Integrand size = 334, antiderivative size = 31 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{e^{e^4 (1+3 x) \left (\frac {5 e^{-x}}{x}+x-\log (2)\right )^2}} \] Output:
exp(exp((1+3*x)*exp(2)^2*(5/exp(x)/x-ln(2)+x)^2))
\[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=\int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx \] Input:
Integrate[(E^(E^((E^4*(25 + 75*x) + E^x*(E^4*(10*x^2 + 30*x^3) + E^4*(-10* x - 30*x^2)*Log[2]) + E^(2*x)*(E^4*(x^4 + 3*x^5) + E^4*(-2*x^3 - 6*x^4)*Lo g[2] + E^4*(x^2 + 3*x^3)*Log[2]^2))/(E^(2*x)*x^2)) - 2*x + (E^4*(25 + 75*x ) + E^x*(E^4*(10*x^2 + 30*x^3) + E^4*(-10*x - 30*x^2)*Log[2]) + E^(2*x)*(E ^4*(x^4 + 3*x^5) + E^4*(-2*x^3 - 6*x^4)*Log[2] + E^4*(x^2 + 3*x^3)*Log[2]^ 2))/(E^(2*x)*x^2))*(E^4*(-50 - 125*x - 150*x^2) + E^x*(E^4*(20*x^3 - 30*x^ 4) + E^4*(10*x + 10*x^2 + 30*x^3)*Log[2]) + E^(2*x)*(E^4*(2*x^4 + 9*x^5) + E^4*(-2*x^3 - 12*x^4)*Log[2] + 3*E^4*x^3*Log[2]^2)))/x^3,x]
Output:
Integrate[(E^(E^((E^4*(25 + 75*x) + E^x*(E^4*(10*x^2 + 30*x^3) + E^4*(-10* x - 30*x^2)*Log[2]) + E^(2*x)*(E^4*(x^4 + 3*x^5) + E^4*(-2*x^3 - 6*x^4)*Lo g[2] + E^4*(x^2 + 3*x^3)*Log[2]^2))/(E^(2*x)*x^2)) - 2*x + (E^4*(25 + 75*x ) + E^x*(E^4*(10*x^2 + 30*x^3) + E^4*(-10*x - 30*x^2)*Log[2]) + E^(2*x)*(E ^4*(x^4 + 3*x^5) + E^4*(-2*x^3 - 6*x^4)*Log[2] + E^4*(x^2 + 3*x^3)*Log[2]^ 2))/(E^(2*x)*x^2))*(E^4*(-50 - 125*x - 150*x^2) + E^x*(E^4*(20*x^3 - 30*x^ 4) + E^4*(10*x + 10*x^2 + 30*x^3)*Log[2]) + E^(2*x)*(E^4*(2*x^4 + 9*x^5) + E^4*(-2*x^3 - 12*x^4)*Log[2] + 3*E^4*x^3*Log[2]^2)))/x^3, 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.
| \(\displaystyle \int \frac {\left (e^4 \left (-150 x^2-125 x-50\right )+e^{2 x} \left (3 e^4 x^3 \log ^2(2)+e^4 \left (9 x^5+2 x^4\right )+e^4 \left (-12 x^4-2 x^3\right ) \log (2)\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (30 x^3+10 x^2+10 x\right ) \log (2)\right )\right ) \exp \left (\exp \left (\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}\right )+\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}-2 x\right )}{x^3} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {25 \left (6 x^2+5 x+2\right ) \exp \left (\exp \left (\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}\right )+\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}-2 x+4\right )}{x^3}+(x-\log (2)) (9 x+2-\log (8)) \exp \left (\exp \left (\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}\right )+\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}+4\right )+\frac {10 \left (-3 x^3+x^2 (2+\log (8))+x \log (2)+\log (2)\right ) \exp \left (\exp \left (\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}\right )+\frac {e^{-2 x} \left (e^x \left (e^4 \left (-30 x^2-10 x\right ) \log (2)+e^4 \left (30 x^3+10 x^2\right )\right )+e^{2 x} \left (e^4 \left (3 x^5+x^4\right )+e^4 \left (-6 x^4-2 x^3\right ) \log (2)+e^4 \left (3 x^3+x^2\right ) \log ^2(2)\right )+e^4 (75 x+25)\right )}{x^2}-x+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+10 x^2 \left (e^x \log (2)-15\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 x^2+x (2-\log (4096))-\log (2) (2-\log (8))\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )+10 e^{4-x} (3 x+1)+4\right )-\frac {25\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (6 x^2+5 x+2\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}+\frac {5\ 2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (-6 x^3+2 x^2 (2+\log (8))+x \log (4)+\log (4)\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-x+10 e^{4-x} (3 x+1)+4\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \left (9 e^{2 x} x^5-e^x x^4 \left (e^x (\log (4096)-2)+30\right )+e^x x^3 \left (e^x \log (2) (\log (8)-2)+10 (2+\log (8))\right )+5 x^2 \left (e^x \log (4)-30\right )+5 x \left (e^x \log (4)-25\right )-50\right ) \exp \left (2^{-\frac {2 e^{4-x} (3 x+1) \left (e^x x^2+5\right )}{x}} \exp \left (\frac {e^{4-2 x} (3 x+1) \left (10 e^x x^2+e^{2 x} x^2 \left (x^2+\log ^2(2)\right )+25\right )}{x^2}\right )+\frac {25 e^{4-2 x} (3 x+1)}{x^2}+e^4 (3 x+1) \left (x^2+\log ^2(2)\right )-2 x+10 e^{4-x} (3 x+1)+4\right )}{x^3}dx\) |
Input:
Int[(E^(E^((E^4*(25 + 75*x) + E^x*(E^4*(10*x^2 + 30*x^3) + E^4*(-10*x - 30 *x^2)*Log[2]) + E^(2*x)*(E^4*(x^4 + 3*x^5) + E^4*(-2*x^3 - 6*x^4)*Log[2] + E^4*(x^2 + 3*x^3)*Log[2]^2))/(E^(2*x)*x^2)) - 2*x + (E^4*(25 + 75*x) + E^ x*(E^4*(10*x^2 + 30*x^3) + E^4*(-10*x - 30*x^2)*Log[2]) + E^(2*x)*(E^4*(x^ 4 + 3*x^5) + E^4*(-2*x^3 - 6*x^4)*Log[2] + E^4*(x^2 + 3*x^3)*Log[2]^2))/(E ^(2*x)*x^2))*(E^4*(-50 - 125*x - 150*x^2) + E^x*(E^4*(20*x^3 - 30*x^4) + E ^4*(10*x + 10*x^2 + 30*x^3)*Log[2]) + E^(2*x)*(E^4*(2*x^4 + 9*x^5) + E^4*( -2*x^3 - 12*x^4)*Log[2] + 3*E^4*x^3*Log[2]^2)))/x^3,x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(29)=58\).
Time = 0.62 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.19
\[{\mathrm e}^{{\mathrm e}^{-\frac {\left (-\ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{2}+2 \ln \left (2\right ) {\mathrm e}^{2 x} x^{3}-{\mathrm e}^{2 x} x^{4}+10 x \ln \left (2\right ) {\mathrm e}^{x}-10 \,{\mathrm e}^{x} x^{2}-25\right ) \left (1+3 x \right ) {\mathrm e}^{4-2 x}}{x^{2}}}}\]
Input:
int(((3*x^3*exp(2)^2*ln(2)^2+(-12*x^4-2*x^3)*exp(2)^2*ln(2)+(9*x^5+2*x^4)* exp(2)^2)*exp(x)^2+((30*x^3+10*x^2+10*x)*exp(2)^2*ln(2)+(-30*x^4+20*x^3)*e xp(2)^2)*exp(x)+(-150*x^2-125*x-50)*exp(2)^2)*exp((((3*x^3+x^2)*exp(2)^2*l n(2)^2+(-6*x^4-2*x^3)*exp(2)^2*ln(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+((-30* x^2-10*x)*exp(2)^2*ln(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)*exp(2) ^2)/exp(x)^2/x^2)*exp(exp((((3*x^3+x^2)*exp(2)^2*ln(2)^2+(-6*x^4-2*x^3)*ex p(2)^2*ln(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+((-30*x^2-10*x)*exp(2)^2*ln(2) +(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)*exp(2)^2)/exp(x)^2/x^2))/exp(x )^2/x^3,x)
Output:
exp(exp(-1/x^2*(-ln(2)^2*exp(2*x)*x^2+2*ln(2)*exp(2*x)*x^3-exp(2*x)*x^4+10 *x*ln(2)*exp(x)-10*exp(x)*x^2-25)*(1+3*x)*exp(4-2*x)))
Leaf count of result is larger than twice the leaf count of optimal. 311 vs. \(2 (27) = 54\).
Time = 0.08 (sec) , antiderivative size = 311, normalized size of antiderivative = 10.03 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{\left (2 \, x + \frac {{\left (x^{2} e^{\left (2 \, x + \frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}}\right )} + 25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, x^{3} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}} - \frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}}\right )} \] Input:
integrate(((3*x^3*exp(2)^2*log(2)^2+(-12*x^4-2*x^3)*exp(2)^2*log(2)+(9*x^5 +2*x^4)*exp(2)^2)*exp(x)^2+((30*x^3+10*x^2+10*x)*exp(2)^2*log(2)+(-30*x^4+ 20*x^3)*exp(2)^2)*exp(x)+(-150*x^2-125*x-50)*exp(2)^2)*exp((((3*x^3+x^2)*e xp(2)^2*log(2)^2+(-6*x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp( x)^2+((-30*x^2-10*x)*exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75* x+25)*exp(2)^2)/exp(x)^2/x^2)*exp(exp((((3*x^3+x^2)*exp(2)^2*log(2)^2+(-6* x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+((-30*x^2-10*x)* exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)*exp(2)^2)/exp(x )^2/x^2))/exp(x)^2/x^3,x, algorithm="fricas")
Output:
e^(2*x + (x^2*e^(2*x + (25*(3*x + 1)*e^4 + ((3*x^3 + x^2)*e^4*log(2)^2 - 2 *(3*x^4 + x^3)*e^4*log(2) + (3*x^5 + x^4)*e^4)*e^(2*x) - 10*((3*x^2 + x)*e ^4*log(2) - (3*x^3 + x^2)*e^4)*e^x)*e^(-2*x)/x^2) + 25*(3*x + 1)*e^4 + ((3 *x^3 + x^2)*e^4*log(2)^2 - 2*x^3 - 2*(3*x^4 + x^3)*e^4*log(2) + (3*x^5 + x ^4)*e^4)*e^(2*x) - 10*((3*x^2 + x)*e^4*log(2) - (3*x^3 + x^2)*e^4)*e^x)*e^ (-2*x)/x^2 - (25*(3*x + 1)*e^4 + ((3*x^3 + x^2)*e^4*log(2)^2 - 2*(3*x^4 + x^3)*e^4*log(2) + (3*x^5 + x^4)*e^4)*e^(2*x) - 10*((3*x^2 + x)*e^4*log(2) - (3*x^3 + x^2)*e^4)*e^x)*e^(-2*x)/x^2)
Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (24) = 48\).
Time = 6.27 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.39 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{e^{\frac {\left (\left (75 x + 25\right ) e^{4} + \left (\left (- 30 x^{2} - 10 x\right ) e^{4} \log {\left (2 \right )} + \left (30 x^{3} + 10 x^{2}\right ) e^{4}\right ) e^{x} + \left (\left (3 x^{3} + x^{2}\right ) e^{4} \log {\left (2 \right )}^{2} + \left (- 6 x^{4} - 2 x^{3}\right ) e^{4} \log {\left (2 \right )} + \left (3 x^{5} + x^{4}\right ) e^{4}\right ) e^{2 x}\right ) e^{- 2 x}}{x^{2}}}} \] Input:
integrate(((3*x**3*exp(2)**2*ln(2)**2+(-12*x**4-2*x**3)*exp(2)**2*ln(2)+(9 *x**5+2*x**4)*exp(2)**2)*exp(x)**2+((30*x**3+10*x**2+10*x)*exp(2)**2*ln(2) +(-30*x**4+20*x**3)*exp(2)**2)*exp(x)+(-150*x**2-125*x-50)*exp(2)**2)*exp( (((3*x**3+x**2)*exp(2)**2*ln(2)**2+(-6*x**4-2*x**3)*exp(2)**2*ln(2)+(3*x** 5+x**4)*exp(2)**2)*exp(x)**2+((-30*x**2-10*x)*exp(2)**2*ln(2)+(30*x**3+10* x**2)*exp(2)**2)*exp(x)+(75*x+25)*exp(2)**2)/exp(x)**2/x**2)*exp(exp((((3* x**3+x**2)*exp(2)**2*ln(2)**2+(-6*x**4-2*x**3)*exp(2)**2*ln(2)+(3*x**5+x** 4)*exp(2)**2)*exp(x)**2+((-30*x**2-10*x)*exp(2)**2*ln(2)+(30*x**3+10*x**2) *exp(2)**2)*exp(x)+(75*x+25)*exp(2)**2)/exp(x)**2/x**2))/exp(x)**2/x**3,x)
Output:
exp(exp(((75*x + 25)*exp(4) + ((-30*x**2 - 10*x)*exp(4)*log(2) + (30*x**3 + 10*x**2)*exp(4))*exp(x) + ((3*x**3 + x**2)*exp(4)*log(2)**2 + (-6*x**4 - 2*x**3)*exp(4)*log(2) + (3*x**5 + x**4)*exp(4))*exp(2*x))*exp(-2*x)/x**2) )
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (27) = 54\).
Time = 2.43 (sec) , antiderivative size = 110, normalized size of antiderivative = 3.55 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{\left (e^{\left (3 \, x^{3} e^{4} - 6 \, x^{2} e^{4} \log \left (2\right ) + 3 \, x e^{4} \log \left (2\right )^{2} + x^{2} e^{4} - 2 \, x e^{4} \log \left (2\right ) + e^{4} \log \left (2\right )^{2} + 30 \, x e^{\left (-x + 4\right )} - 30 \, e^{\left (-x + 4\right )} \log \left (2\right ) - \frac {10 \, e^{\left (-x + 4\right )} \log \left (2\right )}{x} + \frac {75 \, e^{\left (-2 \, x + 4\right )}}{x} + \frac {25 \, e^{\left (-2 \, x + 4\right )}}{x^{2}} + 10 \, e^{\left (-x + 4\right )}\right )}\right )} \] Input:
integrate(((3*x^3*exp(2)^2*log(2)^2+(-12*x^4-2*x^3)*exp(2)^2*log(2)+(9*x^5 +2*x^4)*exp(2)^2)*exp(x)^2+((30*x^3+10*x^2+10*x)*exp(2)^2*log(2)+(-30*x^4+ 20*x^3)*exp(2)^2)*exp(x)+(-150*x^2-125*x-50)*exp(2)^2)*exp((((3*x^3+x^2)*e xp(2)^2*log(2)^2+(-6*x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp( x)^2+((-30*x^2-10*x)*exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75* x+25)*exp(2)^2)/exp(x)^2/x^2)*exp(exp((((3*x^3+x^2)*exp(2)^2*log(2)^2+(-6* x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+((-30*x^2-10*x)* exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)*exp(2)^2)/exp(x )^2/x^2))/exp(x)^2/x^3,x, algorithm="maxima")
Output:
e^(e^(3*x^3*e^4 - 6*x^2*e^4*log(2) + 3*x*e^4*log(2)^2 + x^2*e^4 - 2*x*e^4* log(2) + e^4*log(2)^2 + 30*x*e^(-x + 4) - 30*e^(-x + 4)*log(2) - 10*e^(-x + 4)*log(2)/x + 75*e^(-2*x + 4)/x + 25*e^(-2*x + 4)/x^2 + 10*e^(-x + 4)))
\[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=\int { -\frac {{\left (25 \, {\left (6 \, x^{2} + 5 \, x + 2\right )} e^{4} - {\left (3 \, x^{3} e^{4} \log \left (2\right )^{2} - 2 \, {\left (6 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (9 \, x^{5} + 2 \, x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{3} + x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{4} - 2 \, x^{3}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x + \frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}} + e^{\left (\frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}}\right )}\right )}}{x^{3}} \,d x } \] Input:
integrate(((3*x^3*exp(2)^2*log(2)^2+(-12*x^4-2*x^3)*exp(2)^2*log(2)+(9*x^5 +2*x^4)*exp(2)^2)*exp(x)^2+((30*x^3+10*x^2+10*x)*exp(2)^2*log(2)+(-30*x^4+ 20*x^3)*exp(2)^2)*exp(x)+(-150*x^2-125*x-50)*exp(2)^2)*exp((((3*x^3+x^2)*e xp(2)^2*log(2)^2+(-6*x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp( x)^2+((-30*x^2-10*x)*exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75* x+25)*exp(2)^2)/exp(x)^2/x^2)*exp(exp((((3*x^3+x^2)*exp(2)^2*log(2)^2+(-6* x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+((-30*x^2-10*x)* exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)*exp(2)^2)/exp(x )^2/x^2))/exp(x)^2/x^3,x, algorithm="giac")
Output:
integrate(-(25*(6*x^2 + 5*x + 2)*e^4 - (3*x^3*e^4*log(2)^2 - 2*(6*x^4 + x^ 3)*e^4*log(2) + (9*x^5 + 2*x^4)*e^4)*e^(2*x) - 10*((3*x^3 + x^2 + x)*e^4*l og(2) - (3*x^4 - 2*x^3)*e^4)*e^x)*e^(-2*x + (25*(3*x + 1)*e^4 + ((3*x^3 + x^2)*e^4*log(2)^2 - 2*(3*x^4 + x^3)*e^4*log(2) + (3*x^5 + x^4)*e^4)*e^(2*x ) - 10*((3*x^2 + x)*e^4*log(2) - (3*x^3 + x^2)*e^4)*e^x)*e^(-2*x)/x^2 + e^ ((25*(3*x + 1)*e^4 + ((3*x^3 + x^2)*e^4*log(2)^2 - 2*(3*x^4 + x^3)*e^4*log (2) + (3*x^5 + x^4)*e^4)*e^(2*x) - 10*((3*x^2 + x)*e^4*log(2) - (3*x^3 + x ^2)*e^4)*e^x)*e^(-2*x)/x^2))/x^3, x)
Time = 2.68 (sec) , antiderivative size = 125, normalized size of antiderivative = 4.03 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx={\mathrm {e}}^{\frac {{\mathrm {e}}^{x^2\,{\mathrm {e}}^4}\,{\mathrm {e}}^{3\,x^3\,{\mathrm {e}}^4}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^4}{x^2}}\,{\mathrm {e}}^{\frac {75\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^4}{x}}\,{\mathrm {e}}^{10\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^4\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{30\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{{\mathrm {e}}^4\,{\ln \left (2\right )}^2}}{2^{\frac {10\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}{x}}\,2^{30\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}\,2^{2\,x\,{\mathrm {e}}^4}\,2^{6\,x^2\,{\mathrm {e}}^4}}} \] Input:
int((exp((exp(-2*x)*(exp(2*x)*(exp(4)*(x^4 + 3*x^5) - exp(4)*log(2)*(2*x^3 + 6*x^4) + exp(4)*log(2)^2*(x^2 + 3*x^3)) + exp(x)*(exp(4)*(10*x^2 + 30*x ^3) - exp(4)*log(2)*(10*x + 30*x^2)) + exp(4)*(75*x + 25)))/x^2)*exp(-2*x) *exp(exp((exp(-2*x)*(exp(2*x)*(exp(4)*(x^4 + 3*x^5) - exp(4)*log(2)*(2*x^3 + 6*x^4) + exp(4)*log(2)^2*(x^2 + 3*x^3)) + exp(x)*(exp(4)*(10*x^2 + 30*x ^3) - exp(4)*log(2)*(10*x + 30*x^2)) + exp(4)*(75*x + 25)))/x^2))*(exp(x)* (exp(4)*(20*x^3 - 30*x^4) + exp(4)*log(2)*(10*x + 10*x^2 + 30*x^3)) - exp( 4)*(125*x + 150*x^2 + 50) + exp(2*x)*(exp(4)*(2*x^4 + 9*x^5) + 3*x^3*exp(4 )*log(2)^2 - exp(4)*log(2)*(2*x^3 + 12*x^4))))/x^3,x)
Output:
exp((exp(x^2*exp(4))*exp(3*x^3*exp(4))*exp((25*exp(-2*x)*exp(4))/x^2)*exp( (75*exp(-2*x)*exp(4))/x)*exp(10*exp(-x)*exp(4))*exp(3*x*exp(4)*log(2)^2)*e xp(30*x*exp(-x)*exp(4))*exp(exp(4)*log(2)^2))/(2^((10*exp(-x)*exp(4))/x)*2 ^(30*exp(-x)*exp(4))*2^(2*x*exp(4))*2^(6*x^2*exp(4))))
\[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=\text {too large to display} \] Input:
int(((3*x^3*exp(2)^2*log(2)^2+(-12*x^4-2*x^3)*exp(2)^2*log(2)+(9*x^5+2*x^4 )*exp(2)^2)*exp(x)^2+((30*x^3+10*x^2+10*x)*exp(2)^2*log(2)+(-30*x^4+20*x^3 )*exp(2)^2)*exp(x)+(-150*x^2-125*x-50)*exp(2)^2)*exp((((3*x^3+x^2)*exp(2)^ 2*log(2)^2+(-6*x^4-2*x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+( (-30*x^2-10*x)*exp(2)^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)* exp(2)^2)/exp(x)^2/x^2)*exp(exp((((3*x^3+x^2)*exp(2)^2*log(2)^2+(-6*x^4-2* x^3)*exp(2)^2*log(2)+(3*x^5+x^4)*exp(2)^2)*exp(x)^2+((-30*x^2-10*x)*exp(2) ^2*log(2)+(30*x^3+10*x^2)*exp(2)^2)*exp(x)+(75*x+25)*exp(2)^2)/exp(x)^2/x^ 2))/exp(x)^2/x^3,x)
Output:
e**4*(10*int(e**((e**((3*e**(2*x)*log(2)**2*e**4*x**3 + e**(2*x)*log(2)**2 *e**4*x**2 + 3*e**(2*x)*e**4*x**5 + e**(2*x)*e**4*x**4 + 2*e**(2*x)*x**3 + 30*e**x*e**4*x**3 + 10*e**x*e**4*x**2 + 75*e**4*x + 25*e**4)/(e**(2*x)*x* *2))*x**2 + 3*e**((2*e**x*x**2 + 30*log(2)*e**4*x + 10*log(2)*e**4)/(e**x* x))*2**(2*e**4*x)*2**(6*e**4*x**2)*log(2)**2*e**4*x**3 + e**((2*e**x*x**2 + 30*log(2)*e**4*x + 10*log(2)*e**4)/(e**x*x))*2**(2*e**4*x)*2**(6*e**4*x* *2)*log(2)**2*e**4*x**2 + 3*e**((2*e**x*x**2 + 30*log(2)*e**4*x + 10*log(2 )*e**4)/(e**x*x))*2**(2*e**4*x)*2**(6*e**4*x**2)*e**4*x**5 + e**((2*e**x*x **2 + 30*log(2)*e**4*x + 10*log(2)*e**4)/(e**x*x))*2**(2*e**4*x)*2**(6*e** 4*x**2)*e**4*x**4 + 30*e**((e**x*x**2 + 30*log(2)*e**4*x + 10*log(2)*e**4) /(e**x*x))*2**(2*e**4*x)*2**(6*e**4*x**2)*e**4*x**3 + 10*e**((e**x*x**2 + 30*log(2)*e**4*x + 10*log(2)*e**4)/(e**x*x))*2**(2*e**4*x)*2**(6*e**4*x**2 )*e**4*x**2 + 75*e**((30*log(2)*e**4*x + 10*log(2)*e**4)/(e**x*x))*2**(2*e **4*x)*2**(6*e**4*x**2)*e**4*x + 25*e**((30*log(2)*e**4*x + 10*log(2)*e**4 )/(e**x*x))*2**(2*e**4*x)*2**(6*e**4*x**2)*e**4)/(e**((2*e**x*x**2 + 30*lo g(2)*e**4*x + 10*log(2)*e**4)/(e**x*x))*2**(2*e**4*x)*2**(6*e**4*x**2)*x** 2))/(e**((e**x*x**2 + 30*log(2)*e**4*x + 10*log(2)*e**4)/(e**x*x))*2**(2*e **4*x)*2**(6*e**4*x**2)*x**2),x)*log(2) + 10*int(e**((e**((3*e**(2*x)*log( 2)**2*e**4*x**3 + e**(2*x)*log(2)**2*e**4*x**2 + 3*e**(2*x)*e**4*x**5 + e* *(2*x)*e**4*x**4 + 2*e**(2*x)*x**3 + 30*e**x*e**4*x**3 + 10*e**x*e**4*x...