Integrand size = 726, antiderivative size = 34 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=\frac {1}{4+\frac {\left (x+5 \left (e^4+\frac {x+\frac {4 x}{4+x}}{x}\right )^2\right )^2}{x^2}} \] Output:
1/(4+(x+5*(exp(4)+(4*x/(4+x)+x)/x)^2)^2/x^2)
Leaf count is larger than twice the leaf count of optimal. \(158\) vs. \(2(34)=68\).
Time = 0.56 (sec) , antiderivative size = 158, normalized size of antiderivative = 4.65 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {\left (8+x+e^4 (4+x)\right )^2 \left (320+112 x+21 x^2+2 x^3+5 e^8 (4+x)^2+10 e^4 \left (32+12 x+x^2\right )\right )}{5 \left (20480+12288 x+3712 x^2+832 x^3+149 x^4+18 x^5+x^6+5 e^{16} (4+x)^4+20 e^{12} (4+x)^3 (8+x)+2 e^8 (4+x)^2 \left (960+256 x+23 x^2+x^3\right )+4 e^4 \left (10240+6912 x+1888 x^2+284 x^3+25 x^4+x^5\right )\right )} \] Input:
Integrate[(10485760*x + 18874368*x^2 + 14155776*x^3 + 5914624*x^4 + 154572 8*x^5 + 267520*x^6 + 31232*x^7 + 2384*x^8 + 106*x^9 + 2*x^10 + E^16*(65536 0*x + 1310720*x^2 + 1146880*x^3 + 573440*x^4 + 179200*x^5 + 35840*x^6 + 44 80*x^7 + 320*x^8 + 10*x^9) + E^12*(5242880*x + 10158080*x^2 + 8519680*x^3 + 4034560*x^4 + 1177600*x^5 + 216320*x^6 + 24320*x^7 + 1520*x^8 + 40*x^9) + E^8*(15728640*x + 29622272*x^2 + 23855104*x^3 + 10735616*x^4 + 2956288*x ^5 + 512000*x^6 + 55168*x^7 + 3536*x^8 + 124*x^9 + 2*x^10) + E^4*(20971520 *x + 38535168*x^2 + 29884416*x^3 + 12881920*x^4 + 3414016*x^5 + 581120*x^6 + 64512*x^7 + 4624*x^8 + 200*x^9 + 4*x^10))/(2097152000 + 2516582400*x + 1515192320*x^2 + 626524160*x^3 + 201646080*x^4 + 52879360*x^5 + 11408640*x ^6 + 2030720*x^7 + 297885*x^8 + 35140*x^9 + 3110*x^10 + 180*x^11 + 5*x^12 + E^32*(8192000 + 16384000*x + 14336000*x^2 + 7168000*x^3 + 2240000*x^4 + 448000*x^5 + 56000*x^6 + 4000*x^7 + 125*x^8) + E^28*(131072000 + 245760000 *x + 200704000*x^2 + 93184000*x^3 + 26880000*x^4 + 4928000*x^5 + 560000*x^ 6 + 36000*x^7 + 1000*x^8) + E^24*(917504000 + 1612185600*x + 1231667200*x^ 2 + 534732800*x^3 + 144614400*x^4 + 25088000*x^5 + 2766400*x^6 + 184800*x^ 7 + 6700*x^8 + 100*x^9) + E^20*(3670016000 + 6042419200*x + 4333568000*x^2 + 1776230400*x^3 + 459110400*x^4 + 77952000*x^5 + 8780800*x^6 + 644000*x^ 7 + 28600*x^8 + 600*x^9) + E^16*(9175040000 + 14155776000*x + 9581035520*x ^2 + 3757015040*x^3 + 951324160*x^4 + 164334080*x^5 + 19918400*x^6 + 17028 80*x^7 + 100110*x^8 + 3740*x^9 + 70*x^10) + E^12*(14680064000 + 2123366400 0*x + 13668188160*x^2 + 5221580800*x^3 + 1335685120*x^4 + 244779520*x^5 + 33366400*x^6 + 3407840*x^7 + 251800*x^8 + 12080*x^9 + 280*x^10) + E^8*(146 80064000 + 19922944000*x + 12332564480*x^2 + 4699586560*x^3 + 1257328640*x ^4 + 253757440*x^5 + 39852480*x^6 + 4837920*x^7 + 436140*x^8 + 27260*x^9 + 1060*x^10 + 20*x^11) + E^4*(8388608000 + 10695475200*x + 6464471040*x^2 + 2527723520*x^3 + 731463680*x^4 + 166676480*x^5 + 30293760*x^6 + 4308960*x ^7 + 462280*x^8 + 35320*x^9 + 1720*x^10 + 40*x^11)),x]
Output:
-1/5*((8 + x + E^4*(4 + x))^2*(320 + 112*x + 21*x^2 + 2*x^3 + 5*E^8*(4 + x )^2 + 10*E^4*(32 + 12*x + x^2)))/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 1 49*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E ^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x ^2 + 284*x^3 + 25*x^4 + x^5))
Leaf count is larger than twice the leaf count of optimal. \(766\) vs. \(2(34)=68\).
Time = 22.86 (sec) , antiderivative size = 766, normalized size of antiderivative = 22.53, number of steps used = 14, number of rules used = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2462, 7239, 27, 2527, 25, 2527, 27, 2527, 27, 2527, 27, 2527, 27, 2021}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {2 x^{10}+106 x^9+2384 x^8+31232 x^7+267520 x^6+1545728 x^5+5914624 x^4+14155776 x^3+18874368 x^2+e^{16} \left (10 x^9+320 x^8+4480 x^7+35840 x^6+179200 x^5+573440 x^4+1146880 x^3+1310720 x^2+655360 x\right )+e^{12} \left (40 x^9+1520 x^8+24320 x^7+216320 x^6+1177600 x^5+4034560 x^4+8519680 x^3+10158080 x^2+5242880 x\right )+e^8 \left (2 x^{10}+124 x^9+3536 x^8+55168 x^7+512000 x^6+2956288 x^5+10735616 x^4+23855104 x^3+29622272 x^2+15728640 x\right )+e^4 \left (4 x^{10}+200 x^9+4624 x^8+64512 x^7+581120 x^6+3414016 x^5+12881920 x^4+29884416 x^3+38535168 x^2+20971520 x\right )+10485760 x}{5 x^{12}+180 x^{11}+3110 x^{10}+35140 x^9+297885 x^8+2030720 x^7+11408640 x^6+52879360 x^5+201646080 x^4+626524160 x^3+1515192320 x^2+e^{32} \left (125 x^8+4000 x^7+56000 x^6+448000 x^5+2240000 x^4+7168000 x^3+14336000 x^2+16384000 x+8192000\right )+e^{28} \left (1000 x^8+36000 x^7+560000 x^6+4928000 x^5+26880000 x^4+93184000 x^3+200704000 x^2+245760000 x+131072000\right )+e^{24} \left (100 x^9+6700 x^8+184800 x^7+2766400 x^6+25088000 x^5+144614400 x^4+534732800 x^3+1231667200 x^2+1612185600 x+917504000\right )+e^{20} \left (600 x^9+28600 x^8+644000 x^7+8780800 x^6+77952000 x^5+459110400 x^4+1776230400 x^3+4333568000 x^2+6042419200 x+3670016000\right )+e^{16} \left (70 x^{10}+3740 x^9+100110 x^8+1702880 x^7+19918400 x^6+164334080 x^5+951324160 x^4+3757015040 x^3+9581035520 x^2+14155776000 x+9175040000\right )+e^{12} \left (280 x^{10}+12080 x^9+251800 x^8+3407840 x^7+33366400 x^6+244779520 x^5+1335685120 x^4+5221580800 x^3+13668188160 x^2+21233664000 x+14680064000\right )+2516582400 x+e^8 \left (20 x^{11}+1060 x^{10}+27260 x^9+436140 x^8+4837920 x^7+39852480 x^6+253757440 x^5+1257328640 x^4+4699586560 x^3+12332564480 x^2+19922944000 x+14680064000\right )+e^4 \left (40 x^{11}+1720 x^{10}+35320 x^9+462280 x^8+4308960 x^7+30293760 x^6+166676480 x^5+731463680 x^4+2527723520 x^3+6464471040 x^2+10695475200 x+8388608000\right )+2097152000} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {2 \left (\left (1+e^4\right )^2 x^4+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (2135+2872 e^4-1100 e^8-4728 e^{12}-3622 e^{16}-1016 e^{20}+20 e^{24}+56 e^{28}+7 e^{32}\right ) x+41 e^{40}+410 e^{36}+1957 e^{32}+6096 e^{28}+12650 e^{24}+12276 e^{20}-12582 e^{16}-50688 e^{12}-53715 e^8-19038 e^4+961\right )}{5 \left (x^6+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )\right )}+\frac {2 \left (-48373 \left (1+\frac {e^4 \left (181420+170170 e^4-127988 e^8-415141 e^{12}-421352 e^{16}-237620 e^{20}-65416 e^{24}+10011 e^{28}+17212 e^{32}+7066 e^{36}+1404 e^{40}+117 e^{44}\right )}{48373}\right ) x^5-945813 \left (1+\frac {e^4 \left (3115326+1757447 e^4-5561836 e^8-12168283 e^{12}-11709062 e^{16}-6140721 e^{20}-1057288 e^{24}+942951 e^{28}+871506 e^{32}+378717 e^{36}+106420 e^{40}+21087 e^{44}+2870 e^{48}+205 e^{52}\right )}{945813}\right ) x^4-7438528 \left (1+\frac {e^4 \left (1231447-428651 e^4-5518414 e^8-9587746 e^{12}-8466299 e^{16}-3830109 e^{20}-28516 e^{24}+1182304 e^{28}+873985 e^{32}+371195 e^{36}+108626 e^{40}+22582 e^{44}+3075 e^{48}+205 e^{52}\right )}{464908}\right ) x^3-28823168 \left (1+\frac {e^4 \left (1336564-5790417 e^4-21316796 e^8-31233470 e^{12}-24535704 e^{16}-8734047 e^{20}+2364680 e^{24}+4851000 e^{28}+3124372 e^{32}+1274025 e^{36}+367956 e^{40}+75186 e^{44}+9840 e^{48}+615 e^{52}\right )}{900724}\right ) x^2-50290688 \left (1+\frac {e^4 \left (-279636-3949012 e^4-10086545 e^8-12735510 e^{12}-8665919 e^{16}-2057411 e^{20}+1811630 e^{24}+2236024 e^{28}+1299558 e^{32}+506082 e^{36}+141683 e^{40}+27942 e^{44}+3485 e^{48}+205 e^{52}\right )}{196448}\right ) x-19681280 \left (1+\frac {e^4 \left (-273856-1445592 e^4-2979112 e^8-3263831 e^{12}-1871478 e^{16}-165955 e^{20}+645616 e^{24}+615610 e^{28}+328964 e^{32}+122162 e^{36}+32904 e^{40}+6221 e^{44}+738 e^{48}+41 e^{52}\right )}{15376}\right )\right )}{5 \left (x^6+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x (x+4)^3 \left (x^6+41 x^5+652 x^4+5760 x^3+30720 x^2+20 e^{12} (x+4)^3 \left (x^2+14 x+32\right )+e^8 (x+4)^2 \left (x^4+42 x^3+768 x^2+4864 x+7680\right )+2 e^4 \left (x^6+38 x^5+652 x^4+6416 x^3+34560 x^2+89088 x+81920\right )+86016 x+5 e^{16} (x+4)^5+81920\right )}{5 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{5} \int \frac {x (x+4)^3 \left (x^6+41 x^5+652 x^4+5760 x^3+30720 x^2+86016 x+5 e^{16} (x+4)^5+20 e^{12} (x+4)^3 \left (x^2+14 x+32\right )+e^8 (x+4)^2 \left (x^4+42 x^3+768 x^2+4864 x+7680\right )+2 e^4 \left (x^6+38 x^5+652 x^4+6416 x^3+34560 x^2+89088 x+81920\right )+81920\right )}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle \frac {2}{5} \left (-\int -\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^9+\left (1341+2710 e^4+2179 e^8+1004 e^{12}+267 e^{16}+30 e^{20}+5 e^{24}\right ) x^8+32 \left (540+1183 e^4+1113 e^8+590 e^{12}+182 e^{16}+35 e^{20}+5 e^{24}\right ) x^7+32 \left (4528+10484 e^4+10397 e^8+5624 e^{12}+1778 e^{16}+360 e^{20}+45 e^{24}\right ) x^6+256 \left (3211+7484 e^4+7198 e^8+3608 e^{12}+1018 e^{16}+180 e^{20}+20 e^{24}\right ) x^5+256 \left (11952+26760 e^4+23568 e^8+10080 e^{12}+2145 e^{16}+250 e^{20}+25 e^{24}\right ) x^4+16384 \left (2+e^4\right )^2 \left (108+120 e^4+35 e^8\right ) x^3+32768 \left (2+e^4\right )^2 \left (72+75 e^4+20 e^8\right ) x^2+327680 \left (2+e^4\right )^4 x}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}\right )\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle \frac {2}{5} \left (\int \frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^9+\left (1341+2710 e^4+2179 e^8+1004 e^{12}+267 e^{16}+30 e^{20}+5 e^{24}\right ) x^8+32 \left (540+1183 e^4+1113 e^8+590 e^{12}+182 e^{16}+35 e^{20}+5 e^{24}\right ) x^7+32 \left (4528+10484 e^4+10397 e^8+5624 e^{12}+1778 e^{16}+360 e^{20}+45 e^{24}\right ) x^6+256 \left (3211+7484 e^4+7198 e^8+3608 e^{12}+1018 e^{16}+180 e^{20}+20 e^{24}\right ) x^5+256 \left (11952+26760 e^4+23568 e^8+10080 e^{12}+2145 e^{16}+250 e^{20}+25 e^{24}\right ) x^4+16384 \left (2+e^4\right )^2 \left (108+120 e^4+35 e^8\right ) x^3+32768 \left (2+e^4\right )^2 \left (72+75 e^4+20 e^8\right ) x^2+327680 \left (2+e^4\right )^4 x}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle \frac {2}{5} \left (-\frac {1}{2} \int -\frac {16 \left (3 \left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^8+4 \left (540+1183 e^4+1113 e^8+590 e^{12}+182 e^{16}+35 e^{20}+5 e^{24}\right ) x^7+\left (20868+50899 e^4+54933 e^8+34963 e^{12}+15091 e^{16}+4985 e^{20}+1275 e^{24}+225 e^{28}+25 e^{32}\right ) x^6+4 \left (31836+83980 e^4+99559 e^8+71686 e^{12}+36321 e^{16}+13920 e^{20}+3945 e^{24}+750 e^{28}+75 e^{32}\right ) x^5+16 \left (31536+85092 e^4+103092 e^8+76293 e^{12}+39897 e^{16}+15650 e^{20}+4460 e^{24}+825 e^{28}+75 e^{32}\right ) x^4+64 \left (2+e^4\right )^2 \left (4516+6900 e^4+4625 e^8+2140 e^{12}+810 e^{16}+200 e^{20}+25 e^{24}\right ) x^3+4096 \left (2+e^4\right )^2 \left (72+75 e^4+20 e^8\right ) x^2+40960 \left (2+e^4\right )^4 x\right )}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{5} \left (8 \int \frac {3 \left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^8+4 \left (540+1183 e^4+1113 e^8+590 e^{12}+182 e^{16}+35 e^{20}+5 e^{24}\right ) x^7+\left (20868+50899 e^4+54933 e^8+34963 e^{12}+15091 e^{16}+4985 e^{20}+1275 e^{24}+225 e^{28}+25 e^{32}\right ) x^6+4 \left (31836+83980 e^4+99559 e^8+71686 e^{12}+36321 e^{16}+13920 e^{20}+3945 e^{24}+750 e^{28}+75 e^{32}\right ) x^5+16 \left (31536+85092 e^4+103092 e^8+76293 e^{12}+39897 e^{16}+15650 e^{20}+4460 e^{24}+825 e^{28}+75 e^{32}\right ) x^4+64 \left (2+e^4\right )^2 \left (4516+6900 e^4+4625 e^8+2140 e^{12}+810 e^{16}+200 e^{20}+25 e^{24}\right ) x^3+4096 \left (2+e^4\right )^2 \left (72+75 e^4+20 e^8\right ) x^2+40960 \left (2+e^4\right )^4 x}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )}\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle \frac {2}{5} \left (8 \left (-\frac {1}{3} \int -\frac {12 \left (2 \left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^7+\left (3876+9180 e^4+9277 e^8+5104 e^{12}+1678 e^{16}+360 e^{20}+45 e^{24}\right ) x^6+\left (31836+83980 e^4+99559 e^8+71686 e^{12}+36321 e^{16}+13920 e^{20}+3945 e^{24}+750 e^{28}+75 e^{32}\right ) x^5+4 \left (39888+118556 e^4+165020 e^8+145439 e^{12}+90771 e^{16}+40950 e^{20}+12780 e^{24}+2475 e^{28}+225 e^{32}\right ) x^4+16 \left (2+e^4\right )^2 \left (7972+18036 e^4+20057 e^8+14220 e^{12}+6570 e^{16}+1800 e^{20}+225 e^{24}\right ) x^3+64 \left (2+e^4\right )^2 \left (3312+7620 e^4+8540 e^8+5985 e^{12}+2655 e^{16}+675 e^{20}+75 e^{24}\right ) x^2+10240 \left (2+e^4\right )^4 x\right )}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}\right )-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{5} \left (8 \left (4 \int \frac {2 \left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^7+\left (3876+9180 e^4+9277 e^8+5104 e^{12}+1678 e^{16}+360 e^{20}+45 e^{24}\right ) x^6+\left (31836+83980 e^4+99559 e^8+71686 e^{12}+36321 e^{16}+13920 e^{20}+3945 e^{24}+750 e^{28}+75 e^{32}\right ) x^5+4 \left (39888+118556 e^4+165020 e^8+145439 e^{12}+90771 e^{16}+40950 e^{20}+12780 e^{24}+2475 e^{28}+225 e^{32}\right ) x^4+16 \left (2+e^4\right )^2 \left (7972+18036 e^4+20057 e^8+14220 e^{12}+6570 e^{16}+1800 e^{20}+225 e^{24}\right ) x^3+64 \left (2+e^4\right )^2 \left (3312+7620 e^4+8540 e^8+5985 e^{12}+2655 e^{16}+675 e^{20}+75 e^{24}\right ) x^2+10240 \left (2+e^4\right )^4 x}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}\right )-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )}\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle \frac {2}{5} \left (-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}+8 \left (4 \left (-\frac {\left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}-\frac {1}{4} \int -\frac {16 \left (5 \left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x^6+2 \left (2+e^4\right )^2 \left (492+696 e^4+363 e^8+100 e^{12}+20 e^{16}\right ) x^5+\left (2+e^4\right )^2 \left (7164+12505 e^4+10017 e^8+5310 e^{12}+2060 e^{16}+525 e^{20}+75 e^{24}\right ) x^4+4 \left (2+e^4\right )^2 \left (7972+18036 e^4+20057 e^8+14220 e^{12}+6570 e^{16}+1800 e^{20}+225 e^{24}\right ) x^3+16 \left (2+e^4\right )^2 \left (5904+16524 e^4+21764 e^8+16835 e^{12}+7825 e^{16}+2025 e^{20}+225 e^{24}\right ) x^2+320 \left (2+e^4\right )^4 \left (116+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x\right )}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx\right )-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}\right )\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{5} \left (-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}+8 \left (4 \left (4 \int \frac {5 \left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x^6+2 \left (2+e^4\right )^2 \left (492+696 e^4+363 e^8+100 e^{12}+20 e^{16}\right ) x^5+\left (2+e^4\right )^2 \left (7164+12505 e^4+10017 e^8+5310 e^{12}+2060 e^{16}+525 e^{20}+75 e^{24}\right ) x^4+4 \left (2+e^4\right )^2 \left (7972+18036 e^4+20057 e^8+14220 e^{12}+6570 e^{16}+1800 e^{20}+225 e^{24}\right ) x^3+16 \left (2+e^4\right )^2 \left (5904+16524 e^4+21764 e^8+16835 e^{12}+7825 e^{16}+2025 e^{20}+225 e^{24}\right ) x^2+320 \left (2+e^4\right )^4 \left (116+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}\right )-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}\right )\right )\) |
| \(\Big \downarrow \) 2527 |
| \(\displaystyle \frac {2}{5} \left (-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}+8 \left (4 \left (4 \left (-\frac {\left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}-\frac {1}{5} \int -\frac {50 \left (3 \left (2+e^4\right )^4 x^5+5 \left (2+e^4\right )^4 \left (9+2 e^4+e^8\right ) x^4+2 \left (2+e^4\right )^4 \left (149+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^3+24 \left (2+e^4\right )^4 \left (52+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^2+32 \left (2+e^4\right )^4 \left (116+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x+128 \left (2+e^4\right )^6 \left (12+15 e^4+5 e^8\right )\right )}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx\right )-\frac {\left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}\right )-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}\right )\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2}{5} \left (-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}+8 \left (4 \left (4 \left (10 \int \frac {3 \left (2+e^4\right )^4 x^5+5 \left (2+e^4\right )^4 \left (9+2 e^4+e^8\right ) x^4+2 \left (2+e^4\right )^4 \left (149+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^3+24 \left (2+e^4\right )^4 \left (52+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^2+32 \left (2+e^4\right )^4 \left (116+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x+128 \left (2+e^4\right )^6 \left (12+15 e^4+5 e^8\right )}{\left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )^2}dx-\frac {\left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}\right )-\frac {\left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480\right )}\right )-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+20480}\right )\right )\) |
| \(\Big \downarrow \) 2021 |
| \(\displaystyle \frac {2}{5} \left (-\frac {\left (1+e^4\right )^2 x^5}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}-\frac {\left (53+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )}+8 \left (4 \left (4 \left (-\frac {\left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}-\frac {5 \left (2+e^4\right )^4}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}\right )-\frac {\left (108+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2}{2 \left (x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480\right )}\right )-\frac {\left (36+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3}{x^6+18 x^5+149 x^4+832 x^3+3712 x^2+2 e^8 (x+4)^2 \left (x^3+23 x^2+256 x+960\right )+4 e^4 \left (x^5+25 x^4+284 x^3+1888 x^2+6912 x+10240\right )+12288 x+5 e^{16} (x+4)^4+20 e^{12} (x+4)^3 (x+8)+20480}\right )\right )\) |
Input:
Int[(10485760*x + 18874368*x^2 + 14155776*x^3 + 5914624*x^4 + 1545728*x^5 + 267520*x^6 + 31232*x^7 + 2384*x^8 + 106*x^9 + 2*x^10 + E^16*(655360*x + 1310720*x^2 + 1146880*x^3 + 573440*x^4 + 179200*x^5 + 35840*x^6 + 4480*x^7 + 320*x^8 + 10*x^9) + E^12*(5242880*x + 10158080*x^2 + 8519680*x^3 + 4034 560*x^4 + 1177600*x^5 + 216320*x^6 + 24320*x^7 + 1520*x^8 + 40*x^9) + E^8* (15728640*x + 29622272*x^2 + 23855104*x^3 + 10735616*x^4 + 2956288*x^5 + 5 12000*x^6 + 55168*x^7 + 3536*x^8 + 124*x^9 + 2*x^10) + E^4*(20971520*x + 3 8535168*x^2 + 29884416*x^3 + 12881920*x^4 + 3414016*x^5 + 581120*x^6 + 645 12*x^7 + 4624*x^8 + 200*x^9 + 4*x^10))/(2097152000 + 2516582400*x + 151519 2320*x^2 + 626524160*x^3 + 201646080*x^4 + 52879360*x^5 + 11408640*x^6 + 2 030720*x^7 + 297885*x^8 + 35140*x^9 + 3110*x^10 + 180*x^11 + 5*x^12 + E^32 *(8192000 + 16384000*x + 14336000*x^2 + 7168000*x^3 + 2240000*x^4 + 448000 *x^5 + 56000*x^6 + 4000*x^7 + 125*x^8) + E^28*(131072000 + 245760000*x + 2 00704000*x^2 + 93184000*x^3 + 26880000*x^4 + 4928000*x^5 + 560000*x^6 + 36 000*x^7 + 1000*x^8) + E^24*(917504000 + 1612185600*x + 1231667200*x^2 + 53 4732800*x^3 + 144614400*x^4 + 25088000*x^5 + 2766400*x^6 + 184800*x^7 + 67 00*x^8 + 100*x^9) + E^20*(3670016000 + 6042419200*x + 4333568000*x^2 + 177 6230400*x^3 + 459110400*x^4 + 77952000*x^5 + 8780800*x^6 + 644000*x^7 + 28 600*x^8 + 600*x^9) + E^16*(9175040000 + 14155776000*x + 9581035520*x^2 + 3 757015040*x^3 + 951324160*x^4 + 164334080*x^5 + 19918400*x^6 + 1702880*x^7 + 100110*x^8 + 3740*x^9 + 70*x^10) + E^12*(14680064000 + 21233664000*x + 13668188160*x^2 + 5221580800*x^3 + 1335685120*x^4 + 244779520*x^5 + 333664 00*x^6 + 3407840*x^7 + 251800*x^8 + 12080*x^9 + 280*x^10) + E^8*(146800640 00 + 19922944000*x + 12332564480*x^2 + 4699586560*x^3 + 1257328640*x^4 + 2 53757440*x^5 + 39852480*x^6 + 4837920*x^7 + 436140*x^8 + 27260*x^9 + 1060* x^10 + 20*x^11) + E^4*(8388608000 + 10695475200*x + 6464471040*x^2 + 25277 23520*x^3 + 731463680*x^4 + 166676480*x^5 + 30293760*x^6 + 4308960*x^7 + 4 62280*x^8 + 35320*x^9 + 1720*x^10 + 40*x^11)),x]
Output:
(2*(-1/2*((53 + 100*E^4 + 62*E^8 + 20*E^12 + 5*E^16)*x^4)/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^1 2*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4 *(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)) - ((1 + E^4)^2*x^5) /(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*( 4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x ^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)) + 8*(-(((36 + 71*E^4 + 57*E^8 + 25*E^12 + 5*E^16)*x^3)/(20480 + 12288*x + 37 12*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(102 40 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5))) + 4*(-1/2*((108 + 236*E ^4 + 211*E^8 + 90*E^12 + 15*E^16)*x^2)/(20480 + 12288*x + 3712*x^2 + 832*x ^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)) + 4*((-5*(2 + E^4)^4)/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^1 2*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4 *(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)) - ((2 + E^4)^2*(12 + 15*E^4 + 5*E^8)*x)/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18* x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x...
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Pp_)*(Qq_)^(m_.), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x ]}, Simp[Coeff[Pp, x, p]*x^(p - q + 1)*(Qq^(m + 1)/((p + m*q + 1)*Coeff[Qq, x, q])), x] /; NeQ[p + m*q + 1, 0] && EqQ[(p + m*q + 1)*Coeff[Qq, x, q]*Pp , Coeff[Pp, x, p]*x^(p - q)*((p - q + 1)*Qq + (m + 1)*x*D[Qq, x])]] /; Free Q[m, x] && PolyQ[Pp, x] && PolyQ[Qq, x] && NeQ[m, -1]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Int[(Pm_)*(Qn_)^(p_.), x_Symbol] :> With[{m = Expon[Pm, x], n = Expon[Qn, x ]}, Simp[Coeff[Pm, x, m]*x^(m - n + 1)*(Qn^(p + 1)/((m + n*p + 1)*Coeff[Qn, x, n])), x] + Simp[1/((m + n*p + 1)*Coeff[Qn, x, n]) Int[ExpandToSum[(m + n*p + 1)*Coeff[Qn, x, n]*Pm - Coeff[Pm, x, m]*x^(m - n)*((m - n + 1)*Qn + (p + 1)*x*D[Qn, x]), x]*Qn^p, x], x] /; LtQ[1, n, m + 1] && m + n*p + 1 < 0] /; FreeQ[p, x] && PolyQ[Pm, x] && PolyQ[Qn, x] && LtQ[p, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(284\) vs. \(2(33)=66\).
Time = 6.92 (sec) , antiderivative size = 285, normalized size of antiderivative = 8.38
| method | result | size |
| risch | \(\frac {\left (-\frac {2 \,{\mathrm e}^{8}}{25}-\frac {4 \,{\mathrm e}^{4}}{25}-\frac {2}{25}\right ) x^{5}+\left (-\frac {{\mathrm e}^{16}}{5}-\frac {4 \,{\mathrm e}^{12}}{5}-\frac {62 \,{\mathrm e}^{8}}{25}-4 \,{\mathrm e}^{4}-\frac {53}{25}\right ) x^{4}+\left (-\frac {16 \,{\mathrm e}^{16}}{5}-16 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{25}-\frac {1136 \,{\mathrm e}^{4}}{25}-\frac {576}{25}\right ) x^{3}+\left (-\frac {96 \,{\mathrm e}^{16}}{5}-\frac {576 \,{\mathrm e}^{12}}{5}-\frac {6752 \,{\mathrm e}^{8}}{25}-\frac {7552 \,{\mathrm e}^{4}}{25}-\frac {3456}{25}\right ) x^{2}+\left (-\frac {256 \,{\mathrm e}^{16}}{5}-\frac {1792 \,{\mathrm e}^{12}}{5}-\frac {23552 \,{\mathrm e}^{8}}{25}-\frac {27648 \,{\mathrm e}^{4}}{25}-\frac {12288}{25}\right ) x -\frac {256 \,{\mathrm e}^{16}}{5}-\frac {2048 \,{\mathrm e}^{12}}{5}-\frac {6144 \,{\mathrm e}^{8}}{5}-\frac {8192 \,{\mathrm e}^{4}}{5}-\frac {4096}{5}}{4096+\frac {12288 x}{5}+96 x^{2} {\mathrm e}^{16}+256 x \,{\mathrm e}^{16}+\frac {1136 x^{3} {\mathrm e}^{4}}{5}+\frac {7552 x^{2} {\mathrm e}^{4}}{5}+2048 \,{\mathrm e}^{12}+1792 \,{\mathrm e}^{12} x +\frac {4 x^{5} {\mathrm e}^{4}}{5}+20 x^{4} {\mathrm e}^{4}+6144 \,{\mathrm e}^{8}+256 \,{\mathrm e}^{16}+\frac {27648 x \,{\mathrm e}^{4}}{5}+8192 \,{\mathrm e}^{4}+\frac {149 x^{4}}{5}+\frac {832 x^{3}}{5}+\frac {3712 x^{2}}{5}+\frac {x^{6}}{5}+\frac {18 x^{5}}{5}+\frac {6752 x^{2} {\mathrm e}^{8}}{5}+\frac {912 x^{3} {\mathrm e}^{8}}{5}+x^{4} {\mathrm e}^{16}+\frac {62 x^{4} {\mathrm e}^{8}}{5}+80 x^{3} {\mathrm e}^{12}+\frac {2 x^{5} {\mathrm e}^{8}}{5}+16 x^{3} {\mathrm e}^{16}+4 x^{4} {\mathrm e}^{12}+\frac {23552 x \,{\mathrm e}^{8}}{5}+576 x^{2} {\mathrm e}^{12}}\) | \(285\) |
| gosper | \(-\frac {\left (5 x^{3} {\mathrm e}^{12}+60 x^{2} {\mathrm e}^{12}+15 x^{3} {\mathrm e}^{8}+2 x^{4} {\mathrm e}^{4}+240 \,{\mathrm e}^{12} x +240 x^{2} {\mathrm e}^{8}+39 x^{3} {\mathrm e}^{4}+2 x^{4}+320 \,{\mathrm e}^{12}+1200 x \,{\mathrm e}^{8}+396 x^{2} {\mathrm e}^{4}+37 x^{3}+1920 \,{\mathrm e}^{8}+2048 x \,{\mathrm e}^{4}+280 x^{2}+3840 \,{\mathrm e}^{4}+1216 x +2560\right ) \left (x \,{\mathrm e}^{4}+4 \,{\mathrm e}^{4}+x +8\right )}{5 \left (20480+12288 x +480 x^{2} {\mathrm e}^{16}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+10240 \,{\mathrm e}^{12}+8960 \,{\mathrm e}^{12} x +4 x^{5} {\mathrm e}^{4}+100 x^{4} {\mathrm e}^{4}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+149 x^{4}+832 x^{3}+3712 x^{2}+x^{6}+18 x^{5}+6752 x^{2} {\mathrm e}^{8}+912 x^{3} {\mathrm e}^{8}+5 x^{4} {\mathrm e}^{16}+62 x^{4} {\mathrm e}^{8}+400 x^{3} {\mathrm e}^{12}+2 x^{5} {\mathrm e}^{8}+80 x^{3} {\mathrm e}^{16}+20 x^{4} {\mathrm e}^{12}+23552 x \,{\mathrm e}^{8}+2880 x^{2} {\mathrm e}^{12}\right )}\) | \(322\) |
| norman | \(\frac {\left (-\frac {2}{5}-\frac {4 \,{\mathrm e}^{4}}{5}-\frac {2 \,{\mathrm e}^{8}}{5}\right ) x^{5}+\left (-256 \,{\mathrm e}^{16}-1792 \,{\mathrm e}^{12}-\frac {23552 \,{\mathrm e}^{8}}{5}-\frac {27648 \,{\mathrm e}^{4}}{5}-\frac {12288}{5}\right ) x +\left (-96 \,{\mathrm e}^{16}-576 \,{\mathrm e}^{12}-\frac {6752 \,{\mathrm e}^{8}}{5}-\frac {7552 \,{\mathrm e}^{4}}{5}-\frac {3456}{5}\right ) x^{2}+\left (-16 \,{\mathrm e}^{16}-80 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{5}-\frac {1136 \,{\mathrm e}^{4}}{5}-\frac {576}{5}\right ) x^{3}+\left (-{\mathrm e}^{16}-4 \,{\mathrm e}^{12}-\frac {62 \,{\mathrm e}^{8}}{5}-20 \,{\mathrm e}^{4}-\frac {53}{5}\right ) x^{4}-256 \,{\mathrm e}^{16}-2048 \,{\mathrm e}^{12}-6144 \,{\mathrm e}^{8}-8192 \,{\mathrm e}^{4}-4096}{20480+12288 x +480 x^{2} {\mathrm e}^{16}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+10240 \,{\mathrm e}^{12}+8960 \,{\mathrm e}^{12} x +4 x^{5} {\mathrm e}^{4}+100 x^{4} {\mathrm e}^{4}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+149 x^{4}+832 x^{3}+3712 x^{2}+x^{6}+18 x^{5}+6752 x^{2} {\mathrm e}^{8}+912 x^{3} {\mathrm e}^{8}+5 x^{4} {\mathrm e}^{16}+62 x^{4} {\mathrm e}^{8}+400 x^{3} {\mathrm e}^{12}+2 x^{5} {\mathrm e}^{8}+80 x^{3} {\mathrm e}^{16}+20 x^{4} {\mathrm e}^{12}+23552 x \,{\mathrm e}^{8}+2880 x^{2} {\mathrm e}^{12}}\) | \(348\) |
| parallelrisch | \(\frac {-20480-12288 x -480 x^{2} {\mathrm e}^{16}-1280 x \,{\mathrm e}^{16}-1136 x^{3} {\mathrm e}^{4}-7552 x^{2} {\mathrm e}^{4}-10240 \,{\mathrm e}^{12}-8960 \,{\mathrm e}^{12} x -4 x^{5} {\mathrm e}^{4}-100 x^{4} {\mathrm e}^{4}-30720 \,{\mathrm e}^{8}-1280 \,{\mathrm e}^{16}-27648 x \,{\mathrm e}^{4}-40960 \,{\mathrm e}^{4}-53 x^{4}-576 x^{3}-3456 x^{2}-2 x^{5}-6752 x^{2} {\mathrm e}^{8}-912 x^{3} {\mathrm e}^{8}-5 x^{4} {\mathrm e}^{16}-62 x^{4} {\mathrm e}^{8}-400 x^{3} {\mathrm e}^{12}-2 x^{5} {\mathrm e}^{8}-80 x^{3} {\mathrm e}^{16}-20 x^{4} {\mathrm e}^{12}-23552 x \,{\mathrm e}^{8}-2880 x^{2} {\mathrm e}^{12}}{102400+61440 x +2400 x^{2} {\mathrm e}^{16}+6400 x \,{\mathrm e}^{16}+5680 x^{3} {\mathrm e}^{4}+37760 x^{2} {\mathrm e}^{4}+51200 \,{\mathrm e}^{12}+44800 \,{\mathrm e}^{12} x +20 x^{5} {\mathrm e}^{4}+500 x^{4} {\mathrm e}^{4}+153600 \,{\mathrm e}^{8}+6400 \,{\mathrm e}^{16}+138240 x \,{\mathrm e}^{4}+204800 \,{\mathrm e}^{4}+745 x^{4}+4160 x^{3}+18560 x^{2}+5 x^{6}+90 x^{5}+33760 x^{2} {\mathrm e}^{8}+4560 x^{3} {\mathrm e}^{8}+25 x^{4} {\mathrm e}^{16}+310 x^{4} {\mathrm e}^{8}+2000 x^{3} {\mathrm e}^{12}+10 x^{5} {\mathrm e}^{8}+400 x^{3} {\mathrm e}^{16}+100 x^{4} {\mathrm e}^{12}+117760 x \,{\mathrm e}^{8}+14400 x^{2} {\mathrm e}^{12}}\) | \(390\) |
| default | \(\text {Expression too large to display}\) | \(1183\) |
Input:
int(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+ 1310720*x^2+655360*x)*exp(4)^4+(40*x^9+1520*x^8+24320*x^7+216320*x^6+11776 00*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x^10+12 4*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+ 29622272*x^2+15728640*x)*exp(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7+58112 0*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x)*exp(4 )+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+141 55776*x^3+18874368*x^2+10485760*x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5 +2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+(1000*x ^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^ 2+245760000*x+131072000)*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6 +25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+1612185600*x+9175 04000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459 110400*x^4+1776230400*x^3+4333568000*x^2+6042419200*x+3670016000)*exp(4)^5 +(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080*x^5+95132 4160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+ (280*x^10+12080*x^9+251800*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335 685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+14680064000)*exp(4 )^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+25375 7440*x^5+1257328640*x^4+4699586560*x^3+12332564480*x^2+19922944000*x+14680 064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+4308960*x^7+30293 760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475 200*x+8388608000)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+20 30720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+626524160*x^3+1515192320 *x^2+2516582400*x+2097152000),x,method=_RETURNVERBOSE)
Output:
((-2/25*exp(8)-4/25*exp(4)-2/25)*x^5+(-1/5*exp(16)-4/5*exp(12)-62/25*exp(8 )-4*exp(4)-53/25)*x^4+(-16/5*exp(16)-16*exp(12)-912/25*exp(8)-1136/25*exp( 4)-576/25)*x^3+(-96/5*exp(16)-576/5*exp(12)-6752/25*exp(8)-7552/25*exp(4)- 3456/25)*x^2+(-256/5*exp(16)-1792/5*exp(12)-23552/25*exp(8)-27648/25*exp(4 )-12288/25)*x-256/5*exp(16)-2048/5*exp(12)-6144/5*exp(8)-8192/5*exp(4)-409 6/5)/(4096+12288/5*x+96*x^2*exp(16)+256*x*exp(16)+1136/5*x^3*exp(4)+7552/5 *x^2*exp(4)+2048*exp(12)+1792*exp(12)*x+4/5*x^5*exp(4)+20*x^4*exp(4)+6144* exp(8)+256*exp(16)+27648/5*x*exp(4)+8192*exp(4)+149/5*x^4+832/5*x^3+3712/5 *x^2+1/5*x^6+18/5*x^5+6752/5*x^2*exp(8)+912/5*x^3*exp(8)+x^4*exp(16)+62/5* x^4*exp(8)+80*x^3*exp(12)+2/5*x^5*exp(8)+16*x^3*exp(16)+4*x^4*exp(12)+2355 2/5*x*exp(8)+576*x^2*exp(12))
Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (33) = 66\).
Time = 0.11 (sec) , antiderivative size = 253, normalized size of antiderivative = 7.44 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {2 \, x^{5} + 53 \, x^{4} + 576 \, x^{3} + 3456 \, x^{2} + 5 \, {\left (x^{4} + 16 \, x^{3} + 96 \, x^{2} + 256 \, x + 256\right )} e^{16} + 20 \, {\left (x^{4} + 20 \, x^{3} + 144 \, x^{2} + 448 \, x + 512\right )} e^{12} + 2 \, {\left (x^{5} + 31 \, x^{4} + 456 \, x^{3} + 3376 \, x^{2} + 11776 \, x + 15360\right )} e^{8} + 4 \, {\left (x^{5} + 25 \, x^{4} + 284 \, x^{3} + 1888 \, x^{2} + 6912 \, x + 10240\right )} e^{4} + 12288 \, x + 20480}{5 \, {\left (x^{6} + 18 \, x^{5} + 149 \, x^{4} + 832 \, x^{3} + 3712 \, x^{2} + 5 \, {\left (x^{4} + 16 \, x^{3} + 96 \, x^{2} + 256 \, x + 256\right )} e^{16} + 20 \, {\left (x^{4} + 20 \, x^{3} + 144 \, x^{2} + 448 \, x + 512\right )} e^{12} + 2 \, {\left (x^{5} + 31 \, x^{4} + 456 \, x^{3} + 3376 \, x^{2} + 11776 \, x + 15360\right )} e^{8} + 4 \, {\left (x^{5} + 25 \, x^{4} + 284 \, x^{3} + 1888 \, x^{2} + 6912 \, x + 10240\right )} e^{4} + 12288 \, x + 20480\right )}} \] Input:
integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+114688 0*x^3+1310720*x^2+655360*x)*exp(4)^4+(40*x^9+1520*x^8+24320*x^7+216320*x^6 +1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x ^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+2385510 4*x^3+29622272*x^2+15728640*x)*exp(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7 +581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x) *exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x ^4+14155776*x^3+18874368*x^2+10485760*x)/((125*x^8+4000*x^7+56000*x^6+4480 00*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+( 1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704 000*x^2+245760000*x+131072000)*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+27664 00*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+1612185600* x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x ^5+459110400*x^4+1776230400*x^3+4333568000*x^2+6042419200*x+3670016000)*ex p(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080*x^5 +951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp (4)^4+(280*x^10+12080*x^9+251800*x^8+3407840*x^7+33366400*x^6+244779520*x^ 5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+14680064000) *exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6 +253757440*x^5+1257328640*x^4+4699586560*x^3+12332564480*x^2+19922944000*x +14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+4308960*x^7 +30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10 695475200*x+8388608000)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885* x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+626524160*x^3+1515 192320*x^2+2516582400*x+2097152000),x, algorithm="fricas")
Output:
-1/5*(2*x^5 + 53*x^4 + 576*x^3 + 3456*x^2 + 5*(x^4 + 16*x^3 + 96*x^2 + 256 *x + 256)*e^16 + 20*(x^4 + 20*x^3 + 144*x^2 + 448*x + 512)*e^12 + 2*(x^5 + 31*x^4 + 456*x^3 + 3376*x^2 + 11776*x + 15360)*e^8 + 4*(x^5 + 25*x^4 + 28 4*x^3 + 1888*x^2 + 6912*x + 10240)*e^4 + 12288*x + 20480)/(x^6 + 18*x^5 + 149*x^4 + 832*x^3 + 3712*x^2 + 5*(x^4 + 16*x^3 + 96*x^2 + 256*x + 256)*e^1 6 + 20*(x^4 + 20*x^3 + 144*x^2 + 448*x + 512)*e^12 + 2*(x^5 + 31*x^4 + 456 *x^3 + 3376*x^2 + 11776*x + 15360)*e^8 + 4*(x^5 + 25*x^4 + 284*x^3 + 1888* x^2 + 6912*x + 10240)*e^4 + 12288*x + 20480)
Leaf count of result is larger than twice the leaf count of optimal. 287 vs. \(2 (26) = 52\).
Time = 85.74 (sec) , antiderivative size = 287, normalized size of antiderivative = 8.44 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=\frac {x^{5} \left (- 2 e^{8} - 4 e^{4} - 2\right ) + x^{4} \left (- 5 e^{16} - 20 e^{12} - 62 e^{8} - 100 e^{4} - 53\right ) + x^{3} \left (- 80 e^{16} - 400 e^{12} - 912 e^{8} - 1136 e^{4} - 576\right ) + x^{2} \left (- 480 e^{16} - 2880 e^{12} - 6752 e^{8} - 7552 e^{4} - 3456\right ) + x \left (- 1280 e^{16} - 8960 e^{12} - 23552 e^{8} - 27648 e^{4} - 12288\right ) - 1280 e^{16} - 10240 e^{12} - 30720 e^{8} - 40960 e^{4} - 20480}{5 x^{6} + x^{5} \cdot \left (90 + 20 e^{4} + 10 e^{8}\right ) + x^{4} \cdot \left (745 + 500 e^{4} + 310 e^{8} + 100 e^{12} + 25 e^{16}\right ) + x^{3} \cdot \left (4160 + 5680 e^{4} + 4560 e^{8} + 2000 e^{12} + 400 e^{16}\right ) + x^{2} \cdot \left (18560 + 37760 e^{4} + 33760 e^{8} + 14400 e^{12} + 2400 e^{16}\right ) + x \left (61440 + 138240 e^{4} + 117760 e^{8} + 44800 e^{12} + 6400 e^{16}\right ) + 102400 + 204800 e^{4} + 153600 e^{8} + 51200 e^{12} + 6400 e^{16}} \] Input:
integrate(((10*x**9+320*x**8+4480*x**7+35840*x**6+179200*x**5+573440*x**4+ 1146880*x**3+1310720*x**2+655360*x)*exp(4)**4+(40*x**9+1520*x**8+24320*x** 7+216320*x**6+1177600*x**5+4034560*x**4+8519680*x**3+10158080*x**2+5242880 *x)*exp(4)**3+(2*x**10+124*x**9+3536*x**8+55168*x**7+512000*x**6+2956288*x **5+10735616*x**4+23855104*x**3+29622272*x**2+15728640*x)*exp(4)**2+(4*x** 10+200*x**9+4624*x**8+64512*x**7+581120*x**6+3414016*x**5+12881920*x**4+29 884416*x**3+38535168*x**2+20971520*x)*exp(4)+2*x**10+106*x**9+2384*x**8+31 232*x**7+267520*x**6+1545728*x**5+5914624*x**4+14155776*x**3+18874368*x**2 +10485760*x)/((125*x**8+4000*x**7+56000*x**6+448000*x**5+2240000*x**4+7168 000*x**3+14336000*x**2+16384000*x+8192000)*exp(4)**8+(1000*x**8+36000*x**7 +560000*x**6+4928000*x**5+26880000*x**4+93184000*x**3+200704000*x**2+24576 0000*x+131072000)*exp(4)**7+(100*x**9+6700*x**8+184800*x**7+2766400*x**6+2 5088000*x**5+144614400*x**4+534732800*x**3+1231667200*x**2+1612185600*x+91 7504000)*exp(4)**6+(600*x**9+28600*x**8+644000*x**7+8780800*x**6+77952000* x**5+459110400*x**4+1776230400*x**3+4333568000*x**2+6042419200*x+367001600 0)*exp(4)**5+(70*x**10+3740*x**9+100110*x**8+1702880*x**7+19918400*x**6+16 4334080*x**5+951324160*x**4+3757015040*x**3+9581035520*x**2+14155776000*x+ 9175040000)*exp(4)**4+(280*x**10+12080*x**9+251800*x**8+3407840*x**7+33366 400*x**6+244779520*x**5+1335685120*x**4+5221580800*x**3+13668188160*x**2+2 1233664000*x+14680064000)*exp(4)**3+(20*x**11+1060*x**10+27260*x**9+436140 *x**8+4837920*x**7+39852480*x**6+253757440*x**5+1257328640*x**4+4699586560 *x**3+12332564480*x**2+19922944000*x+14680064000)*exp(4)**2+(40*x**11+1720 *x**10+35320*x**9+462280*x**8+4308960*x**7+30293760*x**6+166676480*x**5+73 1463680*x**4+2527723520*x**3+6464471040*x**2+10695475200*x+8388608000)*exp (4)+5*x**12+180*x**11+3110*x**10+35140*x**9+297885*x**8+2030720*x**7+11408 640*x**6+52879360*x**5+201646080*x**4+626524160*x**3+1515192320*x**2+25165 82400*x+2097152000),x)
Output:
(x**5*(-2*exp(8) - 4*exp(4) - 2) + x**4*(-5*exp(16) - 20*exp(12) - 62*exp( 8) - 100*exp(4) - 53) + x**3*(-80*exp(16) - 400*exp(12) - 912*exp(8) - 113 6*exp(4) - 576) + x**2*(-480*exp(16) - 2880*exp(12) - 6752*exp(8) - 7552*e xp(4) - 3456) + x*(-1280*exp(16) - 8960*exp(12) - 23552*exp(8) - 27648*exp (4) - 12288) - 1280*exp(16) - 10240*exp(12) - 30720*exp(8) - 40960*exp(4) - 20480)/(5*x**6 + x**5*(90 + 20*exp(4) + 10*exp(8)) + x**4*(745 + 500*exp (4) + 310*exp(8) + 100*exp(12) + 25*exp(16)) + x**3*(4160 + 5680*exp(4) + 4560*exp(8) + 2000*exp(12) + 400*exp(16)) + x**2*(18560 + 37760*exp(4) + 3 3760*exp(8) + 14400*exp(12) + 2400*exp(16)) + x*(61440 + 138240*exp(4) + 1 17760*exp(8) + 44800*exp(12) + 6400*exp(16)) + 102400 + 204800*exp(4) + 15 3600*exp(8) + 51200*exp(12) + 6400*exp(16))
Leaf count of result is larger than twice the leaf count of optimal. 247 vs. \(2 (33) = 66\).
Time = 0.09 (sec) , antiderivative size = 247, normalized size of antiderivative = 7.26 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {2 \, x^{5} {\left (e^{8} + 2 \, e^{4} + 1\right )} + x^{4} {\left (5 \, e^{16} + 20 \, e^{12} + 62 \, e^{8} + 100 \, e^{4} + 53\right )} + 16 \, x^{3} {\left (5 \, e^{16} + 25 \, e^{12} + 57 \, e^{8} + 71 \, e^{4} + 36\right )} + 32 \, x^{2} {\left (15 \, e^{16} + 90 \, e^{12} + 211 \, e^{8} + 236 \, e^{4} + 108\right )} + 256 \, x {\left (5 \, e^{16} + 35 \, e^{12} + 92 \, e^{8} + 108 \, e^{4} + 48\right )} + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480}{5 \, {\left (x^{6} + 2 \, x^{5} {\left (e^{8} + 2 \, e^{4} + 9\right )} + x^{4} {\left (5 \, e^{16} + 20 \, e^{12} + 62 \, e^{8} + 100 \, e^{4} + 149\right )} + 16 \, x^{3} {\left (5 \, e^{16} + 25 \, e^{12} + 57 \, e^{8} + 71 \, e^{4} + 52\right )} + 32 \, x^{2} {\left (15 \, e^{16} + 90 \, e^{12} + 211 \, e^{8} + 236 \, e^{4} + 116\right )} + 256 \, x {\left (5 \, e^{16} + 35 \, e^{12} + 92 \, e^{8} + 108 \, e^{4} + 48\right )} + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480\right )}} \] Input:
integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+114688 0*x^3+1310720*x^2+655360*x)*exp(4)^4+(40*x^9+1520*x^8+24320*x^7+216320*x^6 +1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x ^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+2385510 4*x^3+29622272*x^2+15728640*x)*exp(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7 +581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x) *exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x ^4+14155776*x^3+18874368*x^2+10485760*x)/((125*x^8+4000*x^7+56000*x^6+4480 00*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+( 1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704 000*x^2+245760000*x+131072000)*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+27664 00*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+1612185600* x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x ^5+459110400*x^4+1776230400*x^3+4333568000*x^2+6042419200*x+3670016000)*ex p(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080*x^5 +951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp (4)^4+(280*x^10+12080*x^9+251800*x^8+3407840*x^7+33366400*x^6+244779520*x^ 5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+14680064000) *exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6 +253757440*x^5+1257328640*x^4+4699586560*x^3+12332564480*x^2+19922944000*x +14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+4308960*x^7 +30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10 695475200*x+8388608000)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885* x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+626524160*x^3+1515 192320*x^2+2516582400*x+2097152000),x, algorithm="maxima")
Output:
-1/5*(2*x^5*(e^8 + 2*e^4 + 1) + x^4*(5*e^16 + 20*e^12 + 62*e^8 + 100*e^4 + 53) + 16*x^3*(5*e^16 + 25*e^12 + 57*e^8 + 71*e^4 + 36) + 32*x^2*(15*e^16 + 90*e^12 + 211*e^8 + 236*e^4 + 108) + 256*x*(5*e^16 + 35*e^12 + 92*e^8 + 108*e^4 + 48) + 1280*e^16 + 10240*e^12 + 30720*e^8 + 40960*e^4 + 20480)/(x ^6 + 2*x^5*(e^8 + 2*e^4 + 9) + x^4*(5*e^16 + 20*e^12 + 62*e^8 + 100*e^4 + 149) + 16*x^3*(5*e^16 + 25*e^12 + 57*e^8 + 71*e^4 + 52) + 32*x^2*(15*e^16 + 90*e^12 + 211*e^8 + 236*e^4 + 116) + 256*x*(5*e^16 + 35*e^12 + 92*e^8 + 108*e^4 + 48) + 1280*e^16 + 10240*e^12 + 30720*e^8 + 40960*e^4 + 20480)
Leaf count of result is larger than twice the leaf count of optimal. 325 vs. \(2 (33) = 66\).
Time = 1.69 (sec) , antiderivative size = 325, normalized size of antiderivative = 9.56 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {2 \, x^{5} e^{8} + 4 \, x^{5} e^{4} + 2 \, x^{5} + 5 \, x^{4} e^{16} + 20 \, x^{4} e^{12} + 62 \, x^{4} e^{8} + 100 \, x^{4} e^{4} + 53 \, x^{4} + 80 \, x^{3} e^{16} + 400 \, x^{3} e^{12} + 912 \, x^{3} e^{8} + 1136 \, x^{3} e^{4} + 576 \, x^{3} + 480 \, x^{2} e^{16} + 2880 \, x^{2} e^{12} + 6752 \, x^{2} e^{8} + 7552 \, x^{2} e^{4} + 3456 \, x^{2} + 1280 \, x e^{16} + 8960 \, x e^{12} + 23552 \, x e^{8} + 27648 \, x e^{4} + 12288 \, x + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480}{5 \, {\left (x^{6} + 2 \, x^{5} e^{8} + 4 \, x^{5} e^{4} + 18 \, x^{5} + 5 \, x^{4} e^{16} + 20 \, x^{4} e^{12} + 62 \, x^{4} e^{8} + 100 \, x^{4} e^{4} + 149 \, x^{4} + 80 \, x^{3} e^{16} + 400 \, x^{3} e^{12} + 912 \, x^{3} e^{8} + 1136 \, x^{3} e^{4} + 832 \, x^{3} + 480 \, x^{2} e^{16} + 2880 \, x^{2} e^{12} + 6752 \, x^{2} e^{8} + 7552 \, x^{2} e^{4} + 3712 \, x^{2} + 1280 \, x e^{16} + 8960 \, x e^{12} + 23552 \, x e^{8} + 27648 \, x e^{4} + 12288 \, x + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480\right )}} \] Input:
integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+114688 0*x^3+1310720*x^2+655360*x)*exp(4)^4+(40*x^9+1520*x^8+24320*x^7+216320*x^6 +1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x ^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+2385510 4*x^3+29622272*x^2+15728640*x)*exp(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7 +581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x) *exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x ^4+14155776*x^3+18874368*x^2+10485760*x)/((125*x^8+4000*x^7+56000*x^6+4480 00*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+( 1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704 000*x^2+245760000*x+131072000)*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+27664 00*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+1612185600* x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x ^5+459110400*x^4+1776230400*x^3+4333568000*x^2+6042419200*x+3670016000)*ex p(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080*x^5 +951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp (4)^4+(280*x^10+12080*x^9+251800*x^8+3407840*x^7+33366400*x^6+244779520*x^ 5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+14680064000) *exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6 +253757440*x^5+1257328640*x^4+4699586560*x^3+12332564480*x^2+19922944000*x +14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+4308960*x^7 +30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10 695475200*x+8388608000)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885* x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+626524160*x^3+1515 192320*x^2+2516582400*x+2097152000),x, algorithm="giac")
Output:
-1/5*(2*x^5*e^8 + 4*x^5*e^4 + 2*x^5 + 5*x^4*e^16 + 20*x^4*e^12 + 62*x^4*e^ 8 + 100*x^4*e^4 + 53*x^4 + 80*x^3*e^16 + 400*x^3*e^12 + 912*x^3*e^8 + 1136 *x^3*e^4 + 576*x^3 + 480*x^2*e^16 + 2880*x^2*e^12 + 6752*x^2*e^8 + 7552*x^ 2*e^4 + 3456*x^2 + 1280*x*e^16 + 8960*x*e^12 + 23552*x*e^8 + 27648*x*e^4 + 12288*x + 1280*e^16 + 10240*e^12 + 30720*e^8 + 40960*e^4 + 20480)/(x^6 + 2*x^5*e^8 + 4*x^5*e^4 + 18*x^5 + 5*x^4*e^16 + 20*x^4*e^12 + 62*x^4*e^8 + 1 00*x^4*e^4 + 149*x^4 + 80*x^3*e^16 + 400*x^3*e^12 + 912*x^3*e^8 + 1136*x^3 *e^4 + 832*x^3 + 480*x^2*e^16 + 2880*x^2*e^12 + 6752*x^2*e^8 + 7552*x^2*e^ 4 + 3712*x^2 + 1280*x*e^16 + 8960*x*e^12 + 23552*x*e^8 + 27648*x*e^4 + 122 88*x + 1280*e^16 + 10240*e^12 + 30720*e^8 + 40960*e^4 + 20480)
Time = 3.20 (sec) , antiderivative size = 192, normalized size of antiderivative = 5.65 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {{\left (x+4\,{\mathrm {e}}^4+x\,{\mathrm {e}}^4+8\right )}^2\,\left (112\,x+320\,{\mathrm {e}}^4+80\,{\mathrm {e}}^8+120\,x\,{\mathrm {e}}^4+40\,x\,{\mathrm {e}}^8+10\,x^2\,{\mathrm {e}}^4+5\,x^2\,{\mathrm {e}}^8+21\,x^2+2\,x^3+320\right )}{5\,\left (x^6+\left (4\,{\mathrm {e}}^4+2\,{\mathrm {e}}^8+18\right )\,x^5+\left (100\,{\mathrm {e}}^4+62\,{\mathrm {e}}^8+20\,{\mathrm {e}}^{12}+5\,{\mathrm {e}}^{16}+149\right )\,x^4+\left (1136\,{\mathrm {e}}^4+912\,{\mathrm {e}}^8+400\,{\mathrm {e}}^{12}+80\,{\mathrm {e}}^{16}+832\right )\,x^3+\left (7552\,{\mathrm {e}}^4+6752\,{\mathrm {e}}^8+2880\,{\mathrm {e}}^{12}+480\,{\mathrm {e}}^{16}+3712\right )\,x^2+\left (27648\,{\mathrm {e}}^4+23552\,{\mathrm {e}}^8+8960\,{\mathrm {e}}^{12}+1280\,{\mathrm {e}}^{16}+12288\right )\,x+40960\,{\mathrm {e}}^4+30720\,{\mathrm {e}}^8+10240\,{\mathrm {e}}^{12}+1280\,{\mathrm {e}}^{16}+20480\right )} \] Input:
int((10485760*x + exp(16)*(655360*x + 1310720*x^2 + 1146880*x^3 + 573440*x ^4 + 179200*x^5 + 35840*x^6 + 4480*x^7 + 320*x^8 + 10*x^9) + exp(12)*(5242 880*x + 10158080*x^2 + 8519680*x^3 + 4034560*x^4 + 1177600*x^5 + 216320*x^ 6 + 24320*x^7 + 1520*x^8 + 40*x^9) + 18874368*x^2 + 14155776*x^3 + 5914624 *x^4 + 1545728*x^5 + 267520*x^6 + 31232*x^7 + 2384*x^8 + 106*x^9 + 2*x^10 + exp(8)*(15728640*x + 29622272*x^2 + 23855104*x^3 + 10735616*x^4 + 295628 8*x^5 + 512000*x^6 + 55168*x^7 + 3536*x^8 + 124*x^9 + 2*x^10) + exp(4)*(20 971520*x + 38535168*x^2 + 29884416*x^3 + 12881920*x^4 + 3414016*x^5 + 5811 20*x^6 + 64512*x^7 + 4624*x^8 + 200*x^9 + 4*x^10))/(2516582400*x + exp(12) *(21233664000*x + 13668188160*x^2 + 5221580800*x^3 + 1335685120*x^4 + 2447 79520*x^5 + 33366400*x^6 + 3407840*x^7 + 251800*x^8 + 12080*x^9 + 280*x^10 + 14680064000) + exp(32)*(16384000*x + 14336000*x^2 + 7168000*x^3 + 22400 00*x^4 + 448000*x^5 + 56000*x^6 + 4000*x^7 + 125*x^8 + 8192000) + exp(20)* (6042419200*x + 4333568000*x^2 + 1776230400*x^3 + 459110400*x^4 + 77952000 *x^5 + 8780800*x^6 + 644000*x^7 + 28600*x^8 + 600*x^9 + 3670016000) + exp( 8)*(19922944000*x + 12332564480*x^2 + 4699586560*x^3 + 1257328640*x^4 + 25 3757440*x^5 + 39852480*x^6 + 4837920*x^7 + 436140*x^8 + 27260*x^9 + 1060*x ^10 + 20*x^11 + 14680064000) + exp(28)*(245760000*x + 200704000*x^2 + 9318 4000*x^3 + 26880000*x^4 + 4928000*x^5 + 560000*x^6 + 36000*x^7 + 1000*x^8 + 131072000) + exp(16)*(14155776000*x + 9581035520*x^2 + 3757015040*x^3 + 951324160*x^4 + 164334080*x^5 + 19918400*x^6 + 1702880*x^7 + 100110*x^8 + 3740*x^9 + 70*x^10 + 9175040000) + exp(24)*(1612185600*x + 1231667200*x^2 + 534732800*x^3 + 144614400*x^4 + 25088000*x^5 + 2766400*x^6 + 184800*x^7 + 6700*x^8 + 100*x^9 + 917504000) + 1515192320*x^2 + 626524160*x^3 + 20164 6080*x^4 + 52879360*x^5 + 11408640*x^6 + 2030720*x^7 + 297885*x^8 + 35140* x^9 + 3110*x^10 + 180*x^11 + 5*x^12 + exp(4)*(10695475200*x + 6464471040*x ^2 + 2527723520*x^3 + 731463680*x^4 + 166676480*x^5 + 30293760*x^6 + 43089 60*x^7 + 462280*x^8 + 35320*x^9 + 1720*x^10 + 40*x^11 + 8388608000) + 2097 152000),x)
Output:
-((x + 4*exp(4) + x*exp(4) + 8)^2*(112*x + 320*exp(4) + 80*exp(8) + 120*x* exp(4) + 40*x*exp(8) + 10*x^2*exp(4) + 5*x^2*exp(8) + 21*x^2 + 2*x^3 + 320 ))/(5*(40960*exp(4) + 30720*exp(8) + 10240*exp(12) + 1280*exp(16) + x^5*(4 *exp(4) + 2*exp(8) + 18) + x*(27648*exp(4) + 23552*exp(8) + 8960*exp(12) + 1280*exp(16) + 12288) + x^4*(100*exp(4) + 62*exp(8) + 20*exp(12) + 5*exp( 16) + 149) + x^3*(1136*exp(4) + 912*exp(8) + 400*exp(12) + 80*exp(16) + 83 2) + x^2*(7552*exp(4) + 6752*exp(8) + 2880*exp(12) + 480*exp(16) + 3712) + x^6 + 20480))
Time = 17.63 (sec) , antiderivative size = 469, normalized size of antiderivative = 13.79 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=\frac {-40 e^{16} x^{4}-640 e^{16} x^{3}-3840 e^{16} x^{2}-10240 e^{16} x -10240 e^{16}-160 e^{12} x^{4}-3200 e^{12} x^{3}-23040 e^{12} x^{2}+e^{8} x^{6}-71680 e^{12} x -81920 e^{12}-400 e^{8} x^{4}-7040 e^{8} x^{3}-53760 e^{8} x^{2}+2 e^{4} x^{6}-188416 e^{8} x -245760 e^{8}-608 e^{4} x^{4}-8576 e^{4} x^{3}-59904 e^{4} x^{2}+x^{6}-221184 e^{4} x -327680 e^{4}-328 x^{4}-4352 x^{3}-27392 x^{2}-98304 x -163840}{25 e^{24} x^{4}+400 e^{24} x^{3}+2400 e^{24} x^{2}+6400 e^{24} x +6400 e^{24}+150 e^{20} x^{4}+2800 e^{20} x^{3}+19200 e^{20} x^{2}+57600 e^{20} x +10 e^{16} x^{5}+64000 e^{20}+735 e^{16} x^{4}+12160 e^{16} x^{3}+84160 e^{16} x^{2}+264960 e^{16} x +40 e^{12} x^{5}+313600 e^{16}+2020 e^{12} x^{4}+32800 e^{12} x^{3}+234880 e^{12} x^{2}+5 e^{8} x^{6}+776960 e^{12} x +220 e^{8} x^{5}+972800 e^{12}+4535 e^{8} x^{4}+56560 e^{8} x^{3}+397920 e^{8} x^{2}+10 e^{4} x^{6}+1397760 e^{8} x +360 e^{4} x^{5}+1894400 e^{8}+5990 e^{4} x^{4}+59440 e^{4} x^{3}+376960 e^{4} x^{2}+45 x^{6}+1367040 e^{4} x +810 x^{5}+2048000 e^{4}+6705 x^{4}+37440 x^{3}+167040 x^{2}+552960 x +921600} \] Input:
int(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+ 1310720*x^2+655360*x)*exp(4)^4+(40*x^9+1520*x^8+24320*x^7+216320*x^6+11776 00*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x^10+12 4*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+ 29622272*x^2+15728640*x)*exp(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7+58112 0*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x)*exp(4 )+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+141 55776*x^3+18874368*x^2+10485760*x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5 +2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+(1000*x ^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^ 2+245760000*x+131072000)*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6 +25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+1612185600*x+9175 04000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459 110400*x^4+1776230400*x^3+4333568000*x^2+6042419200*x+3670016000)*exp(4)^5 +(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080*x^5+95132 4160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+ (280*x^10+12080*x^9+251800*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335 685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+14680064000)*exp(4 )^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+25375 7440*x^5+1257328640*x^4+4699586560*x^3+12332564480*x^2+19922944000*x+14680 064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+4308960*x^7+30293 760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475 200*x+8388608000)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+20 30720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+626524160*x^3+1515192320 *x^2+2516582400*x+2097152000),x)
Output:
( - 40*e**16*x**4 - 640*e**16*x**3 - 3840*e**16*x**2 - 10240*e**16*x - 102 40*e**16 - 160*e**12*x**4 - 3200*e**12*x**3 - 23040*e**12*x**2 - 71680*e** 12*x - 81920*e**12 + e**8*x**6 - 400*e**8*x**4 - 7040*e**8*x**3 - 53760*e* *8*x**2 - 188416*e**8*x - 245760*e**8 + 2*e**4*x**6 - 608*e**4*x**4 - 8576 *e**4*x**3 - 59904*e**4*x**2 - 221184*e**4*x - 327680*e**4 + x**6 - 328*x* *4 - 4352*x**3 - 27392*x**2 - 98304*x - 163840)/(5*(5*e**24*x**4 + 80*e**2 4*x**3 + 480*e**24*x**2 + 1280*e**24*x + 1280*e**24 + 30*e**20*x**4 + 560* e**20*x**3 + 3840*e**20*x**2 + 11520*e**20*x + 12800*e**20 + 2*e**16*x**5 + 147*e**16*x**4 + 2432*e**16*x**3 + 16832*e**16*x**2 + 52992*e**16*x + 62 720*e**16 + 8*e**12*x**5 + 404*e**12*x**4 + 6560*e**12*x**3 + 46976*e**12* x**2 + 155392*e**12*x + 194560*e**12 + e**8*x**6 + 44*e**8*x**5 + 907*e**8 *x**4 + 11312*e**8*x**3 + 79584*e**8*x**2 + 279552*e**8*x + 378880*e**8 + 2*e**4*x**6 + 72*e**4*x**5 + 1198*e**4*x**4 + 11888*e**4*x**3 + 75392*e**4 *x**2 + 273408*e**4*x + 409600*e**4 + 9*x**6 + 162*x**5 + 1341*x**4 + 7488 *x**3 + 33408*x**2 + 110592*x + 184320))