp (2*x) + (10*log(2) + 10)*exp(x) + 25)*exp(-2*x)/x)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (21) = 42\).
Time = 0.41 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.12 \begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=e^{\left (\frac {10 \, e^{\left (-x\right )} \log \left (2\right )}{x} - \frac {2 \, e^{x} \log \left (2\right )}{x} + \frac {\log \left (2\right )^{2}}{x} + \frac {e^{\left (2 \, x\right )}}{x} + \frac {10 \, e^{\left (-x\right )}}{x} + \frac {25 \, e^{\left (-2 \, x\right )}}{x} - \frac {2 \, e^{x}}{x} + \frac {2 \, \log \left (2\right )}{x} - \frac {9}{x}\right )} \end {dmath*}
integrate(((-1+2*x)*exp(x)^4+((2-2*x)*log(2)-2*x+2)*exp(x)^3+(-log(2)^2-2* log(2)+9)*exp(x)^2+((-10*x-10)*log(2)-10*x-10)*exp(x)-50*x-25)*exp((exp(x) ^4+(-2*log(2)-2)*exp(x)^3+(log(2)^2+2*log(2)-9)*exp(x)^2+(10*log(2)+10)*ex p(x)+25)/x/exp(x)^2)/exp(x)^2/x^2,x, algorithm=\
e^(10*e^(-x)*log(2)/x - 2*e^x*log(2)/x + log(2)^2/x + e^(2*x)/x + 10*e^(-x )/x + 25*e^(-2*x)/x - 2*e^x/x + 2*log(2)/x - 9/x)
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (21) = 42\).
Time = 0.29 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.58 \begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=e^{\left (\frac {{\left (e^{\left (2 \, x\right )} \log \left (2\right )^{2} - 2 \, e^{\left (3 \, x\right )} \log \left (2\right ) + 2 \, e^{\left (2 \, x\right )} \log \left (2\right ) + 10 \, e^{x} \log \left (2\right ) + e^{\left (4 \, x\right )} - 2 \, e^{\left (3 \, x\right )} - 9 \, e^{\left (2 \, x\right )} + 10 \, e^{x} + 25\right )} e^{\left (-2 \, x\right )}}{x}\right )} \end {dmath*}
integrate(((-1+2*x)*exp(x)^4+((2-2*x)*log(2)-2*x+2)*exp(x)^3+(-log(2)^2-2* log(2)+9)*exp(x)^2+((-10*x-10)*log(2)-10*x-10)*exp(x)-50*x-25)*exp((exp(x) ^4+(-2*log(2)-2)*exp(x)^3+(log(2)^2+2*log(2)-9)*exp(x)^2+(10*log(2)+10)*ex p(x)+25)/x/exp(x)^2)/exp(x)^2/x^2,x, algorithm=\
e^((e^(2*x)*log(2)^2 - 2*e^(3*x)*log(2) + 2*e^(2*x)*log(2) + 10*e^x*log(2) + e^(4*x) - 2*e^(3*x) - 9*e^(2*x) + 10*e^x + 25)*e^(-2*x)/x)
Time = 14.33 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.04 \begin {dmath*} \int \frac {e^{-2 x+\frac {e^{-2 x} \left (25+e^{4 x}+e^{3 x} (-2-2 \log (2))+e^x (10+10 \log (2))+e^{2 x} \left (-9+2 \log (2)+\log ^2(2)\right )\right )}{x}} \left (-25-50 x+e^{4 x} (-1+2 x)+e^x (-10-10 x+(-10-10 x) \log (2))+e^{3 x} (2-2 x+(2-2 x) \log (2))+e^{2 x} \left (9-2 \log (2)-\log ^2(2)\right )\right )}{x^2} \, dx=4^{\frac {{\mathrm {e}}^{-x}\,\left ({\mathrm {e}}^x-{\mathrm {e}}^{2\,x}+5\right )}{x}}\,{\mathrm {e}}^{\frac {{\ln \left (2\right )}^2}{x}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{-\frac {9}{x}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{x}}\,{\mathrm {e}}^{\frac {10\,{\mathrm {e}}^{-x}}{x}}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{-2\,x}}{x}} \end {dmath*}
int(-(exp((exp(-2*x)*(exp(4*x) + exp(x)*(10*log(2) + 10) + exp(2*x)*(2*log (2) + log(2)^2 - 9) - exp(3*x)*(2*log(2) + 2) + 25))/x)*exp(-2*x)*(50*x + exp(x)*(10*x + log(2)*(10*x + 10) + 10) + exp(2*x)*(2*log(2) + log(2)^2 - 9) - exp(4*x)*(2*x - 1) + exp(3*x)*(2*x + log(2)*(2*x - 2) - 2) + 25))/x^2 ,x)