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}} \]
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\[ \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=\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 \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {2 \left (-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 )-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-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^2-7438528 \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^3-945813 \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^4-48373 \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\right )}{5 \left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )^2}+\frac {2 \left (961-19038 e^4-53715 e^8-50688 e^{12}-12582 e^{16}+12276 e^{20}+12650 e^{24}+6096 e^{28}+1957 e^{32}+410 e^{36}+41 e^{40}+\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+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (1+e^4\right )^2 x^4\right )}{5 \left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )}\right ) \, dx \\ & = \frac {2}{5} \int \frac {-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 )-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-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^2-7438528 \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^3-945813 \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^4-48373 \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}{\left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )^2} \, dx+\frac {2}{5} \int \frac {961-19038 e^4-53715 e^8-50688 e^{12}-12582 e^{16}+12276 e^{20}+12650 e^{24}+6096 e^{28}+1957 e^{32}+410 e^{36}+41 e^{40}+\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+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (1+e^4\right )^2 x^4}{20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6} \, dx \\ & = \frac {48373+181420 e^4+170170 e^8-127988 e^{12}-415141 e^{16}-421352 e^{20}-237620 e^{24}-65416 e^{28}+10011 e^{32}+17212 e^{36}+7066 e^{40}+1404 e^{44}+117 e^{48}}{15 \left (1280 \left (2+e^4\right )^4+256 \left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x+32 \left (116+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2+16 \left (52+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3+\left (149+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4+2 \left (9+2 e^4+e^8\right ) x^5+x^6\right )}+\frac {1}{15} \int \frac {256 \left (2+e^4\right )^2 \left (465156+5071875 e^4+13706735 e^8+15023294 e^{12}+3153188 e^{16}-10365919 e^{20}-13861085 e^{24}-9073852 e^{28}-3395068 e^{32}-437291 e^{36}+280197 e^{40}+191678 e^{44}+56564 e^{48}+8775 e^{52}+585 e^{56}\right )+64 \left (896516+39172012 e^4+167537831 e^8+310023782 e^{12}+280249981 e^{16}+52163080 e^{20}-174186249 e^{24}-235333478 e^{28}-162228091 e^{32}-68339060 e^{36}-14603699 e^{40}+1981530 e^{44}+2864479 e^{48}+1134336 e^{52}+252117 e^{56}+31590 e^{60}+1755 e^{64}\right ) x-48 \left (1087500-7522067 e^4-47648589 e^8-102244143 e^{12}-108736455 e^{16}-44623535 e^{20}+33347931 e^{24}+64766901 e^{28}+49681809 e^{32}+22667655 e^{36}+5759489 e^{40}-7149 e^{44}-688141 e^{48}-311685 e^{52}-74639 e^{56}-9945 e^{60}-585 e^{64}\right ) x^2-4 \left (3950215-2314152 e^4-56784080 e^8-142604224 e^{12}-169871900 e^{16}-95270872 e^{20}+13065616 e^{24}+67891184 e^{28}+58660442 e^{32}+28324904 e^{36}+8010384 e^{40}+750944 e^{44}-448252 e^{48}-252328 e^{52}-65744 e^{56}-9360 e^{60}-585 e^{64}\right ) x^3-4 \left (330327+349174 e^4-2220687 e^8-6767424 e^{12}-8697237 e^{16}-5687498 e^{20}-720019 e^{24}+2127408 e^{28}+2110309 e^{32}+1033474 e^{36}+298003 e^{40}+49680 e^{44}+4313 e^{48}+210 e^{52}+15 e^{56}\right ) x^4}{\left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )^2} \, dx+\frac {2}{5} \int \frac {961-19038 e^4-53715 e^8-50688 e^{12}-12582 e^{16}+12276 e^{20}+12650 e^{24}+6096 e^{28}+1957 e^{32}+410 e^{36}+41 e^{40}+\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+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (1+e^4\right )^2 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^{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 )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(158\) vs. \(2(34)=68\).
Time = 0.83 (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 )} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(284\) vs. \(2(33)=66\).
Time = 3.82 (sec) , antiderivative size = 285, normalized size of antiderivative = 8.38
method | result | size |
risch | \(\frac {\left (-\frac {2 \,{\mathrm e}^{8}}{25}-\frac {4 \,{\mathrm e}^{4}}{25}-\frac {2}{25}\right ) x^{5}+\left (-\frac {{\mathrm e}^{16}}{5}-\frac {4 \,{\mathrm e}^{12}}{5}-\frac {62 \,{\mathrm e}^{8}}{25}-4 \,{\mathrm e}^{4}-\frac {53}{25}\right ) x^{4}+\left (-\frac {16 \,{\mathrm e}^{16}}{5}-16 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{25}-\frac {1136 \,{\mathrm e}^{4}}{25}-\frac {576}{25}\right ) x^{3}+\left (-\frac {96 \,{\mathrm e}^{16}}{5}-\frac {576 \,{\mathrm e}^{12}}{5}-\frac {6752 \,{\mathrm e}^{8}}{25}-\frac {7552 \,{\mathrm e}^{4}}{25}-\frac {3456}{25}\right ) x^{2}+\left (-\frac {256 \,{\mathrm e}^{16}}{5}-\frac {1792 \,{\mathrm e}^{12}}{5}-\frac {23552 \,{\mathrm e}^{8}}{25}-\frac {27648 \,{\mathrm e}^{4}}{25}-\frac {12288}{25}\right ) x -\frac {256 \,{\mathrm e}^{16}}{5}-\frac {2048 \,{\mathrm e}^{12}}{5}-\frac {6144 \,{\mathrm e}^{8}}{5}-\frac {8192 \,{\mathrm e}^{4}}{5}-\frac {4096}{5}}{4096+\frac {12288 x}{5}+96 x^{2} {\mathrm e}^{16}+{\mathrm e}^{16} x^{4}+4 \,{\mathrm e}^{12} x^{4}+80 \,{\mathrm e}^{12} x^{3}+\frac {912 \,{\mathrm e}^{8} x^{3}}{5}+\frac {23552 x \,{\mathrm e}^{8}}{5}+256 x \,{\mathrm e}^{16}+\frac {1136 x^{3} {\mathrm e}^{4}}{5}+\frac {7552 x^{2} {\mathrm e}^{4}}{5}+2048 \,{\mathrm e}^{12}+20 x^{4} {\mathrm e}^{4}+\frac {4 x^{5} {\mathrm e}^{4}}{5}+6144 \,{\mathrm e}^{8}+256 \,{\mathrm e}^{16}+16 x^{3} {\mathrm e}^{16}+\frac {27648 x \,{\mathrm e}^{4}}{5}+8192 \,{\mathrm e}^{4}+\frac {149 x^{4}}{5}+\frac {832 x^{3}}{5}+\frac {3712 x^{2}}{5}+\frac {x^{6}}{5}+\frac {18 x^{5}}{5}+\frac {6752 x^{2} {\mathrm e}^{8}}{5}+\frac {62 x^{4} {\mathrm e}^{8}}{5}+\frac {2 x^{5} {\mathrm e}^{8}}{5}+1792 x \,{\mathrm e}^{12}+576 x^{2} {\mathrm e}^{12}}\) | \(285\) |
gosper | \(-\frac {\left (5 \,{\mathrm e}^{12} x^{3}+60 x^{2} {\mathrm e}^{12}+15 \,{\mathrm e}^{8} x^{3}+2 x^{4} {\mathrm e}^{4}+240 x \,{\mathrm e}^{12}+240 x^{2} {\mathrm e}^{8}+39 x^{3} {\mathrm e}^{4}+2 x^{4}+320 \,{\mathrm e}^{12}+1200 x \,{\mathrm e}^{8}+396 x^{2} {\mathrm e}^{4}+37 x^{3}+1920 \,{\mathrm e}^{8}+2048 x \,{\mathrm e}^{4}+280 x^{2}+3840 \,{\mathrm e}^{4}+1216 x +2560\right ) \left (x \,{\mathrm e}^{4}+4 \,{\mathrm e}^{4}+x +8\right )}{5 \left (20480+12288 x +480 x^{2} {\mathrm e}^{16}+5 \,{\mathrm e}^{16} x^{4}+20 \,{\mathrm e}^{12} x^{4}+400 \,{\mathrm e}^{12} x^{3}+912 \,{\mathrm e}^{8} x^{3}+23552 x \,{\mathrm e}^{8}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+10240 \,{\mathrm e}^{12}+100 x^{4} {\mathrm e}^{4}+4 x^{5} {\mathrm e}^{4}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+80 x^{3} {\mathrm e}^{16}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+149 x^{4}+832 x^{3}+3712 x^{2}+x^{6}+18 x^{5}+6752 x^{2} {\mathrm e}^{8}+62 x^{4} {\mathrm e}^{8}+2 x^{5} {\mathrm e}^{8}+8960 x \,{\mathrm e}^{12}+2880 x^{2} {\mathrm e}^{12}\right )}\) | \(322\) |
norman | \(\frac {\left (-\frac {2}{5}-\frac {4 \,{\mathrm e}^{4}}{5}-\frac {2 \,{\mathrm e}^{8}}{5}\right ) x^{5}+\left (-256 \,{\mathrm e}^{16}-1792 \,{\mathrm e}^{12}-\frac {23552 \,{\mathrm e}^{8}}{5}-\frac {27648 \,{\mathrm e}^{4}}{5}-\frac {12288}{5}\right ) x +\left (-96 \,{\mathrm e}^{16}-576 \,{\mathrm e}^{12}-\frac {6752 \,{\mathrm e}^{8}}{5}-\frac {7552 \,{\mathrm e}^{4}}{5}-\frac {3456}{5}\right ) x^{2}+\left (-16 \,{\mathrm e}^{16}-80 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{5}-\frac {1136 \,{\mathrm e}^{4}}{5}-\frac {576}{5}\right ) x^{3}+\left (-{\mathrm e}^{16}-4 \,{\mathrm e}^{12}-\frac {62 \,{\mathrm e}^{8}}{5}-20 \,{\mathrm e}^{4}-\frac {53}{5}\right ) x^{4}-256 \,{\mathrm e}^{16}-2048 \,{\mathrm e}^{12}-6144 \,{\mathrm e}^{8}-8192 \,{\mathrm e}^{4}-4096}{20480+12288 x +480 x^{2} {\mathrm e}^{16}+5 \,{\mathrm e}^{16} x^{4}+20 \,{\mathrm e}^{12} x^{4}+400 \,{\mathrm e}^{12} x^{3}+912 \,{\mathrm e}^{8} x^{3}+23552 x \,{\mathrm e}^{8}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+10240 \,{\mathrm e}^{12}+100 x^{4} {\mathrm e}^{4}+4 x^{5} {\mathrm e}^{4}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+80 x^{3} {\mathrm e}^{16}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+149 x^{4}+832 x^{3}+3712 x^{2}+x^{6}+18 x^{5}+6752 x^{2} {\mathrm e}^{8}+62 x^{4} {\mathrm e}^{8}+2 x^{5} {\mathrm e}^{8}+8960 x \,{\mathrm e}^{12}+2880 x^{2} {\mathrm e}^{12}}\) | \(348\) |
parallelrisch | \(\frac {-20480-12288 x -480 x^{2} {\mathrm e}^{16}-5 \,{\mathrm e}^{16} x^{4}-20 \,{\mathrm e}^{12} x^{4}-400 \,{\mathrm e}^{12} x^{3}-912 \,{\mathrm e}^{8} x^{3}-23552 x \,{\mathrm e}^{8}-1280 x \,{\mathrm e}^{16}-1136 x^{3} {\mathrm e}^{4}-7552 x^{2} {\mathrm e}^{4}-10240 \,{\mathrm e}^{12}-100 x^{4} {\mathrm e}^{4}-4 x^{5} {\mathrm e}^{4}-30720 \,{\mathrm e}^{8}-1280 \,{\mathrm e}^{16}-80 x^{3} {\mathrm e}^{16}-27648 x \,{\mathrm e}^{4}-40960 \,{\mathrm e}^{4}-53 x^{4}-576 x^{3}-3456 x^{2}-2 x^{5}-6752 x^{2} {\mathrm e}^{8}-62 x^{4} {\mathrm e}^{8}-2 x^{5} {\mathrm e}^{8}-8960 x \,{\mathrm e}^{12}-2880 x^{2} {\mathrm e}^{12}}{102400+61440 x +2400 x^{2} {\mathrm e}^{16}+25 \,{\mathrm e}^{16} x^{4}+100 \,{\mathrm e}^{12} x^{4}+2000 \,{\mathrm e}^{12} x^{3}+4560 \,{\mathrm e}^{8} x^{3}+117760 x \,{\mathrm e}^{8}+6400 x \,{\mathrm e}^{16}+5680 x^{3} {\mathrm e}^{4}+37760 x^{2} {\mathrm e}^{4}+51200 \,{\mathrm e}^{12}+500 x^{4} {\mathrm e}^{4}+20 x^{5} {\mathrm e}^{4}+153600 \,{\mathrm e}^{8}+6400 \,{\mathrm e}^{16}+400 x^{3} {\mathrm e}^{16}+138240 x \,{\mathrm e}^{4}+204800 \,{\mathrm e}^{4}+745 x^{4}+4160 x^{3}+18560 x^{2}+5 x^{6}+90 x^{5}+33760 x^{2} {\mathrm e}^{8}+310 x^{4} {\mathrm e}^{8}+10 x^{5} {\mathrm e}^{8}+44800 x \,{\mathrm e}^{12}+14400 x^{2} {\mathrm e}^{12}}\) | \(390\) |
default | \(\text {Expression too large to display}\) | \(1183\) |
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Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (33) = 66\).
Time = 0.27 (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 )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 287 vs. \(2 (26) = 52\).
Time = 76.41 (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}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 247 vs. \(2 (33) = 66\).
Time = 0.24 (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 )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 325 vs. \(2 (33) = 66\).
Time = 1.89 (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 )}} \]
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Time = 11.71 (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 )} \]
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