Integrand size = 236, antiderivative size = 30 \[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=e^{e^{4+x \left (4+\frac {e^x x^2}{3+\frac {3}{4+x}}\right )^2}} \] Output:
exp(exp(4+x*(x^2/(3/(4+x)+3)*exp(x)+4)^2))
Time = 1.15 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=e^{e^{4+16 x+\frac {e^{2 x} x^5 (4+x)^2}{9 (5+x)^2}+\frac {8 e^x x^3 (4+x)}{3 (5+x)}}} \] Input:
Integrate[(E^(E^((900 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x ^4 + 24*x^5) + E^(2*x)*(16*x^5 + 8*x^6 + x^7))/(225 + 90*x + 9*x^2)) + (90 0 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 24*x^5) + E^(2* x)*(16*x^5 + 8*x^6 + x^7))/(225 + 90*x + 9*x^2))*(18000 + 10800*x + 2160*x ^2 + 144*x^3 + E^x*(7200*x^2 + 7200*x^3 + 2592*x^4 + 408*x^5 + 24*x^6) + E ^(2*x)*(400*x^4 + 448*x^5 + 179*x^6 + 31*x^7 + 2*x^8)))/(1125 + 675*x + 13 5*x^2 + 9*x^3),x]
Output:
E^E^(4 + 16*x + (E^(2*x)*x^5*(4 + x)^2)/(9*(5 + x)^2) + (8*E^x*x^3*(4 + x) )/(3*(5 + 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.
| \(\displaystyle \int \frac {\left (144 x^3+2160 x^2+e^{2 x} \left (2 x^8+31 x^7+179 x^6+448 x^5+400 x^4\right )+e^x \left (24 x^6+408 x^5+2592 x^4+7200 x^3+7200 x^2\right )+10800 x+18000\right ) \exp \left (\exp \left (\frac {144 x^3+1476 x^2+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+e^x \left (24 x^5+216 x^4+480 x^3\right )+3960 x+900}{9 x^2+90 x+225}\right )+\frac {144 x^3+1476 x^2+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+e^x \left (24 x^5+216 x^4+480 x^3\right )+3960 x+900}{9 x^2+90 x+225}\right )}{9 x^3+135 x^2+675 x+1125} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {\left (144 x^3+2160 x^2+e^{2 x} \left (2 x^8+31 x^7+179 x^6+448 x^5+400 x^4\right )+e^x \left (24 x^6+408 x^5+2592 x^4+7200 x^3+7200 x^2\right )+10800 x+18000\right ) \exp \left (\exp \left (\frac {144 x^3+1476 x^2+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+e^x \left (24 x^5+216 x^4+480 x^3\right )+3960 x+900}{9 x^2+90 x+225}\right )+\frac {144 x^3+1476 x^2+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+e^x \left (24 x^5+216 x^4+480 x^3\right )+3960 x+900}{9 x^2+90 x+225}\right )}{\left (3^{2/3} x+5\ 3^{2/3}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{2 x+e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}}+\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}} (x+4) \left (2 x^3+23 x^2+87 x+100\right ) x^4}{9 (x+5)^3}+\frac {16 e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}+e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}}} x^3}{(x+5)^3}+\frac {8 e^{x+e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}}+\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}} \left (x^3+12 x^2+48 x+60\right ) x^2}{3 (x+5)^2}+\frac {240 e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}+e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}}} x^2}{(x+5)^3}+\frac {1200 e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}+e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}}} x}{(x+5)^3}+\frac {2000 e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}+e^{\frac {144 x^3+1476 x^2+3960 x+e^x \left (24 x^5+216 x^4+480 x^3\right )+e^{2 x} \left (x^7+8 x^6+16 x^5\right )+900}{9 x^2+90 x+225}}}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (179 e^x+24\right ) x^6+8 e^x \left (56 e^x+51\right ) x^5+16 e^x \left (25 e^x+162\right ) x^4+144 \left (50 e^x+1\right ) x^3+720 \left (10 e^x+3\right ) x^2+10800 x+18000\right ) \exp \left (\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (2 e^x+3\right ) x^5+216 e^x x^4+48 \left (10 e^x+3\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+4\right )}{9 (x+5)^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{9} \int \left (\frac {e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+18 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (2 x^4+31 x^3+179 x^2+448 x+400\right ) x^4}{(x+5)^3}+\frac {144 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^3}{(x+5)^3}+\frac {24 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+17 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} \left (x^3+12 x^2+48 x+60\right ) x^2}{(x+5)^2}+\frac {2160 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x^2}{(x+5)^3}+\frac {10800 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4} x}{(x+5)^3}+\frac {18000 e^{\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+e^{\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}}+4}}{(x+5)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{9} \int \frac {\exp \left (\frac {e^{2 x} (x+4)^2 x^5}{9 (x+5)^2}+\frac {8 e^x (x+4) x^3}{3 (x+5)}+16 x+\exp \left (\frac {e^{2 x} x^7+8 e^{2 x} x^6+8 e^x \left (3+2 e^x\right ) x^5+216 e^x x^4+48 \left (3+10 e^x\right ) x^3+1476 x^2+3960 x+900}{9 (x+5)^2}\right )+4\right ) \left (2 e^{2 x} x^8+31 e^{2 x} x^7+e^x \left (24+179 e^x\right ) x^6+8 e^x \left (51+56 e^x\right ) x^5+16 e^x \left (162+25 e^x\right ) x^4+144 \left (1+50 e^x\right ) x^3+720 \left (3+10 e^x\right ) x^2+10800 x+18000\right )}{(x+5)^3}dx\) |
Input:
Int[(E^(E^((900 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 2 4*x^5) + E^(2*x)*(16*x^5 + 8*x^6 + x^7))/(225 + 90*x + 9*x^2)) + (900 + 39 60*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 24*x^5) + E^(2*x)*(16 *x^5 + 8*x^6 + x^7))/(225 + 90*x + 9*x^2))*(18000 + 10800*x + 2160*x^2 + 1 44*x^3 + E^x*(7200*x^2 + 7200*x^3 + 2592*x^4 + 408*x^5 + 24*x^6) + E^(2*x) *(400*x^4 + 448*x^5 + 179*x^6 + 31*x^7 + 2*x^8)))/(1125 + 675*x + 135*x^2 + 9*x^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(27)=54\).
Time = 214.27 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.27
| method | result | size |
| parallelrisch | \({\mathrm e}^{{\mathrm e}^{\frac {\left (x^{7}+8 x^{6}+16 x^{5}\right ) {\mathrm e}^{2 x}+\left (24 x^{5}+216 x^{4}+480 x^{3}\right ) {\mathrm e}^{x}+144 x^{3}+1476 x^{2}+3960 x +900}{9 x^{2}+90 x +225}}}\) | \(68\) |
| risch | \({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x} x^{7}+8 \,{\mathrm e}^{2 x} x^{6}+24 x^{5} {\mathrm e}^{x}+16 x^{5} {\mathrm e}^{2 x}+216 \,{\mathrm e}^{x} x^{4}+480 \,{\mathrm e}^{x} x^{3}+144 x^{3}+1476 x^{2}+3960 x +900}{9 \left (5+x \right )^{2}}}}\) | \(72\) |
Input:
int(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5+2592* x^4+7200*x^3+7200*x^2)*exp(x)+144*x^3+2160*x^2+10800*x+18000)*exp(((x^7+8* x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960 *x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216 *x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960*x+900)/(9*x^2+90*x+225)))/(9*x^ 3+135*x^2+675*x+1125),x,method=_RETURNVERBOSE)
Output:
exp(exp(1/9/(x^2+10*x+25)*((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480 *x^3)*exp(x)+144*x^3+1476*x^2+3960*x+900)))
Leaf count of result is larger than twice the leaf count of optimal. 205 vs. \(2 (26) = 52\).
Time = 0.09 (sec) , antiderivative size = 205, normalized size of antiderivative = 6.83 \[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 9 \, {\left (x^{2} + 10 \, x + 25\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} - \frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )} \] Input:
integrate(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5 +2592*x^4+7200*x^3+7200*x^2)*exp(x)+144*x^3+2160*x^2+10800*x+18000)*exp((( x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^ 2+3960*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x ^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960*x+900)/(9*x^2+90*x+225))) /(9*x^3+135*x^2+675*x+1125),x, algorithm="fricas")
Output:
e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9* x^4 + 20*x^3)*e^x + 9*(x^2 + 10*x + 25)*e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/ (x^2 + 10*x + 25)) + 3960*x + 900)/(x^2 + 10*x + 25) - 1/9*(144*x^3 + 1476 *x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 39 60*x + 900)/(x^2 + 10*x + 25))
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 5.66 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17 \[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=e^{e^{\frac {144 x^{3} + 1476 x^{2} + 3960 x + \left (24 x^{5} + 216 x^{4} + 480 x^{3}\right ) e^{x} + \left (x^{7} + 8 x^{6} + 16 x^{5}\right ) e^{2 x} + 900}{9 x^{2} + 90 x + 225}}} \] Input:
integrate(((2*x**8+31*x**7+179*x**6+448*x**5+400*x**4)*exp(x)**2+(24*x**6+ 408*x**5+2592*x**4+7200*x**3+7200*x**2)*exp(x)+144*x**3+2160*x**2+10800*x+ 18000)*exp(((x**7+8*x**6+16*x**5)*exp(x)**2+(24*x**5+216*x**4+480*x**3)*ex p(x)+144*x**3+1476*x**2+3960*x+900)/(9*x**2+90*x+225))*exp(exp(((x**7+8*x* *6+16*x**5)*exp(x)**2+(24*x**5+216*x**4+480*x**3)*exp(x)+144*x**3+1476*x** 2+3960*x+900)/(9*x**2+90*x+225)))/(9*x**3+135*x**2+675*x+1125),x)
Output:
exp(exp((144*x**3 + 1476*x**2 + 3960*x + (24*x**5 + 216*x**4 + 480*x**3)*e xp(x) + (x**7 + 8*x**6 + 16*x**5)*exp(2*x) + 900)/(9*x**2 + 90*x + 225)))
\[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=\int { \frac {{\left (144 \, x^{3} + 2160 \, x^{2} + {\left (2 \, x^{8} + 31 \, x^{7} + 179 \, x^{6} + 448 \, x^{5} + 400 \, x^{4}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{6} + 17 \, x^{5} + 108 \, x^{4} + 300 \, x^{3} + 300 \, x^{2}\right )} e^{x} + 10800 \, x + 18000\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} + e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )}\right )}}{9 \, {\left (x^{3} + 15 \, x^{2} + 75 \, x + 125\right )}} \,d x } \] Input:
integrate(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5 +2592*x^4+7200*x^3+7200*x^2)*exp(x)+144*x^3+2160*x^2+10800*x+18000)*exp((( x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^ 2+3960*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x ^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960*x+900)/(9*x^2+90*x+225))) /(9*x^3+135*x^2+675*x+1125),x, algorithm="maxima")
Output:
1/9*integrate((144*x^3 + 2160*x^2 + (2*x^8 + 31*x^7 + 179*x^6 + 448*x^5 + 400*x^4)*e^(2*x) + 24*(x^6 + 17*x^5 + 108*x^4 + 300*x^3 + 300*x^2)*e^x + 1 0800*x + 18000)*e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x ) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25) + e^(1 /9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25)))/(x^3 + 15*x^2 + 75*x + 1 25), x)
\[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=\int { \frac {{\left (144 \, x^{3} + 2160 \, x^{2} + {\left (2 \, x^{8} + 31 \, x^{7} + 179 \, x^{6} + 448 \, x^{5} + 400 \, x^{4}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{6} + 17 \, x^{5} + 108 \, x^{4} + 300 \, x^{3} + 300 \, x^{2}\right )} e^{x} + 10800 \, x + 18000\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} + e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )}\right )}}{9 \, {\left (x^{3} + 15 \, x^{2} + 75 \, x + 125\right )}} \,d x } \] Input:
integrate(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5 +2592*x^4+7200*x^3+7200*x^2)*exp(x)+144*x^3+2160*x^2+10800*x+18000)*exp((( x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^ 2+3960*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x ^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960*x+900)/(9*x^2+90*x+225))) /(9*x^3+135*x^2+675*x+1125),x, algorithm="giac")
Output:
integrate(1/9*(144*x^3 + 2160*x^2 + (2*x^8 + 31*x^7 + 179*x^6 + 448*x^5 + 400*x^4)*e^(2*x) + 24*(x^6 + 17*x^5 + 108*x^4 + 300*x^3 + 300*x^2)*e^x + 1 0800*x + 18000)*e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x ) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25) + e^(1 /9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25)))/(x^3 + 15*x^2 + 75*x + 1 25), x)
Time = 0.91 (sec) , antiderivative size = 184, normalized size of antiderivative = 6.13 \[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx={\mathrm {e}}^{{\mathrm {e}}^{\frac {16\,x^3}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {164\,x^2}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {100}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {8\,x^5\,{\mathrm {e}}^x}{3\,x^2+30\,x+75}}\,{\mathrm {e}}^{\frac {160\,x^3\,{\mathrm {e}}^x}{3\,x^2+30\,x+75}}\,{\mathrm {e}}^{\frac {x^7\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {8\,x^6\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {16\,x^5\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {440\,x}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {24\,x^4\,{\mathrm {e}}^x}{x^2+10\,x+25}}} \] Input:
int((exp(exp((3960*x + exp(2*x)*(16*x^5 + 8*x^6 + x^7) + exp(x)*(480*x^3 + 216*x^4 + 24*x^5) + 1476*x^2 + 144*x^3 + 900)/(90*x + 9*x^2 + 225)))*exp( (3960*x + exp(2*x)*(16*x^5 + 8*x^6 + x^7) + exp(x)*(480*x^3 + 216*x^4 + 24 *x^5) + 1476*x^2 + 144*x^3 + 900)/(90*x + 9*x^2 + 225))*(10800*x + exp(2*x )*(400*x^4 + 448*x^5 + 179*x^6 + 31*x^7 + 2*x^8) + exp(x)*(7200*x^2 + 7200 *x^3 + 2592*x^4 + 408*x^5 + 24*x^6) + 2160*x^2 + 144*x^3 + 18000))/(675*x + 135*x^2 + 9*x^3 + 1125),x)
Output:
exp(exp((16*x^3)/(10*x + x^2 + 25))*exp((164*x^2)/(10*x + x^2 + 25))*exp(1 00/(10*x + x^2 + 25))*exp((8*x^5*exp(x))/(30*x + 3*x^2 + 75))*exp((160*x^3 *exp(x))/(30*x + 3*x^2 + 75))*exp((x^7*exp(2*x))/(90*x + 9*x^2 + 225))*exp ((8*x^6*exp(2*x))/(90*x + 9*x^2 + 225))*exp((16*x^5*exp(2*x))/(90*x + 9*x^ 2 + 225))*exp((440*x)/(10*x + x^2 + 25))*exp((24*x^4*exp(x))/(10*x + x^2 + 25)))
\[ \int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x \left (480 x^3+216 x^4+24 x^5\right )+e^{2 x} \left (16 x^5+8 x^6+x^7\right )}{225+90 x+9 x^2}} \left (18000+10800 x+2160 x^2+144 x^3+e^x \left (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6\right )+e^{2 x} \left (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8\right )\right )}{1125+675 x+135 x^2+9 x^3} \, dx=\text {too large to display} \] Input:
int(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5+2592* x^4+7200*x^3+7200*x^2)*exp(x)+144*x^3+2160*x^2+10800*x+18000)*exp(((x^7+8* x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960 *x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216 *x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+3960*x+900)/(9*x^2+90*x+225)))/(9*x^ 3+135*x^2+675*x+1125),x)
Output:
(e**4*(18000*int(e**((e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e** (2*x)*x**2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x *x**2 + 7800*e**x*x + 19500*e**x + 6*x**3 + 60*x**2 + 150*x)/(3*x**2 + 30* x + 75))*x**7 + 8*e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e**(2*x )*x**2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x*x** 2 + 7800*e**x*x + 19500*e**x + 6*x**3 + 60*x**2 + 150*x)/(3*x**2 + 30*x + 75))*x**6 + 16*e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e**(2*x)*x **2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x*x**2 + 7800*e**x*x + 19500*e**x + 6*x**3 + 60*x**2 + 150*x)/(3*x**2 + 30*x + 75) )*x**5 + 90*e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e**(2*x)*x**2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x*x**2 + 78 00*e**x*x + 19500*e**x + 6*x**3 + 60*x**2 + 150*x)/(3*x**2 + 30*x + 75))*x **4 + 900*e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e**(2*x)*x**2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x*x**2 + 7800 *e**x*x + 19500*e**x + 6*x**3 + 60*x**2 + 150*x)/(3*x**2 + 30*x + 75))*x** 3 + 6750*e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e**(2*x)*x**2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x*x**2 + 7800* e**x*x + 19500*e**x + 6*x**3 + 60*x**2 + 150*x)/(3*x**2 + 30*x + 75))*x**2 + 45000*e**((30*e**(2*x)*x**4 + 300*e**(2*x)*x**3 + 2250*e**(2*x)*x**2 + 15000*e**(2*x)*x + 37500*e**(2*x) + 110*e**x*x**3 + 1080*e**x*x**2 + 78...