Integrand size = 488, antiderivative size = 35 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=-2+\left (\frac {e^{-x+5 (3+x)}}{\left (5+\left (-1-e^5+x\right )^2\right )^2}-\log (3)\right )^2 \] Output:
(exp(4*x+15)/(5+(x-exp(5)-1)^2)^2-ln(3))^2-2
Time = 0.18 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.77 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=\frac {e^{15+4 x} \left (e^{15+4 x}-2 \left (6+e^{10}-2 e^5 (-1+x)-2 x+x^2\right )^2 \log (3)\right )}{\left (6+e^{10}-2 e^5 (-1+x)-2 x+x^2\right )^4} \] Input:
Integrate[(E^(30 + 8*x)*(56 + 8*E^10 + E^5*(24 - 16*x) - 24*x + 8*x^2) + E ^(15 + 4*x)*(-2016 - 8*E^30 + 2208*x - 1760*x^2 + 800*x^3 - 280*x^4 + 56*x ^5 - 8*x^6 + E^25*(-56 + 48*x) + E^20*(-280 + 280*x - 120*x^2) + E^15*(-80 0 + 1120*x - 560*x^2 + 160*x^3) + E^10*(-1760 + 2400*x - 1680*x^2 + 560*x^ 3 - 120*x^4) + E^5*(-2208 + 3520*x - 2400*x^2 + 1120*x^3 - 280*x^4 + 48*x^ 5))*Log[3])/(7776 + E^50 + E^45*(10 - 10*x) - 12960*x + 15120*x^2 - 11520* x^3 + 6960*x^4 - 3152*x^5 + 1160*x^6 - 320*x^7 + 70*x^8 - 10*x^9 + x^10 + E^40*(70 - 90*x + 45*x^2) + E^35*(320 - 560*x + 360*x^2 - 120*x^3) + E^30* (1160 - 2240*x + 1960*x^2 - 840*x^3 + 210*x^4) + E^25*(3152 - 6960*x + 672 0*x^2 - 3920*x^3 + 1260*x^4 - 252*x^5) + E^20*(6960 - 15760*x + 17400*x^2 - 11200*x^3 + 4900*x^4 - 1260*x^5 + 210*x^6) + E^15*(11520 - 27840*x + 315 20*x^2 - 23200*x^3 + 11200*x^4 - 3920*x^5 + 840*x^6 - 120*x^7) + E^10*(151 20 - 34560*x + 41760*x^2 - 31520*x^3 + 17400*x^4 - 6720*x^5 + 1960*x^6 - 3 60*x^7 + 45*x^8) + E^5*(12960 - 30240*x + 34560*x^2 - 27840*x^3 + 15760*x^ 4 - 6960*x^5 + 2240*x^6 - 560*x^7 + 90*x^8 - 10*x^9)),x]
Output:
(E^(15 + 4*x)*(E^(15 + 4*x) - 2*(6 + E^10 - 2*E^5*(-1 + x) - 2*x + x^2)^2* Log[3]))/(6 + E^10 - 2*E^5*(-1 + x) - 2*x + x^2)^4
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.
| \(\displaystyle \int \frac {e^{8 x+30} \left (8 x^2-24 x+e^5 (24-16 x)+8 e^{10}+56\right )+e^{4 x+15} \left (-8 x^6+56 x^5-280 x^4+800 x^3-1760 x^2+e^{20} \left (-120 x^2+280 x-280\right )+e^{15} \left (160 x^3-560 x^2+1120 x-800\right )+e^{10} \left (-120 x^4+560 x^3-1680 x^2+2400 x-1760\right )+e^5 \left (48 x^5-280 x^4+1120 x^3-2400 x^2+3520 x-2208\right )+2208 x+e^{25} (48 x-56)-8 e^{30}-2016\right ) \log (3)}{x^{10}-10 x^9+70 x^8-320 x^7+1160 x^6-3152 x^5+6960 x^4-11520 x^3+15120 x^2+e^{40} \left (45 x^2-90 x+70\right )+e^{35} \left (-120 x^3+360 x^2-560 x+320\right )+e^{30} \left (210 x^4-840 x^3+1960 x^2-2240 x+1160\right )+e^{25} \left (-252 x^5+1260 x^4-3920 x^3+6720 x^2-6960 x+3152\right )+e^{20} \left (210 x^6-1260 x^5+4900 x^4-11200 x^3+17400 x^2-15760 x+6960\right )+e^{15} \left (-120 x^7+840 x^6-3920 x^5+11200 x^4-23200 x^3+31520 x^2-27840 x+11520\right )+e^{10} \left (45 x^8-360 x^7+1960 x^6-6720 x^5+17400 x^4-31520 x^3+41760 x^2-34560 x+15120\right )+e^5 \left (-10 x^9+90 x^8-560 x^7+2240 x^6-6960 x^5+15760 x^4-27840 x^3+34560 x^2-30240 x+12960\right )-12960 x+e^{45} (10-10 x)+e^{50}+7776} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {e^{8 x+30} \left (8 x^2-24 x+e^5 (24-16 x)+8 e^{10}+56\right )+e^{4 x+15} \left (-8 x^6+56 x^5-280 x^4+800 x^3-1760 x^2+e^{20} \left (-120 x^2+280 x-280\right )+e^{15} \left (160 x^3-560 x^2+1120 x-800\right )+e^{10} \left (-120 x^4+560 x^3-1680 x^2+2400 x-1760\right )+e^5 \left (48 x^5-280 x^4+1120 x^3-2400 x^2+3520 x-2208\right )+2208 x+e^{25} (48 x-56)-8 e^{30}-2016\right ) \log (3)}{\left (x^2-2 e^5 x-2 x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {e^{8 x+30} \left (8 x^2-24 x+e^5 (24-16 x)+8 e^{10}+56\right )+e^{4 x+15} \left (-8 x^6+56 x^5-280 x^4+800 x^3-1760 x^2+e^{20} \left (-120 x^2+280 x-280\right )+e^{15} \left (160 x^3-560 x^2+1120 x-800\right )+e^{10} \left (-120 x^4+560 x^3-1680 x^2+2400 x-1760\right )+e^5 \left (48 x^5-280 x^4+1120 x^3-2400 x^2+3520 x-2208\right )+2208 x+e^{25} (48 x-56)-8 e^{30}-2016\right ) \log (3)}{\left (x^2+\left (-2-2 e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {8 e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (x^4 (-\log (3))+4 \left (1+e^5\right ) x^3 \log (3)-16 \left (1+\frac {3}{8} e^5 \left (2+e^5\right )\right ) x^2 \log (3)+e^{4 x+15}+24 \left (1+\frac {1}{6} e^5 \left (8+3 e^5+e^{10}\right )\right ) x \log (3)-36 \left (1+\frac {1}{36} e^5 \left (24+16 e^5+4 e^{10}+e^{15}\right )\right ) \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) x^4+4 \left (1+e^5\right ) \log (3) x^3-2 \left (8+3 e^5 \left (2+e^5\right )\right ) \log (3) x^2+4 \left (6+8 e^5+3 e^{10}+e^{15}\right ) \log (3) x+e^{4 x+15}-\left (6+2 e^5+e^{10}\right )^2 \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) x^4}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+15} (1+e) \left (1-e+e^2-e^3+e^4\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3) x^3}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+15} \left (8+6 e^5+3 e^{10}\right ) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) x^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+15} (1+e) \left (1-e+e^2-e^3+e^4\right ) \left (6+2 e^5+e^{10}\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3) x}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+15} \left (6+2 e^5+e^{10}\right )^2 \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (\frac {e^{4 x+15} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )^2}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+20} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3) \left (x^2-2 x+6\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{8 x+30} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {2 e^{4 x+25} \left (-3 x^2+6 x-8\right ) \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {e^{4 x+35} \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}+\frac {4 e^{4 x+30} (1-x) \left (-x^2+\left (3+2 e^5\right ) x-e^{10}-3 e^5-7\right ) \log (3)}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 8 \int \frac {e^{4 x+15} \left (x^2-\left (3+2 e^5\right ) x+e^{10}+3 e^5+7\right ) \left (-\log (3) \left (x^2-2 x+6\right )^2+e^{4 x+15}+4 e^{15} (x-1) \log (3)-2 e^{10} \left (3 x^2-6 x+8\right ) \log (3)+4 e^5 \left (x^3-3 x^2+8 x-6\right ) \log (3)-e^{20} \log (3)\right )}{\left (x^2-2 \left (1+e^5\right ) x+e^{10}+2 e^5+6\right )^5}dx\) |
Input:
Int[(E^(30 + 8*x)*(56 + 8*E^10 + E^5*(24 - 16*x) - 24*x + 8*x^2) + E^(15 + 4*x)*(-2016 - 8*E^30 + 2208*x - 1760*x^2 + 800*x^3 - 280*x^4 + 56*x^5 - 8 *x^6 + E^25*(-56 + 48*x) + E^20*(-280 + 280*x - 120*x^2) + E^15*(-800 + 11 20*x - 560*x^2 + 160*x^3) + E^10*(-1760 + 2400*x - 1680*x^2 + 560*x^3 - 12 0*x^4) + E^5*(-2208 + 3520*x - 2400*x^2 + 1120*x^3 - 280*x^4 + 48*x^5))*Lo g[3])/(7776 + E^50 + E^45*(10 - 10*x) - 12960*x + 15120*x^2 - 11520*x^3 + 6960*x^4 - 3152*x^5 + 1160*x^6 - 320*x^7 + 70*x^8 - 10*x^9 + x^10 + E^40*( 70 - 90*x + 45*x^2) + E^35*(320 - 560*x + 360*x^2 - 120*x^3) + E^30*(1160 - 2240*x + 1960*x^2 - 840*x^3 + 210*x^4) + E^25*(3152 - 6960*x + 6720*x^2 - 3920*x^3 + 1260*x^4 - 252*x^5) + E^20*(6960 - 15760*x + 17400*x^2 - 1120 0*x^3 + 4900*x^4 - 1260*x^5 + 210*x^6) + E^15*(11520 - 27840*x + 31520*x^2 - 23200*x^3 + 11200*x^4 - 3920*x^5 + 840*x^6 - 120*x^7) + E^10*(15120 - 3 4560*x + 41760*x^2 - 31520*x^3 + 17400*x^4 - 6720*x^5 + 1960*x^6 - 360*x^7 + 45*x^8) + E^5*(12960 - 30240*x + 34560*x^2 - 27840*x^3 + 15760*x^4 - 69 60*x^5 + 2240*x^6 - 560*x^7 + 90*x^8 - 10*x^9)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(60\) vs. \(2(29)=58\).
Time = 11.24 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.74
| method | result | size |
| risch | \(\frac {{\mathrm e}^{8 x +30}}{\left ({\mathrm e}^{10}-2 x \,{\mathrm e}^{5}+x^{2}+2 \,{\mathrm e}^{5}-2 x +6\right )^{4}}-\frac {2 \ln \left (3\right ) {\mathrm e}^{4 x +15}}{\left ({\mathrm e}^{10}-2 x \,{\mathrm e}^{5}+x^{2}+2 \,{\mathrm e}^{5}-2 x +6\right )^{2}}\) | \(61\) |
| norman | \(\frac {{\mathrm e}^{8 x +30}+\left (-2 \ln \left (3\right ) {\mathrm e}^{20}-8 \ln \left (3\right ) {\mathrm e}^{15}-32 \ln \left (3\right ) {\mathrm e}^{10}-48 \ln \left (3\right ) {\mathrm e}^{5}-72 \ln \left (3\right )\right ) {\mathrm e}^{4 x +15}+\left (8 \ln \left (3\right )+8 \ln \left (3\right ) {\mathrm e}^{5}\right ) x^{3} {\mathrm e}^{4 x +15}+\left (-12 \ln \left (3\right ) {\mathrm e}^{10}-24 \ln \left (3\right ) {\mathrm e}^{5}-32 \ln \left (3\right )\right ) x^{2} {\mathrm e}^{4 x +15}+\left (8 \ln \left (3\right ) {\mathrm e}^{15}+24 \ln \left (3\right ) {\mathrm e}^{10}+64 \ln \left (3\right ) {\mathrm e}^{5}+48 \ln \left (3\right )\right ) x \,{\mathrm e}^{4 x +15}-2 x^{4} \ln \left (3\right ) {\mathrm e}^{4 x +15}}{\left ({\mathrm e}^{10}-2 x \,{\mathrm e}^{5}+x^{2}+2 \,{\mathrm e}^{5}-2 x +6\right )^{4}}\) | \(174\) |
| parallelrisch | \(-\frac {-{\mathrm e}^{8 x +30}-8 \ln \left (3\right ) {\mathrm e}^{4 x +15} x^{3}+32 \ln \left (3\right ) {\mathrm e}^{10} {\mathrm e}^{4 x +15}+32 \ln \left (3\right ) {\mathrm e}^{4 x +15} x^{2}+48 \ln \left (3\right ) {\mathrm e}^{5} {\mathrm e}^{4 x +15}-48 \ln \left (3\right ) {\mathrm e}^{4 x +15} x +72 \ln \left (3\right ) {\mathrm e}^{4 x +15}+2 x^{4} \ln \left (3\right ) {\mathrm e}^{4 x +15}+2 \ln \left (3\right ) {\mathrm e}^{20} {\mathrm e}^{4 x +15}+8 \ln \left (3\right ) {\mathrm e}^{15} {\mathrm e}^{4 x +15}-8 \ln \left (3\right ) {\mathrm e}^{15} {\mathrm e}^{4 x +15} x +12 \ln \left (3\right ) {\mathrm e}^{10} {\mathrm e}^{4 x +15} x^{2}-8 \ln \left (3\right ) {\mathrm e}^{5} {\mathrm e}^{4 x +15} x^{3}-24 \ln \left (3\right ) {\mathrm e}^{10} {\mathrm e}^{4 x +15} x +24 \ln \left (3\right ) {\mathrm e}^{5} {\mathrm e}^{4 x +15} x^{2}-64 \ln \left (3\right ) {\mathrm e}^{5} {\mathrm e}^{4 x +15} x}{1296-1728 x -3168 \,{\mathrm e}^{10} x -880 x \,{\mathrm e}^{20}-56 x^{3} {\mathrm e}^{25}+168 x^{2} {\mathrm e}^{25}+880 x^{4} {\mathrm e}^{5}-2080 x^{3} {\mathrm e}^{5}-3456 x \,{\mathrm e}^{5}+3120 \,{\mathrm e}^{10} x^{2}-1760 x^{3} {\mathrm e}^{10}+1728 \,{\mathrm e}^{10}+8 \,{\mathrm e}^{35}-288 x^{5} {\mathrm e}^{5}+1760 x^{2} {\mathrm e}^{15}+1056 \,{\mathrm e}^{15}-288 x \,{\mathrm e}^{25}+56 x^{6} {\mathrm e}^{5}+520 \,{\mathrm e}^{20}+3168 x^{2} {\mathrm e}^{5}+176 \,{\mathrm e}^{25}+x^{8}+1728 \,{\mathrm e}^{5}-176 x^{5}-8 x^{7}+48 x^{6}+1728 x^{2}-1056 x^{3}+520 x^{4}-960 x^{3} {\mathrm e}^{15}+720 \,{\mathrm e}^{10} x^{4}-2080 x \,{\mathrm e}^{15}+280 x^{4} {\mathrm e}^{15}-280 \,{\mathrm e}^{20} x^{3}-168 \,{\mathrm e}^{10} x^{5}-56 \,{\mathrm e}^{15} x^{5}+720 x^{2} {\mathrm e}^{20}+28 x^{6} {\mathrm e}^{10}-8 \,{\mathrm e}^{35} x -56 \,{\mathrm e}^{30} x +70 x^{4} {\mathrm e}^{20}-8 \,{\mathrm e}^{5} x^{7}+28 \,{\mathrm e}^{30} x^{2}+48 \,{\mathrm e}^{30}+{\mathrm e}^{40}}\) | \(526\) |
| parts | \(\text {Expression too large to display}\) | \(9359\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(64531\) |
| default | \(\text {Expression too large to display}\) | \(64531\) |
Input:
int(((8*exp(5)^2+(-16*x+24)*exp(5)+8*x^2-24*x+56)*exp(4*x+15)^2+(-8*exp(5) ^6+(48*x-56)*exp(5)^5+(-120*x^2+280*x-280)*exp(5)^4+(160*x^3-560*x^2+1120* x-800)*exp(5)^3+(-120*x^4+560*x^3-1680*x^2+2400*x-1760)*exp(5)^2+(48*x^5-2 80*x^4+1120*x^3-2400*x^2+3520*x-2208)*exp(5)-8*x^6+56*x^5-280*x^4+800*x^3- 1760*x^2+2208*x-2016)*ln(3)*exp(4*x+15))/(exp(5)^10+(-10*x+10)*exp(5)^9+(4 5*x^2-90*x+70)*exp(5)^8+(-120*x^3+360*x^2-560*x+320)*exp(5)^7+(210*x^4-840 *x^3+1960*x^2-2240*x+1160)*exp(5)^6+(-252*x^5+1260*x^4-3920*x^3+6720*x^2-6 960*x+3152)*exp(5)^5+(210*x^6-1260*x^5+4900*x^4-11200*x^3+17400*x^2-15760* x+6960)*exp(5)^4+(-120*x^7+840*x^6-3920*x^5+11200*x^4-23200*x^3+31520*x^2- 27840*x+11520)*exp(5)^3+(45*x^8-360*x^7+1960*x^6-6720*x^5+17400*x^4-31520* x^3+41760*x^2-34560*x+15120)*exp(5)^2+(-10*x^9+90*x^8-560*x^7+2240*x^6-696 0*x^5+15760*x^4-27840*x^3+34560*x^2-30240*x+12960)*exp(5)+x^10-10*x^9+70*x ^8-320*x^7+1160*x^6-3152*x^5+6960*x^4-11520*x^3+15120*x^2-12960*x+7776),x, method=_RETURNVERBOSE)
Output:
1/(exp(10)-2*x*exp(5)+x^2+2*exp(5)-2*x+6)^4*exp(8*x+30)-2*ln(3)/(exp(10)-2 *x*exp(5)+x^2+2*exp(5)-2*x+6)^2*exp(4*x+15)
Leaf count of result is larger than twice the leaf count of optimal. 285 vs. \(2 (29) = 58\).
Time = 0.11 (sec) , antiderivative size = 285, normalized size of antiderivative = 8.14 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=-\frac {2 \, {\left (x^{4} - 4 \, x^{3} + 16 \, x^{2} - 4 \, {\left (x - 1\right )} e^{15} + 2 \, {\left (3 \, x^{2} - 6 \, x + 8\right )} e^{10} - 4 \, {\left (x^{3} - 3 \, x^{2} + 8 \, x - 6\right )} e^{5} - 24 \, x + e^{20} + 36\right )} e^{\left (4 \, x + 15\right )} \log \left (3\right ) - e^{\left (8 \, x + 30\right )}}{x^{8} - 8 \, x^{7} + 48 \, x^{6} - 176 \, x^{5} + 520 \, x^{4} - 1056 \, x^{3} + 1728 \, x^{2} - 8 \, {\left (x - 1\right )} e^{35} + 4 \, {\left (7 \, x^{2} - 14 \, x + 12\right )} e^{30} - 8 \, {\left (7 \, x^{3} - 21 \, x^{2} + 36 \, x - 22\right )} e^{25} + 10 \, {\left (7 \, x^{4} - 28 \, x^{3} + 72 \, x^{2} - 88 \, x + 52\right )} e^{20} - 8 \, {\left (7 \, x^{5} - 35 \, x^{4} + 120 \, x^{3} - 220 \, x^{2} + 260 \, x - 132\right )} e^{15} + 4 \, {\left (7 \, x^{6} - 42 \, x^{5} + 180 \, x^{4} - 440 \, x^{3} + 780 \, x^{2} - 792 \, x + 432\right )} e^{10} - 8 \, {\left (x^{7} - 7 \, x^{6} + 36 \, x^{5} - 110 \, x^{4} + 260 \, x^{3} - 396 \, x^{2} + 432 \, x - 216\right )} e^{5} - 1728 \, x + e^{40} + 1296} \] Input:
integrate(((8*exp(5)^2+(-16*x+24)*exp(5)+8*x^2-24*x+56)*exp(4*x+15)^2+(-8* exp(5)^6+(48*x-56)*exp(5)^5+(-120*x^2+280*x-280)*exp(5)^4+(160*x^3-560*x^2 +1120*x-800)*exp(5)^3+(-120*x^4+560*x^3-1680*x^2+2400*x-1760)*exp(5)^2+(48 *x^5-280*x^4+1120*x^3-2400*x^2+3520*x-2208)*exp(5)-8*x^6+56*x^5-280*x^4+80 0*x^3-1760*x^2+2208*x-2016)*log(3)*exp(4*x+15))/(exp(5)^10+(-10*x+10)*exp( 5)^9+(45*x^2-90*x+70)*exp(5)^8+(-120*x^3+360*x^2-560*x+320)*exp(5)^7+(210* x^4-840*x^3+1960*x^2-2240*x+1160)*exp(5)^6+(-252*x^5+1260*x^4-3920*x^3+672 0*x^2-6960*x+3152)*exp(5)^5+(210*x^6-1260*x^5+4900*x^4-11200*x^3+17400*x^2 -15760*x+6960)*exp(5)^4+(-120*x^7+840*x^6-3920*x^5+11200*x^4-23200*x^3+315 20*x^2-27840*x+11520)*exp(5)^3+(45*x^8-360*x^7+1960*x^6-6720*x^5+17400*x^4 -31520*x^3+41760*x^2-34560*x+15120)*exp(5)^2+(-10*x^9+90*x^8-560*x^7+2240* x^6-6960*x^5+15760*x^4-27840*x^3+34560*x^2-30240*x+12960)*exp(5)+x^10-10*x ^9+70*x^8-320*x^7+1160*x^6-3152*x^5+6960*x^4-11520*x^3+15120*x^2-12960*x+7 776),x, algorithm="fricas")
Output:
-(2*(x^4 - 4*x^3 + 16*x^2 - 4*(x - 1)*e^15 + 2*(3*x^2 - 6*x + 8)*e^10 - 4* (x^3 - 3*x^2 + 8*x - 6)*e^5 - 24*x + e^20 + 36)*e^(4*x + 15)*log(3) - e^(8 *x + 30))/(x^8 - 8*x^7 + 48*x^6 - 176*x^5 + 520*x^4 - 1056*x^3 + 1728*x^2 - 8*(x - 1)*e^35 + 4*(7*x^2 - 14*x + 12)*e^30 - 8*(7*x^3 - 21*x^2 + 36*x - 22)*e^25 + 10*(7*x^4 - 28*x^3 + 72*x^2 - 88*x + 52)*e^20 - 8*(7*x^5 - 35* x^4 + 120*x^3 - 220*x^2 + 260*x - 132)*e^15 + 4*(7*x^6 - 42*x^5 + 180*x^4 - 440*x^3 + 780*x^2 - 792*x + 432)*e^10 - 8*(x^7 - 7*x^6 + 36*x^5 - 110*x^ 4 + 260*x^3 - 396*x^2 + 432*x - 216)*e^5 - 1728*x + e^40 + 1296)
Leaf count of result is larger than twice the leaf count of optimal. 1217 vs. \(2 (24) = 48\).
Time = 0.55 (sec) , antiderivative size = 1217, normalized size of antiderivative = 34.77 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=\text {Too large to display} \] Input:
integrate(((8*exp(5)**2+(-16*x+24)*exp(5)+8*x**2-24*x+56)*exp(4*x+15)**2+( -8*exp(5)**6+(48*x-56)*exp(5)**5+(-120*x**2+280*x-280)*exp(5)**4+(160*x**3 -560*x**2+1120*x-800)*exp(5)**3+(-120*x**4+560*x**3-1680*x**2+2400*x-1760) *exp(5)**2+(48*x**5-280*x**4+1120*x**3-2400*x**2+3520*x-2208)*exp(5)-8*x** 6+56*x**5-280*x**4+800*x**3-1760*x**2+2208*x-2016)*ln(3)*exp(4*x+15))/(exp (5)**10+(-10*x+10)*exp(5)**9+(45*x**2-90*x+70)*exp(5)**8+(-120*x**3+360*x* *2-560*x+320)*exp(5)**7+(210*x**4-840*x**3+1960*x**2-2240*x+1160)*exp(5)** 6+(-252*x**5+1260*x**4-3920*x**3+6720*x**2-6960*x+3152)*exp(5)**5+(210*x** 6-1260*x**5+4900*x**4-11200*x**3+17400*x**2-15760*x+6960)*exp(5)**4+(-120* x**7+840*x**6-3920*x**5+11200*x**4-23200*x**3+31520*x**2-27840*x+11520)*ex p(5)**3+(45*x**8-360*x**7+1960*x**6-6720*x**5+17400*x**4-31520*x**3+41760* x**2-34560*x+15120)*exp(5)**2+(-10*x**9+90*x**8-560*x**7+2240*x**6-6960*x* *5+15760*x**4-27840*x**3+34560*x**2-30240*x+12960)*exp(5)+x**10-10*x**9+70 *x**8-320*x**7+1160*x**6-3152*x**5+6960*x**4-11520*x**3+15120*x**2-12960*x +7776),x)
Output:
((x**4 - 4*x**3*exp(5) - 4*x**3 + 16*x**2 + 12*x**2*exp(5) + 6*x**2*exp(10 ) - 4*x*exp(15) - 12*x*exp(10) - 32*x*exp(5) - 24*x + 36 + 24*exp(5) + 16* exp(10) + 4*exp(15) + exp(20))*exp(8*x + 30) + (-2*x**8*log(3) + 16*x**7*l og(3) + 16*x**7*exp(5)*log(3) - 56*x**6*exp(10)*log(3) - 112*x**6*exp(5)*l og(3) - 96*x**6*log(3) + 352*x**5*log(3) + 576*x**5*exp(5)*log(3) + 336*x* *5*exp(10)*log(3) + 112*x**5*exp(15)*log(3) - 140*x**4*exp(20)*log(3) - 56 0*x**4*exp(15)*log(3) - 1440*x**4*exp(10)*log(3) - 1760*x**4*exp(5)*log(3) - 1040*x**4*log(3) + 2112*x**3*log(3) + 4160*x**3*exp(5)*log(3) + 3520*x* *3*exp(10)*log(3) + 1920*x**3*exp(15)*log(3) + 560*x**3*exp(20)*log(3) + 1 12*x**3*exp(25)*log(3) - 56*x**2*exp(30)*log(3) - 336*x**2*exp(25)*log(3) - 1440*x**2*exp(20)*log(3) - 3520*x**2*exp(15)*log(3) - 6240*x**2*exp(10)* log(3) - 6336*x**2*exp(5)*log(3) - 3456*x**2*log(3) + 3456*x*log(3) + 6912 *x*exp(5)*log(3) + 6336*x*exp(10)*log(3) + 4160*x*exp(15)*log(3) + 1760*x* exp(20)*log(3) + 576*x*exp(25)*log(3) + 112*x*exp(30)*log(3) + 16*x*exp(35 )*log(3) - 2*exp(40)*log(3) - 16*exp(35)*log(3) - 96*exp(30)*log(3) - 352* exp(25)*log(3) - 1040*exp(20)*log(3) - 2112*exp(15)*log(3) - 3456*exp(10)* log(3) - 3456*exp(5)*log(3) - 2592*log(3))*exp(4*x + 15))/(x**12 - 12*x**1 1*exp(5) - 12*x**11 + 96*x**10 + 132*x**10*exp(5) + 66*x**10*exp(10) - 220 *x**9*exp(15) - 660*x**9*exp(10) - 960*x**9*exp(5) - 520*x**9 + 2220*x**8 + 4680*x**8*exp(5) + 4320*x**8*exp(10) + 1980*x**8*exp(15) + 495*x**8*e...
Leaf count of result is larger than twice the leaf count of optimal. 314 vs. \(2 (29) = 58\).
Time = 0.28 (sec) , antiderivative size = 314, normalized size of antiderivative = 8.97 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=-\frac {2 \, {\left (x^{4} e^{15} \log \left (3\right ) - 4 \, {\left (e^{20} \log \left (3\right ) + e^{15} \log \left (3\right )\right )} x^{3} + 2 \, {\left (3 \, e^{25} \log \left (3\right ) + 6 \, e^{20} \log \left (3\right ) + 8 \, e^{15} \log \left (3\right )\right )} x^{2} - 4 \, {\left (e^{30} \log \left (3\right ) + 3 \, e^{25} \log \left (3\right ) + 8 \, e^{20} \log \left (3\right ) + 6 \, e^{15} \log \left (3\right )\right )} x + e^{35} \log \left (3\right ) + 4 \, e^{30} \log \left (3\right ) + 16 \, e^{25} \log \left (3\right ) + 24 \, e^{20} \log \left (3\right ) + 36 \, e^{15} \log \left (3\right )\right )} e^{\left (4 \, x\right )} - e^{\left (8 \, x + 30\right )}}{x^{8} - 8 \, x^{7} {\left (e^{5} + 1\right )} + 4 \, x^{6} {\left (7 \, e^{10} + 14 \, e^{5} + 12\right )} - 8 \, x^{5} {\left (7 \, e^{15} + 21 \, e^{10} + 36 \, e^{5} + 22\right )} + 10 \, x^{4} {\left (7 \, e^{20} + 28 \, e^{15} + 72 \, e^{10} + 88 \, e^{5} + 52\right )} - 8 \, x^{3} {\left (7 \, e^{25} + 35 \, e^{20} + 120 \, e^{15} + 220 \, e^{10} + 260 \, e^{5} + 132\right )} + 4 \, x^{2} {\left (7 \, e^{30} + 42 \, e^{25} + 180 \, e^{20} + 440 \, e^{15} + 780 \, e^{10} + 792 \, e^{5} + 432\right )} - 8 \, x {\left (e^{35} + 7 \, e^{30} + 36 \, e^{25} + 110 \, e^{20} + 260 \, e^{15} + 396 \, e^{10} + 432 \, e^{5} + 216\right )} + e^{40} + 8 \, e^{35} + 48 \, e^{30} + 176 \, e^{25} + 520 \, e^{20} + 1056 \, e^{15} + 1728 \, e^{10} + 1728 \, e^{5} + 1296} \] Input:
integrate(((8*exp(5)^2+(-16*x+24)*exp(5)+8*x^2-24*x+56)*exp(4*x+15)^2+(-8* exp(5)^6+(48*x-56)*exp(5)^5+(-120*x^2+280*x-280)*exp(5)^4+(160*x^3-560*x^2 +1120*x-800)*exp(5)^3+(-120*x^4+560*x^3-1680*x^2+2400*x-1760)*exp(5)^2+(48 *x^5-280*x^4+1120*x^3-2400*x^2+3520*x-2208)*exp(5)-8*x^6+56*x^5-280*x^4+80 0*x^3-1760*x^2+2208*x-2016)*log(3)*exp(4*x+15))/(exp(5)^10+(-10*x+10)*exp( 5)^9+(45*x^2-90*x+70)*exp(5)^8+(-120*x^3+360*x^2-560*x+320)*exp(5)^7+(210* x^4-840*x^3+1960*x^2-2240*x+1160)*exp(5)^6+(-252*x^5+1260*x^4-3920*x^3+672 0*x^2-6960*x+3152)*exp(5)^5+(210*x^6-1260*x^5+4900*x^4-11200*x^3+17400*x^2 -15760*x+6960)*exp(5)^4+(-120*x^7+840*x^6-3920*x^5+11200*x^4-23200*x^3+315 20*x^2-27840*x+11520)*exp(5)^3+(45*x^8-360*x^7+1960*x^6-6720*x^5+17400*x^4 -31520*x^3+41760*x^2-34560*x+15120)*exp(5)^2+(-10*x^9+90*x^8-560*x^7+2240* x^6-6960*x^5+15760*x^4-27840*x^3+34560*x^2-30240*x+12960)*exp(5)+x^10-10*x ^9+70*x^8-320*x^7+1160*x^6-3152*x^5+6960*x^4-11520*x^3+15120*x^2-12960*x+7 776),x, algorithm="maxima")
Output:
-(2*(x^4*e^15*log(3) - 4*(e^20*log(3) + e^15*log(3))*x^3 + 2*(3*e^25*log(3 ) + 6*e^20*log(3) + 8*e^15*log(3))*x^2 - 4*(e^30*log(3) + 3*e^25*log(3) + 8*e^20*log(3) + 6*e^15*log(3))*x + e^35*log(3) + 4*e^30*log(3) + 16*e^25*l og(3) + 24*e^20*log(3) + 36*e^15*log(3))*e^(4*x) - e^(8*x + 30))/(x^8 - 8* x^7*(e^5 + 1) + 4*x^6*(7*e^10 + 14*e^5 + 12) - 8*x^5*(7*e^15 + 21*e^10 + 3 6*e^5 + 22) + 10*x^4*(7*e^20 + 28*e^15 + 72*e^10 + 88*e^5 + 52) - 8*x^3*(7 *e^25 + 35*e^20 + 120*e^15 + 220*e^10 + 260*e^5 + 132) + 4*x^2*(7*e^30 + 4 2*e^25 + 180*e^20 + 440*e^15 + 780*e^10 + 792*e^5 + 432) - 8*x*(e^35 + 7*e ^30 + 36*e^25 + 110*e^20 + 260*e^15 + 396*e^10 + 432*e^5 + 216) + e^40 + 8 *e^35 + 48*e^30 + 176*e^25 + 520*e^20 + 1056*e^15 + 1728*e^10 + 1728*e^5 + 1296)
Leaf count of result is larger than twice the leaf count of optimal. 616 vs. \(2 (29) = 58\).
Time = 0.43 (sec) , antiderivative size = 616, normalized size of antiderivative = 17.60 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=\text {Too large to display} \] Input:
integrate(((8*exp(5)^2+(-16*x+24)*exp(5)+8*x^2-24*x+56)*exp(4*x+15)^2+(-8* exp(5)^6+(48*x-56)*exp(5)^5+(-120*x^2+280*x-280)*exp(5)^4+(160*x^3-560*x^2 +1120*x-800)*exp(5)^3+(-120*x^4+560*x^3-1680*x^2+2400*x-1760)*exp(5)^2+(48 *x^5-280*x^4+1120*x^3-2400*x^2+3520*x-2208)*exp(5)-8*x^6+56*x^5-280*x^4+80 0*x^3-1760*x^2+2208*x-2016)*log(3)*exp(4*x+15))/(exp(5)^10+(-10*x+10)*exp( 5)^9+(45*x^2-90*x+70)*exp(5)^8+(-120*x^3+360*x^2-560*x+320)*exp(5)^7+(210* x^4-840*x^3+1960*x^2-2240*x+1160)*exp(5)^6+(-252*x^5+1260*x^4-3920*x^3+672 0*x^2-6960*x+3152)*exp(5)^5+(210*x^6-1260*x^5+4900*x^4-11200*x^3+17400*x^2 -15760*x+6960)*exp(5)^4+(-120*x^7+840*x^6-3920*x^5+11200*x^4-23200*x^3+315 20*x^2-27840*x+11520)*exp(5)^3+(45*x^8-360*x^7+1960*x^6-6720*x^5+17400*x^4 -31520*x^3+41760*x^2-34560*x+15120)*exp(5)^2+(-10*x^9+90*x^8-560*x^7+2240* x^6-6960*x^5+15760*x^4-27840*x^3+34560*x^2-30240*x+12960)*exp(5)+x^10-10*x ^9+70*x^8-320*x^7+1160*x^6-3152*x^5+6960*x^4-11520*x^3+15120*x^2-12960*x+7 776),x, algorithm="giac")
Output:
-1024*((4*x + 15)^4*e^(4*x + 15)*log(3) - 16*(4*x + 15)^3*e^(4*x + 20)*log (3) - 76*(4*x + 15)^3*e^(4*x + 15)*log(3) + 96*(4*x + 15)^2*e^(4*x + 25)*l og(3) + 912*(4*x + 15)^2*e^(4*x + 20)*log(3) + 2326*(4*x + 15)^2*e^(4*x + 15)*log(3) - 256*(4*x + 15)*e^(4*x + 30)*log(3) - 3648*(4*x + 15)*e^(4*x + 25)*log(3) - 18608*(4*x + 15)*e^(4*x + 20)*log(3) - 33516*(4*x + 15)*e^(4 *x + 15)*log(3) + 256*e^(4*x + 35)*log(3) + 4864*e^(4*x + 30)*log(3) + 372 16*e^(4*x + 25)*log(3) + 134064*e^(4*x + 20)*log(3) + 194481*e^(4*x + 15)* log(3) - 128*e^(8*x + 30))/((4*x + 15)^8 - 32*(4*x + 15)^7*e^5 - 152*(4*x + 15)^7 + 448*(4*x + 15)^6*e^10 + 4256*(4*x + 15)^6*e^5 + 10428*(4*x + 15) ^6 - 3584*(4*x + 15)^5*e^15 - 51072*(4*x + 15)^5*e^10 - 250272*(4*x + 15)^ 5*e^5 - 420584*(4*x + 15)^5 + 17920*(4*x + 15)^4*e^20 + 340480*(4*x + 15)^ 4*e^15 + 2502720*(4*x + 15)^4*e^10 + 8411680*(4*x + 15)^4*e^5 + 10893670*( 4*x + 15)^4 - 57344*(4*x + 15)^3*e^25 - 1361920*(4*x + 15)^3*e^20 - 133478 40*(4*x + 15)^3*e^15 - 67293440*(4*x + 15)^3*e^10 - 174298720*(4*x + 15)^3 *e^5 - 185477544*(4*x + 15)^3 + 114688*(4*x + 15)^2*e^30 + 3268608*(4*x + 15)^2*e^25 + 40043520*(4*x + 15)^2*e^20 + 269173760*(4*x + 15)^2*e^15 + 10 45792320*(4*x + 15)^2*e^10 + 2225730528*(4*x + 15)^2*e^5 + 2028047868*(4*x + 15)^2 - 131072*(4*x + 15)*e^35 - 4358144*(4*x + 15)*e^30 - 64069632*(4* x + 15)*e^25 - 538347520*(4*x + 15)*e^20 - 2788779520*(4*x + 15)*e^15 - 89 02922112*(4*x + 15)*e^10 - 16224382944*(4*x + 15)*e^5 - 52145801568*x +...
Timed out. \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=\text {Hanged} \] Input:
int((exp(8*x + 30)*(8*exp(10) - 24*x + 8*x^2 - exp(5)*(16*x - 24) + 56) - exp(4*x + 15)*log(3)*(8*exp(30) - 2208*x + exp(20)*(120*x^2 - 280*x + 280) - exp(15)*(1120*x - 560*x^2 + 160*x^3 - 800) + exp(10)*(1680*x^2 - 2400*x - 560*x^3 + 120*x^4 + 1760) - exp(5)*(3520*x - 2400*x^2 + 1120*x^3 - 280* x^4 + 48*x^5 - 2208) + 1760*x^2 - 800*x^3 + 280*x^4 - 56*x^5 + 8*x^6 - exp (25)*(48*x - 56) + 2016))/(exp(50) - 12960*x + exp(20)*(17400*x^2 - 15760* x - 11200*x^3 + 4900*x^4 - 1260*x^5 + 210*x^6 + 6960) + exp(40)*(45*x^2 - 90*x + 70) - exp(15)*(27840*x - 31520*x^2 + 23200*x^3 - 11200*x^4 + 3920*x ^5 - 840*x^6 + 120*x^7 - 11520) - exp(35)*(560*x - 360*x^2 + 120*x^3 - 320 ) + exp(10)*(41760*x^2 - 34560*x - 31520*x^3 + 17400*x^4 - 6720*x^5 + 1960 *x^6 - 360*x^7 + 45*x^8 + 15120) + exp(30)*(1960*x^2 - 2240*x - 840*x^3 + 210*x^4 + 1160) - exp(5)*(30240*x - 34560*x^2 + 27840*x^3 - 15760*x^4 + 69 60*x^5 - 2240*x^6 + 560*x^7 - 90*x^8 + 10*x^9 - 12960) - exp(25)*(6960*x - 6720*x^2 + 3920*x^3 - 1260*x^4 + 252*x^5 - 3152) + 15120*x^2 - 11520*x^3 + 6960*x^4 - 3152*x^5 + 1160*x^6 - 320*x^7 + 70*x^8 - 10*x^9 + x^10 - exp( 45)*(10*x - 10) + 7776),x)
Output:
\text{Hanged}
Time = 0.20 (sec) , antiderivative size = 419, normalized size of antiderivative = 11.97 \[ \int \frac {e^{30+8 x} \left (56+8 e^{10}+e^5 (24-16 x)-24 x+8 x^2\right )+e^{15+4 x} \left (-2016-8 e^{30}+2208 x-1760 x^2+800 x^3-280 x^4+56 x^5-8 x^6+e^{25} (-56+48 x)+e^{20} \left (-280+280 x-120 x^2\right )+e^{15} \left (-800+1120 x-560 x^2+160 x^3\right )+e^{10} \left (-1760+2400 x-1680 x^2+560 x^3-120 x^4\right )+e^5 \left (-2208+3520 x-2400 x^2+1120 x^3-280 x^4+48 x^5\right )\right ) \log (3)}{7776+e^{50}+e^{45} (10-10 x)-12960 x+15120 x^2-11520 x^3+6960 x^4-3152 x^5+1160 x^6-320 x^7+70 x^8-10 x^9+x^{10}+e^{40} \left (70-90 x+45 x^2\right )+e^{35} \left (320-560 x+360 x^2-120 x^3\right )+e^{30} \left (1160-2240 x+1960 x^2-840 x^3+210 x^4\right )+e^{25} \left (3152-6960 x+6720 x^2-3920 x^3+1260 x^4-252 x^5\right )+e^{20} \left (6960-15760 x+17400 x^2-11200 x^3+4900 x^4-1260 x^5+210 x^6\right )+e^{15} \left (11520-27840 x+31520 x^2-23200 x^3+11200 x^4-3920 x^5+840 x^6-120 x^7\right )+e^{10} \left (15120-34560 x+41760 x^2-31520 x^3+17400 x^4-6720 x^5+1960 x^6-360 x^7+45 x^8\right )+e^5 \left (12960-30240 x+34560 x^2-27840 x^3+15760 x^4-6960 x^5+2240 x^6-560 x^7+90 x^8-10 x^9\right )} \, dx=\frac {e^{4 x} e^{15} \left (e^{4 x} e^{15}-2 \,\mathrm {log}\left (3\right ) e^{20}+8 \,\mathrm {log}\left (3\right ) e^{15} x -8 \,\mathrm {log}\left (3\right ) e^{15}-12 \,\mathrm {log}\left (3\right ) e^{10} x^{2}+24 \,\mathrm {log}\left (3\right ) e^{10} x -32 \,\mathrm {log}\left (3\right ) e^{10}+8 \,\mathrm {log}\left (3\right ) e^{5} x^{3}-24 \,\mathrm {log}\left (3\right ) e^{5} x^{2}+64 \,\mathrm {log}\left (3\right ) e^{5} x -48 \,\mathrm {log}\left (3\right ) e^{5}-2 \,\mathrm {log}\left (3\right ) x^{4}+8 \,\mathrm {log}\left (3\right ) x^{3}-32 \,\mathrm {log}\left (3\right ) x^{2}+48 \,\mathrm {log}\left (3\right ) x -72 \,\mathrm {log}\left (3\right )\right )}{e^{40}-8 e^{35} x +8 e^{35}+28 e^{30} x^{2}-56 e^{30} x +48 e^{30}-56 e^{25} x^{3}+168 e^{25} x^{2}-288 e^{25} x +176 e^{25}+70 e^{20} x^{4}-280 e^{20} x^{3}+720 e^{20} x^{2}-880 e^{20} x +520 e^{20}-56 e^{15} x^{5}+280 e^{15} x^{4}-960 e^{15} x^{3}+1760 e^{15} x^{2}-2080 e^{15} x +28 e^{10} x^{6}+1056 e^{15}-168 e^{10} x^{5}+720 e^{10} x^{4}-1760 e^{10} x^{3}+3120 e^{10} x^{2}-8 e^{5} x^{7}-3168 e^{10} x +56 e^{5} x^{6}+1728 e^{10}-288 e^{5} x^{5}+880 e^{5} x^{4}-2080 e^{5} x^{3}+x^{8}+3168 e^{5} x^{2}-8 x^{7}-3456 e^{5} x +48 x^{6}+1728 e^{5}-176 x^{5}+520 x^{4}-1056 x^{3}+1728 x^{2}-1728 x +1296} \] Input:
int(((8*exp(5)^2+(-16*x+24)*exp(5)+8*x^2-24*x+56)*exp(4*x+15)^2+(-8*exp(5) ^6+(48*x-56)*exp(5)^5+(-120*x^2+280*x-280)*exp(5)^4+(160*x^3-560*x^2+1120* x-800)*exp(5)^3+(-120*x^4+560*x^3-1680*x^2+2400*x-1760)*exp(5)^2+(48*x^5-2 80*x^4+1120*x^3-2400*x^2+3520*x-2208)*exp(5)-8*x^6+56*x^5-280*x^4+800*x^3- 1760*x^2+2208*x-2016)*log(3)*exp(4*x+15))/(exp(5)^10+(-10*x+10)*exp(5)^9+( 45*x^2-90*x+70)*exp(5)^8+(-120*x^3+360*x^2-560*x+320)*exp(5)^7+(210*x^4-84 0*x^3+1960*x^2-2240*x+1160)*exp(5)^6+(-252*x^5+1260*x^4-3920*x^3+6720*x^2- 6960*x+3152)*exp(5)^5+(210*x^6-1260*x^5+4900*x^4-11200*x^3+17400*x^2-15760 *x+6960)*exp(5)^4+(-120*x^7+840*x^6-3920*x^5+11200*x^4-23200*x^3+31520*x^2 -27840*x+11520)*exp(5)^3+(45*x^8-360*x^7+1960*x^6-6720*x^5+17400*x^4-31520 *x^3+41760*x^2-34560*x+15120)*exp(5)^2+(-10*x^9+90*x^8-560*x^7+2240*x^6-69 60*x^5+15760*x^4-27840*x^3+34560*x^2-30240*x+12960)*exp(5)+x^10-10*x^9+70* x^8-320*x^7+1160*x^6-3152*x^5+6960*x^4-11520*x^3+15120*x^2-12960*x+7776),x )
Output:
(e**(4*x)*e**15*(e**(4*x)*e**15 - 2*log(3)*e**20 + 8*log(3)*e**15*x - 8*lo g(3)*e**15 - 12*log(3)*e**10*x**2 + 24*log(3)*e**10*x - 32*log(3)*e**10 + 8*log(3)*e**5*x**3 - 24*log(3)*e**5*x**2 + 64*log(3)*e**5*x - 48*log(3)*e* *5 - 2*log(3)*x**4 + 8*log(3)*x**3 - 32*log(3)*x**2 + 48*log(3)*x - 72*log (3)))/(e**40 - 8*e**35*x + 8*e**35 + 28*e**30*x**2 - 56*e**30*x + 48*e**30 - 56*e**25*x**3 + 168*e**25*x**2 - 288*e**25*x + 176*e**25 + 70*e**20*x** 4 - 280*e**20*x**3 + 720*e**20*x**2 - 880*e**20*x + 520*e**20 - 56*e**15*x **5 + 280*e**15*x**4 - 960*e**15*x**3 + 1760*e**15*x**2 - 2080*e**15*x + 1 056*e**15 + 28*e**10*x**6 - 168*e**10*x**5 + 720*e**10*x**4 - 1760*e**10*x **3 + 3120*e**10*x**2 - 3168*e**10*x + 1728*e**10 - 8*e**5*x**7 + 56*e**5* x**6 - 288*e**5*x**5 + 880*e**5*x**4 - 2080*e**5*x**3 + 3168*e**5*x**2 - 3 456*e**5*x + 1728*e**5 + x**8 - 8*x**7 + 48*x**6 - 176*x**5 + 520*x**4 - 1 056*x**3 + 1728*x**2 - 1728*x + 1296)