Integrand size = 207, antiderivative size = 36 \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=\log \left (e^{\frac {2}{4-e^{2 (3-x)+x}}}+x-\frac {3 e^{-x} \log (3)}{x}\right ) \] Output:
ln(exp(2/(4-exp(6-x)))+x-3*ln(3)/exp(x)/x)
Time = 0.86 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.75 \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=-\frac {2}{-4+e^{6-x}}-\log (x)+\log \left (x+e^{\frac {2}{-4+e^{6-x}}} x^2-3 e^{\frac {2}{-4+e^{6-x}}-x} \log (3)\right ) \] Input:
Integrate[(-2*E^(6 - 2/(-4 + E^(6 - x)))*x^2 + E^x*(16*x^2 + E^(12 - 2*x)* x^2 - 8*E^(6 - x)*x^2) + E^(6 - x)*(-24 - 24*x)*Log[3] + E^(12 - 2*x)*(3 + 3*x)*Log[3] + (48 + 48*x)*Log[3])/(E^(-2/(-4 + E^(6 - x)) + x)*(16*x^2 + E^(12 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^x*(16*x^3 + E^(12 - 2*x)*x^3 - 8*E ^(6 - x)*x^3) - 48*x*Log[3] - 3*E^(12 - 2*x)*x*Log[3] + 24*E^(6 - x)*x*Log [3]),x]
Output:
-2/(-4 + E^(6 - x)) - Log[x] + Log[x + E^(2/(-4 + E^(6 - x)))*x^2 - 3*E^(2 /(-4 + E^(6 - x)) - x)*Log[3]]
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.
| \(\displaystyle \int \frac {-2 e^{6-\frac {2}{e^{6-x}-4}} x^2+e^x \left (e^{12-2 x} x^2-8 e^{6-x} x^2+16 x^2\right )+e^{6-x} (-24 x-24) \log (3)+e^{12-2 x} (3 x+3) \log (3)+(48 x+48) \log (3)}{e^x \left (e^{12-2 x} x^3-8 e^{6-x} x^3+16 x^3\right )+e^{x-\frac {2}{e^{6-x}-4}} \left (e^{12-2 x} x^2-8 e^{6-x} x^2+16 x^2\right )-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)-48 x \log (3)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e^{2 x+\frac {2}{e^{6-x}-4}} \left (-2 e^{6-\frac {2}{e^{6-x}-4}} x^2+e^x \left (e^{12-2 x} x^2-8 e^{6-x} x^2+16 x^2\right )+e^{6-x} (-24 x-24) \log (3)+e^{12-2 x} (3 x+3) \log (3)+(48 x+48) \log (3)\right )}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {8 e^{2 x+6} \left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x^2}{\left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}-\frac {8 e^{2 x+6} x}{\left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}-\frac {e^{x-\frac {2}{e^{6-x}-4}} \left (e^{\frac {2}{e^{6-x}-4}} x^2+2 e^{\frac {2}{e^{6-x}-4}} x+x+1\right )}{3 \log (3)}-\frac {e^{2 x-\frac {2}{e^{6-x}-4}} \left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{3 \log (3) \left (-e^{x+\frac {2}{e^{6-x}-4}} x^2-e^x x+3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right ) \left (-e^{\frac {2}{e^{6-x}-4}+6} x^2-e^6 x+12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}-\frac {x+1}{x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-8 e^{2 \left (x+\frac {1}{e^{6-x}-4}+3\right )} x^2+e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )+x} x^2-2 e^{2 x+6} x^2+16 e^{3 x+\frac {2}{e^{6-x}-4}} x^2+3 e^{2 \left (\frac {1}{e^{6-x}-4}+6\right )} (x+1) \log (3)+48 e^{2 \left (x+\frac {1}{e^{6-x}-4}\right )} (x+1) \log (3)-24 e^{x+\frac {2}{e^{6-x}-4}+6} (x+1) \log (3)}{\left (e^6-4 e^x\right )^2 x \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{18} x}{2 \left (e^6-4 e^x\right )^2 \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{12} x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-24 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}{2 \left (e^6-4 e^x\right ) \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2}+\frac {3 e^{\frac {2}{e^{6-x}-4}} \log (3) \left (e^{\frac {6}{e^{6-x}-4}+12} x^6+3 e^{\frac {4}{e^{6-x}-4}+12} x^5+2 e^{\frac {6}{e^{6-x}-4}+12} x^5+3 e^{\frac {2}{e^{6-x}-4}+12} x^4+5 e^{\frac {4}{e^{6-x}-4}+12} x^4-24 e^{\frac {6}{e^{6-x}-4}+6} x^4 \log (3)+4 e^{\frac {2}{e^{6-x}-4}+12} x^3+e^{12} x^3-54 e^{\frac {4}{e^{6-x}-4}+6} x^3 \log (3)-48 e^{\frac {6}{e^{6-x}-4}+6} x^3 \log (3)+e^{12} x^2+144 e^{\frac {6}{e^{6-x}-4}} x^2 \log ^2(3)-30 e^{\frac {2}{e^{6-x}-4}+6} x^2 \log (3)-72 e^{\frac {4}{e^{6-x}-4}+6} x^2 \log (3)+144 e^{\frac {4}{e^{6-x}-4}} x \log ^2(3)+288 e^{\frac {6}{e^{6-x}-4}} x \log ^2(3)+144 e^{\frac {4}{e^{6-x}-4}} \log ^2(3)-24 e^{\frac {2}{e^{6-x}-4}+6} x \log (3)\right )}{\left (e^{\frac {2}{e^{6-x}-4}} x+1\right ) x \left (e^{\frac {2}{e^{6-x}-4}+6} x^2+e^6 x-12 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )^2 \left (e^{x+\frac {2}{e^{6-x}-4}} x^2+e^x x-3 e^{\frac {2}{e^{6-x}-4}} \log (3)\right )}+\frac {e^{\frac {2}{e^{6-x}-4}}}{e^{\frac {2}{e^{6-x}-4}} x+1}\right )dx\) |
Input:
Int[(-2*E^(6 - 2/(-4 + E^(6 - x)))*x^2 + E^x*(16*x^2 + E^(12 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^(6 - x)*(-24 - 24*x)*Log[3] + E^(12 - 2*x)*(3 + 3*x)* Log[3] + (48 + 48*x)*Log[3])/(E^(-2/(-4 + E^(6 - x)) + x)*(16*x^2 + E^(12 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^x*(16*x^3 + E^(12 - 2*x)*x^3 - 8*E^(6 - x)*x^3) - 48*x*Log[3] - 3*E^(12 - 2*x)*x*Log[3] + 24*E^(6 - x)*x*Log[3]),x ]
Output:
$Aborted
Time = 28.86 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.06
| method | result | size |
| parallelrisch | \(-\ln \left (x \right )+\ln \left ({\mathrm e}^{x} x^{2}+x \,{\mathrm e}^{x} {\mathrm e}^{-\frac {2}{{\mathrm e}^{-x +6}-4}}-3 \ln \left (3\right )\right )-x\) | \(38\) |
| risch | \(-\frac {{\mathrm e}^{6}}{2 \left ({\mathrm e}^{6}-4 \,{\mathrm e}^{x}\right )}+\frac {2}{{\mathrm e}^{-x +6}-4}+\ln \left (-\frac {-x^{2}+3 \ln \left (3\right ) {\mathrm e}^{-x}-{\mathrm e}^{-\frac {2}{{\mathrm e}^{-x +6}-4}} x}{x}\right )\) | \(63\) |
Input:
int((-2*x^2*exp(-x+6)*exp(x)*exp(-2/(exp(-x+6)-4))+(x^2*exp(-x+6)^2-8*x^2* exp(-x+6)+16*x^2)*exp(x)+(3*x+3)*ln(3)*exp(-x+6)^2+(-24*x-24)*ln(3)*exp(-x +6)+(48*x+48)*ln(3))/((x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*exp(x)*exp( -2/(exp(-x+6)-4))+(x^3*exp(-x+6)^2-8*x^3*exp(-x+6)+16*x^3)*exp(x)-3*x*ln(3 )*exp(-x+6)^2+24*x*ln(3)*exp(-x+6)-48*x*ln(3)),x,method=_RETURNVERBOSE)
Output:
-ln(x)+ln(exp(x)*x^2+x*exp(x)*exp(-2/(exp(-x+6)-4))-3*ln(3))-x
Time = 0.10 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.31 \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=-x + \log \left (\frac {x^{2} e^{x} + x e^{\left (\frac {x e^{6} - 2 \, {\left (2 \, x + 1\right )} e^{x}}{e^{6} - 4 \, e^{x}}\right )} - 3 \, \log \left (3\right )}{x}\right ) \] Input:
integrate((-2*x^2*exp(6-x)*exp(x)*exp(-2/(exp(6-x)-4))+(x^2*exp(6-x)^2-8*x ^2*exp(6-x)+16*x^2)*exp(x)+(3*x+3)*log(3)*exp(6-x)^2+(-24*x-24)*log(3)*exp (6-x)+(48*x+48)*log(3))/((x^2*exp(6-x)^2-8*x^2*exp(6-x)+16*x^2)*exp(x)*exp (-2/(exp(6-x)-4))+(x^3*exp(6-x)^2-8*x^3*exp(6-x)+16*x^3)*exp(x)-3*x*log(3) *exp(6-x)^2+24*x*log(3)*exp(6-x)-48*x*log(3)),x, algorithm="fricas")
Output:
-x + log((x^2*e^x + x*e^((x*e^6 - 2*(2*x + 1)*e^x)/(e^6 - 4*e^x)) - 3*log( 3))/x)
Time = 0.57 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.86 \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=\log {\left (e^{- \frac {2}{-4 + e^{6} e^{- x}}} + \frac {\left (x^{2} e^{x} - 3 \log {\left (3 \right )}\right ) e^{- x}}{x} \right )} \] Input:
integrate((-2*x**2*exp(6-x)*exp(x)*exp(-2/(exp(6-x)-4))+(x**2*exp(6-x)**2- 8*x**2*exp(6-x)+16*x**2)*exp(x)+(3*x+3)*ln(3)*exp(6-x)**2+(-24*x-24)*ln(3) *exp(6-x)+(48*x+48)*ln(3))/((x**2*exp(6-x)**2-8*x**2*exp(6-x)+16*x**2)*exp (x)*exp(-2/(exp(6-x)-4))+(x**3*exp(6-x)**2-8*x**3*exp(6-x)+16*x**3)*exp(x) -3*x*ln(3)*exp(6-x)**2+24*x*ln(3)*exp(6-x)-48*x*ln(3)),x)
Output:
log(exp(-2/(-4 + exp(6)*exp(-x))) + (x**2*exp(x) - 3*log(3))*exp(-x)/x)
Time = 0.22 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.06 \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=\log \left (\frac {{\left (x^{2} e^{x} + x e^{\left (x - \frac {2 \, e^{x}}{e^{6} - 4 \, e^{x}}\right )} - 3 \, \log \left (3\right )\right )} e^{\left (-x\right )}}{x}\right ) \] Input:
integrate((-2*x^2*exp(6-x)*exp(x)*exp(-2/(exp(6-x)-4))+(x^2*exp(6-x)^2-8*x ^2*exp(6-x)+16*x^2)*exp(x)+(3*x+3)*log(3)*exp(6-x)^2+(-24*x-24)*log(3)*exp (6-x)+(48*x+48)*log(3))/((x^2*exp(6-x)^2-8*x^2*exp(6-x)+16*x^2)*exp(x)*exp (-2/(exp(6-x)-4))+(x^3*exp(6-x)^2-8*x^3*exp(6-x)+16*x^3)*exp(x)-3*x*log(3) *exp(6-x)^2+24*x*log(3)*exp(6-x)-48*x*log(3)),x, algorithm="maxima")
Output:
log((x^2*e^x + x*e^(x - 2*e^x/(e^6 - 4*e^x)) - 3*log(3))*e^(-x)/x)
Timed out. \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=\text {Timed out} \] Input:
integrate((-2*x^2*exp(6-x)*exp(x)*exp(-2/(exp(6-x)-4))+(x^2*exp(6-x)^2-8*x ^2*exp(6-x)+16*x^2)*exp(x)+(3*x+3)*log(3)*exp(6-x)^2+(-24*x-24)*log(3)*exp (6-x)+(48*x+48)*log(3))/((x^2*exp(6-x)^2-8*x^2*exp(6-x)+16*x^2)*exp(x)*exp (-2/(exp(6-x)-4))+(x^3*exp(6-x)^2-8*x^3*exp(6-x)+16*x^3)*exp(x)-3*x*log(3) *exp(6-x)^2+24*x*log(3)*exp(6-x)-48*x*log(3)),x, algorithm="giac")
Output:
Timed out
Timed out. \[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=\int \frac {\ln \left (3\right )\,\left (48\,x+48\right )+{\mathrm {e}}^x\,\left (x^2\,{\mathrm {e}}^{12-2\,x}-8\,x^2\,{\mathrm {e}}^{6-x}+16\,x^2\right )-2\,x^2\,{\mathrm {e}}^{6-\frac {2}{{\mathrm {e}}^{6-x}-4}}+{\mathrm {e}}^{12-2\,x}\,\ln \left (3\right )\,\left (3\,x+3\right )-{\mathrm {e}}^{6-x}\,\ln \left (3\right )\,\left (24\,x+24\right )}{{\mathrm {e}}^x\,\left (x^3\,{\mathrm {e}}^{12-2\,x}-8\,x^3\,{\mathrm {e}}^{6-x}+16\,x^3\right )-48\,x\,\ln \left (3\right )+{\mathrm {e}}^{x-\frac {2}{{\mathrm {e}}^{6-x}-4}}\,\left (x^2\,{\mathrm {e}}^{12-2\,x}-8\,x^2\,{\mathrm {e}}^{6-x}+16\,x^2\right )+24\,x\,{\mathrm {e}}^{6-x}\,\ln \left (3\right )-3\,x\,{\mathrm {e}}^{12-2\,x}\,\ln \left (3\right )} \,d x \] Input:
int((log(3)*(48*x + 48) + exp(x)*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 1 6*x^2) + exp(12 - 2*x)*log(3)*(3*x + 3) - exp(6 - x)*log(3)*(24*x + 24) - 2*x^2*exp(-2/(exp(6 - x) - 4))*exp(6 - x)*exp(x))/(exp(x)*(x^3*exp(12 - 2* x) - 8*x^3*exp(6 - x) + 16*x^3) - 48*x*log(3) + exp(-2/(exp(6 - x) - 4))*e xp(x)*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 16*x^2) + 24*x*exp(6 - x)*lo g(3) - 3*x*exp(12 - 2*x)*log(3)),x)
Output:
int((log(3)*(48*x + 48) + exp(x)*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 1 6*x^2) - 2*x^2*exp(6 - 2/(exp(6 - x) - 4)) + exp(12 - 2*x)*log(3)*(3*x + 3 ) - exp(6 - x)*log(3)*(24*x + 24))/(exp(x)*(x^3*exp(12 - 2*x) - 8*x^3*exp( 6 - x) + 16*x^3) - 48*x*log(3) + exp(x - 2/(exp(6 - x) - 4))*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 16*x^2) + 24*x*exp(6 - x)*log(3) - 3*x*exp(12 - 2*x)*log(3)), x)
\[ \int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} \left (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2\right )+e^x \left (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3\right )-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx=\text {too large to display} \] Input:
int((-2*x^2*exp(6-x)*exp(x)*exp(-2/(exp(6-x)-4))+(x^2*exp(6-x)^2-8*x^2*exp (6-x)+16*x^2)*exp(x)+(3*x+3)*log(3)*exp(6-x)^2+(-24*x-24)*log(3)*exp(6-x)+ (48*x+48)*log(3))/((x^2*exp(6-x)^2-8*x^2*exp(6-x)+16*x^2)*exp(x)*exp(-2/(e xp(6-x)-4))+(x^3*exp(6-x)^2-8*x^3*exp(6-x)+16*x^3)*exp(x)-3*x*log(3)*exp(6 -x)^2+24*x*log(3)*exp(6-x)-48*x*log(3)),x)
Output:
48*int(e**(2*x)/(16*e**((12*e**x*x + 2*e**x - 3*e**6*x)/(4*e**x - e**6))*x **2 - 8*e**((8*e**x*x + 2*e**x - 2*e**6*x)/(4*e**x - e**6))*e**6*x**2 + e* *((4*e**x*x + 2*e**x - e**6*x)/(4*e**x - e**6))*e**12*x**2 + 16*e**(3*x)*x **3 - 48*e**(2*x)*log(3)*x - 8*e**(2*x)*e**6*x**3 + 24*e**x*log(3)*e**6*x + e**x*e**12*x**3 - 3*log(3)*e**12*x),x)*log(3) + 48*int(e**(2*x)/(16*e**( (12*e**x*x + 2*e**x - 3*e**6*x)/(4*e**x - e**6))*x - 8*e**((8*e**x*x + 2*e **x - 2*e**6*x)/(4*e**x - e**6))*e**6*x + e**((4*e**x*x + 2*e**x - e**6*x) /(4*e**x - e**6))*e**12*x + 16*e**(3*x)*x**2 - 48*e**(2*x)*log(3) - 8*e**( 2*x)*e**6*x**2 + 24*e**x*log(3)*e**6 + e**x*e**12*x**2 - 3*log(3)*e**12),x )*log(3) - 24*int(e**x/(16*e**((12*e**x*x + 2*e**x - 3*e**6*x)/(4*e**x - e **6))*x**2 - 8*e**((8*e**x*x + 2*e**x - 2*e**6*x)/(4*e**x - e**6))*e**6*x* *2 + e**((4*e**x*x + 2*e**x - e**6*x)/(4*e**x - e**6))*e**12*x**2 + 16*e** (3*x)*x**3 - 48*e**(2*x)*log(3)*x - 8*e**(2*x)*e**6*x**3 + 24*e**x*log(3)* e**6*x + e**x*e**12*x**3 - 3*log(3)*e**12*x),x)*log(3)*e**6 - 24*int(e**x/ (16*e**((12*e**x*x + 2*e**x - 3*e**6*x)/(4*e**x - e**6))*x - 8*e**((8*e**x *x + 2*e**x - 2*e**6*x)/(4*e**x - e**6))*e**6*x + e**((4*e**x*x + 2*e**x - e**6*x)/(4*e**x - e**6))*e**12*x + 16*e**(3*x)*x**2 - 48*e**(2*x)*log(3) - 8*e**(2*x)*e**6*x**2 + 24*e**x*log(3)*e**6 + e**x*e**12*x**2 - 3*log(3)* e**12),x)*log(3)*e**6 - 2*int((e**((8*e**x*x + 2*e**x - 2*e**6*x)/(4*e**x - e**6))*x)/(16*e**((12*e**x*x + 2*e**x - 3*e**6*x)/(4*e**x - e**6))*x ...