Integrand size = 781, antiderivative size = 31 \begin {dmath*} \text {the integral} =\left (5-\left (\frac {1}{5} \left (4-e^2+2 x\right )+5 \log (3-x)\right )^2\right )^4 \end {dmath*}
Leaf count is larger than twice the leaf count of optimal. \(633\) vs. \(2(31)=62\).
Time = 3.01 (sec) , antiderivative size = 633, normalized size of antiderivative = 20.42 \begin {dmath*} \text {the integral} =\frac {8 \left (\frac {390625}{8}+\frac {e^{16}}{8}-10360232 x-308906 x^2+917344 x^3-16660 x^4-33664 x^5-416 x^6+512 x^7+32 x^8-2 e^{14} (5+x)+e^{12} \left (\frac {575}{2}+56 x+14 x^2\right )-2 e^{10} \left (1625-39 x+168 x^2+28 x^3\right )+\frac {5}{4} e^8 \left (4375-8416 x-312 x^2+896 x^3+112 x^4\right )+e^6 \left (81250+8330 x+42080 x^2+1040 x^3-2240 x^4-224 x^5\right )+e^4 \left (\frac {359375}{2}+688008 x-24990 x^2-84160 x^3-1560 x^4+2688 x^5+224 x^6\right )-2 e^2 \left (-78125-154453 x+688008 x^2-16660 x^3-42080 x^4-624 x^5+896 x^6+64 x^7\right )-25 \left (e^2-2 (2+x)\right ) \left (-109+e^4+16 x+4 x^2-4 e^2 (2+x)\right )^3 \log (3-x)+\frac {625}{2} \left (-13+7 e^4+112 x+28 x^2-28 e^2 (2+x)\right ) \left (-109+e^4+16 x+4 x^2-4 e^2 (2+x)\right )^2 \log ^2(3-x)-15625 \left (-114668+7 e^{10}+8330 x+42080 x^2+1040 x^3-2240 x^4-224 x^5-70 e^8 (2+x)+10 e^6 \left (-13+112 x+28 x^2\right )-20 e^4 \left (-526-39 x+168 x^2+28 x^3\right )+5 e^2 \left (-833-8416 x-312 x^2+896 x^3+112 x^4\right )\right ) \log ^3(3-x)+\frac {1953125}{4} \left (-833+7 e^8-8416 x-312 x^2+896 x^3+112 x^4-56 e^6 (2+x)+6 e^4 \left (-13+112 x+28 x^2\right )-8 e^2 \left (-526-39 x+168 x^2+28 x^3\right )\right ) \log ^4(3-x)-9765625 \left (1052+7 e^6+78 x-336 x^2-56 x^3-42 e^4 (2+x)+e^2 \left (-39+336 x+84 x^2\right )\right ) \log ^5(3-x)+\frac {244140625}{2} \left (-13+7 e^4+112 x+28 x^2-28 e^2 (2+x)\right ) \log ^6(3-x)-6103515625 \left (e^2-2 (2+x)\right ) \log ^7(3-x)+\frac {152587890625}{8} \log ^8(3-x)\right )}{390625} \end {dmath*}
Integrate[(-787377632 + E^14*(-152 - 16*x) - 129835568*x + 204211936*x^2 + 16951616*x^3 - 13325440*x^4 - 1536256*x^5 + 252416*x^6 + 48128*x^7 + 2048 *x^8 + E^12*(4256 + 2576*x + 224*x^2) + E^10*(5928 - 50448*x - 18144*x^2 - 1344*x^3) + E^8*(-799520 - 143440*x + 249120*x^2 + 69440*x^3 + 4480*x^4) + E^6*(633080 + 6462800*x + 910400*x^2 - 656000*x^3 - 156800*x^4 - 8960*x^ 5) + E^4*(52288608 + 1705584*x - 19588320*x^2 - 2494080*x^3 + 971520*x^4 + 209664*x^5 + 10752*x^6) + E^2*(23476856 - 206683184*x - 14419296*x^2 + 26 384320*x^3 + 3167360*x^4 - 767232*x^5 - 154112*x^6 - 7168*x^7) + (-5869214 00 + 5167079600*x + 360482400*x^2 - 659608000*x^3 - 79184000*x^4 + 1918080 0*x^5 + 3852800*x^6 + 179200*x^7 + E^12*(26600 + 2800*x) + E^10*(-638400 - 386400*x - 33600*x^2) + E^8*(-741000 + 6306000*x + 2268000*x^2 + 168000*x ^3) + E^6*(79952000 + 14344000*x - 24912000*x^2 - 6944000*x^3 - 448000*x^4 ) + E^4*(-47481000 - 484710000*x - 68280000*x^2 + 49200000*x^3 + 11760000* x^4 + 672000*x^5) + E^2*(-2614430400 - 85279200*x + 979416000*x^2 + 124704 000*x^3 - 48576000*x^4 - 10483200*x^5 - 537600*x^6))*Log[3 - x] + (3268038 0000 + E^10*(-1995000 - 210000*x) + 1065990000*x - 12242700000*x^2 - 15588 00000*x^3 + 607200000*x^4 + 131040000*x^5 + 6720000*x^6 + E^8*(39900000 + 24150000*x + 2100000*x^2) + E^6*(37050000 - 315300000*x - 113400000*x^2 - 8400000*x^3) + E^4*(-2998200000 - 537900000*x + 934200000*x^2 + 260400000* x^3 + 16800000*x^4) + E^2*(1187025000 + 12117750000*x + 1707000000*x^2 - 1 230000000*x^3 - 294000000*x^4 - 16800000*x^5))*Log[3 - x]^2 + (-9891875000 - 100981250000*x - 14225000000*x^2 + 10250000000*x^3 + 2450000000*x^4 + 1 40000000*x^5 + E^8*(83125000 + 8750000*x) + E^6*(-1330000000 - 805000000*x - 70000000*x^2) + E^4*(-926250000 + 7882500000*x + 2835000000*x^2 + 21000 0000*x^3) + E^2*(49970000000 + 8965000000*x - 15570000000*x^2 - 4340000000 *x^3 - 280000000*x^4))*Log[3 - x]^3 + (-312312500000 + E^6*(-2078125000 - 218750000*x) - 56031250000*x + 97312500000*x^2 + 27125000000*x^3 + 1750000 000*x^4 + E^4*(24937500000 + 15093750000*x + 1312500000*x^2) + E^2*(115781 25000 - 98531250000*x - 35437500000*x^2 - 2625000000*x^3))*Log[3 - x]^4 + (-57890625000 + 492656250000*x + 177187500000*x^2 + 13125000000*x^3 + E^4* (31171875000 + 3281250000*x) + E^2*(-249375000000 - 150937500000*x - 13125 000000*x^2))*Log[3 - x]^5 + (1039062500000 + E^2*(-259765625000 - 27343750 000*x) + 628906250000*x + 54687500000*x^2)*Log[3 - x]^6 + (927734375000 + 97656250000*x)*Log[3 - x]^7)/(-1171875 + 390625*x),x]
(8*(390625/8 + E^16/8 - 10360232*x - 308906*x^2 + 917344*x^3 - 16660*x^4 - 33664*x^5 - 416*x^6 + 512*x^7 + 32*x^8 - 2*E^14*(5 + x) + E^12*(575/2 + 5 6*x + 14*x^2) - 2*E^10*(1625 - 39*x + 168*x^2 + 28*x^3) + (5*E^8*(4375 - 8 416*x - 312*x^2 + 896*x^3 + 112*x^4))/4 + E^6*(81250 + 8330*x + 42080*x^2 + 1040*x^3 - 2240*x^4 - 224*x^5) + E^4*(359375/2 + 688008*x - 24990*x^2 - 84160*x^3 - 1560*x^4 + 2688*x^5 + 224*x^6) - 2*E^2*(-78125 - 154453*x + 68 8008*x^2 - 16660*x^3 - 42080*x^4 - 624*x^5 + 896*x^6 + 64*x^7) - 25*(E^2 - 2*(2 + x))*(-109 + E^4 + 16*x + 4*x^2 - 4*E^2*(2 + x))^3*Log[3 - x] + (62 5*(-13 + 7*E^4 + 112*x + 28*x^2 - 28*E^2*(2 + x))*(-109 + E^4 + 16*x + 4*x ^2 - 4*E^2*(2 + x))^2*Log[3 - x]^2)/2 - 15625*(-114668 + 7*E^10 + 8330*x + 42080*x^2 + 1040*x^3 - 2240*x^4 - 224*x^5 - 70*E^8*(2 + x) + 10*E^6*(-13 + 112*x + 28*x^2) - 20*E^4*(-526 - 39*x + 168*x^2 + 28*x^3) + 5*E^2*(-833 - 8416*x - 312*x^2 + 896*x^3 + 112*x^4))*Log[3 - x]^3 + (1953125*(-833 + 7 *E^8 - 8416*x - 312*x^2 + 896*x^3 + 112*x^4 - 56*E^6*(2 + x) + 6*E^4*(-13 + 112*x + 28*x^2) - 8*E^2*(-526 - 39*x + 168*x^2 + 28*x^3))*Log[3 - x]^4)/ 4 - 9765625*(1052 + 7*E^6 + 78*x - 336*x^2 - 56*x^3 - 42*E^4*(2 + x) + E^2 *(-39 + 336*x + 84*x^2))*Log[3 - x]^5 + (244140625*(-13 + 7*E^4 + 112*x + 28*x^2 - 28*E^2*(2 + x))*Log[3 - x]^6)/2 - 6103515625*(E^2 - 2*(2 + x))*Lo g[3 - x]^7 + (152587890625*Log[3 - x]^8)/8))/390625
Leaf count is larger than twice the leaf count of optimal. \(6532\) vs. \(2(31)=62\).
Time = 34.13 (sec) , antiderivative size = 6532, normalized size of antiderivative = 210.71, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {7239, 27, 7292, 7293, 2009}
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 {2048 x^8+48128 x^7+252416 x^6-1536256 x^5-13325440 x^4+16951616 x^3+204211936 x^2+e^{12} \left (224 x^2+2576 x+4256\right )+\left (54687500000 x^2+628906250000 x+e^2 (-27343750000 x-259765625000)+1039062500000\right ) \log ^6(3-x)+e^{10} \left (-1344 x^3-18144 x^2-50448 x+5928\right )+\left (13125000000 x^3+177187500000 x^2+e^2 \left (-13125000000 x^2-150937500000 x-249375000000\right )+492656250000 x+e^4 (3281250000 x+31171875000)-57890625000\right ) \log ^5(3-x)+e^8 \left (4480 x^4+69440 x^3+249120 x^2-143440 x-799520\right )+\left (1750000000 x^4+27125000000 x^3+97312500000 x^2+e^4 \left (1312500000 x^2+15093750000 x+24937500000\right )+e^2 \left (-2625000000 x^3-35437500000 x^2-98531250000 x+11578125000\right )-56031250000 x+e^6 (-218750000 x-2078125000)-312312500000\right ) \log ^4(3-x)+e^6 \left (-8960 x^5-156800 x^4-656000 x^3+910400 x^2+6462800 x+633080\right )+\left (140000000 x^5+2450000000 x^4+10250000000 x^3-14225000000 x^2+e^6 \left (-70000000 x^2-805000000 x-1330000000\right )+e^4 \left (210000000 x^3+2835000000 x^2+7882500000 x-926250000\right )+e^2 \left (-280000000 x^4-4340000000 x^3-15570000000 x^2+8965000000 x+49970000000\right )-100981250000 x+e^8 (8750000 x+83125000)-9891875000\right ) \log ^3(3-x)+e^4 \left (10752 x^6+209664 x^5+971520 x^4-2494080 x^3-19588320 x^2+1705584 x+52288608\right )+\left (6720000 x^6+131040000 x^5+607200000 x^4-1558800000 x^3-12242700000 x^2+e^8 \left (2100000 x^2+24150000 x+39900000\right )+e^6 \left (-8400000 x^3-113400000 x^2-315300000 x+37050000\right )+e^4 \left (16800000 x^4+260400000 x^3+934200000 x^2-537900000 x-2998200000\right )+e^2 \left (-16800000 x^5-294000000 x^4-1230000000 x^3+1707000000 x^2+12117750000 x+1187025000\right )+1065990000 x+e^{10} (-210000 x-1995000)+32680380000\right ) \log ^2(3-x)+e^2 \left (-7168 x^7-154112 x^6-767232 x^5+3167360 x^4+26384320 x^3-14419296 x^2-206683184 x+23476856\right )+\left (179200 x^7+3852800 x^6+19180800 x^5-79184000 x^4-659608000 x^3+360482400 x^2+e^{10} \left (-33600 x^2-386400 x-638400\right )+e^8 \left (168000 x^3+2268000 x^2+6306000 x-741000\right )+e^6 \left (-448000 x^4-6944000 x^3-24912000 x^2+14344000 x+79952000\right )+e^4 \left (672000 x^5+11760000 x^4+49200000 x^3-68280000 x^2-484710000 x-47481000\right )+e^2 \left (-537600 x^6-10483200 x^5-48576000 x^4+124704000 x^3+979416000 x^2-85279200 x-2614430400\right )+5167079600 x+e^{12} (2800 x+26600)-586921400\right ) \log (3-x)-129835568 x+e^{14} (-16 x-152)+(97656250000 x+927734375000) \log ^7(3-x)-787377632}{390625 x-1171875} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 (2 x+19) \left (2 x+25 \log (3-x)+4 \left (1-\frac {e^2}{4}\right )\right ) \left (-4 x^2-16 x+4 e^2 (x+2)-625 \log ^2(3-x)+50 \left (e^2-2 (x+2)\right ) \log (3-x)+109 \left (1-\frac {e^4}{109}\right )\right )^3}{390625 (3-x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {8 \int \frac {(2 x+19) \left (2 x+25 \log (3-x)-e^2+4\right ) \left (-4 x^2-16 x-625 \log ^2(3-x)+4 e^2 (x+2)+50 \left (e^2-2 (x+2)\right ) \log (3-x)-e^4+109\right )^3}{3-x}dx}{390625}\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \frac {8 \int \frac {(2 x+19) \left (2 x+25 \log (3-x)+4 \left (1-\frac {e^2}{4}\right )\right ) \left (-4 x^2-16 x-625 \log ^2(3-x)+4 e^2 (x+2)+50 \left (e^2-2 (x+2)\right ) \log (3-x)+109 \left (1-\frac {e^4}{109}\right )\right )^3}{3-x}dx}{390625}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {8 \int \left (\frac {128 (2 x+19) x^7}{x-3}+\frac {1536 \left (1-\frac {1}{24} (-2+e) (2+e)\right ) (2 x+19) x^6}{x-3}-\frac {384 e^2 (x+2) (2 x+19) x^5}{x-3}+\frac {6144 \left (1+\frac {1}{64} \left (-77-8 e^2+e^4\right )\right ) (2 x+19) x^5}{x-3}-\frac {3072 e^2 \left (1-\frac {1}{16} (-2+e) (2+e)\right ) (x+2) (2 x+19) x^4}{x-3}+\frac {8192 \left (1-\frac {3}{512} \left (1924-45 e^2-20 e^4+e^6\right )\right ) (2 x+19) x^4}{x-3}+\frac {384 e^4 (x+2)^2 (2 x+19) x^3}{x-3}-\frac {6144 e^2 \left (1+\frac {1}{32} \left (-77-8 e^2+e^4\right )\right ) (x+2) (2 x+19) x^3}{x-3}-\frac {4096 (-2+e) (2+e) \left (1-\frac {3 \left (-109+e^4\right ) \left (19-16 e^2+e^4\right )}{512 \left (-4+e^2\right )}\right ) (2 x+19) x^3}{x-3}+\frac {1536 e^4 \left (1-\frac {1}{8} (-2+e) (2+e)\right ) (x+2)^2 (2 x+19) x^2}{x-3}+\frac {3072 (-2+e) e^2 (2+e) \left (1+\frac {\left (-12+e^2\right ) \left (-109+e^4\right )}{32 \left (-4+e^2\right )}\right ) (x+2) (2 x+19) x^2}{x-3}-\frac {768 (-2+e) (2+e) \left (-109+e^4\right ) \left (1+\frac {\left (-12+e^2\right ) \left (-109+e^4\right )}{64 \left (-4+e^2\right )}\right ) (2 x+19) x^2}{x-3}-\frac {128 e^6 (x+2)^3 (2 x+19) x}{x-3}-\frac {768 (-2+e) e^4 (2+e) \left (1-\frac {-109+e^4}{8 \left (-4+e^2\right )}\right ) (x+2)^2 (2 x+19) x}{x-3}+\frac {384 (-2+e) e^2 (2+e) \left (-109+e^4\right ) \left (1-\frac {-109+e^4}{16 \left (-4+e^2\right )}\right ) (x+2) (2 x+19) x}{x-3}-\frac {48 (-2+e) (2+e) \left (-109+e^4\right )^2 \left (1-\frac {-109+e^4}{24 \left (-4+e^2\right )}\right ) (2 x+19) x}{x-3}+\frac {6103515625 (2 x+19) \log ^7(3-x)}{x-3}+\frac {1708984375 (2 x+19) \left (2 x-e^2+4\right ) \log ^6(3-x)}{x-3}+\frac {29296875 (2 x+19) \left (-28 x^2-28 \left (4-e^2\right ) x-7 e^4+56 e^2+13\right ) \log ^5(3-x)}{3-x}+\frac {1953125 (2 x+19) \left (-56 x^3-84 \left (4-e^2\right ) x^2+6 \left (13+56 e^2-7 e^4\right ) x+7 e^6-84 e^4-39 e^2+1052\right ) \log ^4(3-x)}{3-x}+\frac {78125 (2 x+19) \left (-112 x^4-224 \left (4-e^2\right ) x^3+24 \left (13+56 e^2-7 e^4\right ) x^2+8 \left (1052-39 e^2-84 e^4+7 e^6\right ) x-7 e^8+112 e^6+78 e^4-4208 e^2+833\right ) \log ^3(3-x)}{3-x}+\frac {1875 (2 x+19) \left (-224 x^5-2240 \left (1-\frac {e^2}{4}\right ) x^4+1040 \left (1-\frac {7}{13} e^2 \left (-8+e^2\right )\right ) x^3+42080 \left (1+\frac {e^2 \left (-39-84 e^2+7 e^4\right )}{1052}\right ) x^2+8330 \left (1-\frac {1}{833} e^2 \left (4208-78 e^2-112 e^4+7 e^6\right )\right ) x-114668 \left (1-\frac {e^2 \left (-4165+10520 e^2-130 e^4-140 e^6+7 e^8\right )}{114668}\right )\right ) \log ^2(3-x)}{3-x}+\frac {64 (-2+e) e^6 (2+e) (x+2)^3 (2 x+19)}{x-3}-\frac {48 (-2+e) e^4 (2+e) \left (-109+e^4\right ) (x+2)^2 (2 x+19)}{x-3}+\frac {12 (-2+e) e^2 (2+e) \left (-109+e^4\right )^2 (x+2) (2 x+19)}{x-3}-\frac {(-2+e) (2+e) \left (-109+e^4\right )^3 (2 x+19)}{x-3}+\frac {25 (2 x+19) \left (-28 x^2-28 \left (4-e^2\right ) x-7 e^4+56 e^2+13\right ) \left (-4 x^2-4 \left (4-e^2\right ) x-e^4+8 e^2+109\right )^2 \log (3-x)}{3-x}\right )dx}{390625}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {8 \left (32 x^8+3200 \log (3-x) x^7+\frac {128}{7} \left (28-e^2\right ) x^7-\frac {768 e^2 x^7}{7}+140000 \log ^2(3-x) x^6+\frac {5600}{3} \left (49-6 e^2\right ) \log (3-x) x^6-32 \left (13+8 e^2-e^4\right ) x^6+\frac {800}{3} \left (28-e^2\right ) x^6-64 e^2 \left (20-e^2\right ) x^6-\frac {2800}{9} \left (49-6 e^2\right ) x^6+128 e^4 x^6-1856 e^2 x^6+420000 \left (9-e^2\right ) \log ^2(3-x) x^5+2400 \left (337-126 e^2+7 e^4\right ) \log (3-x) x^5-\frac {32}{5} \left (5260-135 e^2-60 e^4+3 e^6\right ) x^5-480 \left (337-126 e^2+7 e^4\right ) x^5+\frac {384}{5} e^2 \left (45+8 e^2-e^4\right ) x^5-480 \left (13+8 e^2-e^4\right ) x^5+960 \left (28-e^2\right ) x^5-\frac {5568}{5} e^2 \left (20-e^2\right ) x^5+\frac {384}{5} e^4 \left (12-e^2\right ) x^5-1120 \left (49-6 e^2\right ) x^5-\frac {256 e^6 x^5}{5}+\frac {12672 e^4 x^5}{5}-9600 e^2 x^5+37500 \left (884-287 e^2+14 e^4\right ) \log ^2(3-x) x^4+500 \left (1117-5304 e^2+861 e^4-28 e^6\right ) \log (3-x) x^4-4 \left (4165-4720 e^2+270 e^4+48 e^6-3 e^8\right ) x^4-100 \left (5260-135 e^2-60 e^4+3 e^6\right ) x^4+48 e^2 \left (1180-77 e^2-12 e^4+e^6\right ) x^4-125 \left (1117-5304 e^2+861 e^4-28 e^6\right ) x^4-1800 \left (337-126 e^2+7 e^4\right ) x^4-48 e^4 \left (77+8 e^2-e^4\right ) x^4+1392 e^2 \left (45+8 e^2-e^4\right ) x^4-1800 \left (13+8 e^2-e^4\right ) x^4+3600 \left (28-e^2\right ) x^4-6000 e^2 \left (20-e^2\right ) x^4+1584 e^4 \left (12-e^2\right ) x^4-4200 \left (49-6 e^2\right ) x^4-32 (2-e) e^6 (2+e) x^4-1184 e^6 x^4+17568 e^4 x^4-36000 e^2 x^4+50000 \left (1353-1886 e^2+259 e^4-7 e^6\right ) \log ^2(3-x) x^3-\frac {1000}{3} \left (75749+16236 e^2-11316 e^4+1036 e^6-21 e^8\right ) \log (3-x) x^3-\frac {200}{3} \left (4165-4720 e^2+270 e^4+48 e^6-3 e^8\right ) x^3+\frac {1000}{9} \left (75749+16236 e^2-11316 e^4+1036 e^6-21 e^8\right ) x^3-400 \left (5260-135 e^2-60 e^4+3 e^6\right ) x^3+8 \left (109-e^4\right ) \left (1052-45 e^2-12 e^4+e^6\right ) x^3+928 e^2 \left (1180-77 e^2-12 e^4+e^6\right ) x^3-500 \left (1117-5304 e^2+861 e^4-28 e^6\right ) x^3-7200 \left (337-126 e^2+7 e^4\right ) x^3-16 e^2 \left (109-e^4\right ) \left (45+16 e^2-e^4\right ) x^3-1056 e^4 \left (77+8 e^2-e^4\right ) x^3+8000 e^2 \left (45+8 e^2-e^4\right ) x^3-7200 \left (13+8 e^2-e^4\right ) x^3-32 (2-e) e^4 (2+e) \left (109-e^4\right ) x^3+14400 \left (28-e^2\right ) x^3-24000 e^2 \left (20-e^2\right ) x^3+11712 e^4 \left (12-e^2\right ) x^3-16800 \left (49-6 e^2\right ) x^3-\frac {2368}{3} (2-e) e^6 (2+e) x^3-10624 e^6 x^3+80000 e^4 x^3-144000 e^2 x^3-150 \left (607289-245730 e^2-84710 e^4+20740 e^6-1155 e^8+14 e^{10}\right ) \log (3-x) x^2+75 \left (607289-245730 e^2-84710 e^4+20740 e^6-1155 e^8+14 e^{10}\right ) x^2-300 \left (4165-4720 e^2+270 e^4+48 e^6-3 e^8\right ) x^2+500 \left (75749+16236 e^2-11316 e^4+1036 e^6-21 e^8\right ) x^2-1800 \left (5260-135 e^2-60 e^4+3 e^6\right ) x^2+150 \left (109-e^4\right ) \left (1052-45 e^2-12 e^4+e^6\right ) x^2+6000 e^2 \left (1180-77 e^2-12 e^4+e^6\right ) x^2-2250 \left (1117-5304 e^2+861 e^4-28 e^6\right ) x^2-32400 \left (337-126 e^2+7 e^4\right ) x^2-2 \left (109-e^4\right )^2 \left (13+24 e^2-e^4\right ) x^2-348 e^2 \left (109-e^4\right ) \left (45+16 e^2-e^4\right ) x^2-8784 e^4 \left (77+8 e^2-e^4\right ) x^2+36000 e^2 \left (45+8 e^2-e^4\right ) x^2-32400 \left (13+8 e^2-e^4\right ) x^2-12 (2-e) e^2 (2+e) \left (109-e^4\right )^2 x^2-792 (2-e) e^4 (2+e) \left (109-e^4\right ) x^2+64800 \left (28-e^2\right ) x^2-108000 e^2 \left (20-e^2\right ) x^2+60000 e^4 \left (12-e^2\right ) x^2-75600 \left (49-6 e^2\right ) x^2-7968 (2-e) e^6 (2+e) x^2-63424 e^6 x^2+360000 e^4 x^2-648000 e^2 x^2-50 \left (1986497+4209942 e^2+313005 e^4-337460 e^6+36555 e^8-1218 e^{10}+7 e^{12}\right ) x+450 \left (607289-245730 e^2-84710 e^4+20740 e^6-1155 e^8+14 e^{10}\right ) x-7500 \left (701657+104335 e^2-168730 e^4+24370 e^6-1015 e^8+7 e^{10}\right ) x-937500 \left (20867-67492 e^2+14622 e^4-812 e^6+7 e^8\right ) x-1800 \left (4165-4720 e^2+270 e^4+48 e^6-3 e^8\right ) x-225000 \left (24573+16942 e^2-6222 e^4+462 e^6-7 e^8\right ) x+3000 \left (75749+16236 e^2-11316 e^4+1036 e^6-21 e^8\right ) x-10800 \left (5260-135 e^2-60 e^4+3 e^6\right ) x+900 \left (109-e^4\right ) \left (1052-45 e^2-12 e^4+e^6\right ) x+36000 e^2 \left (1180-77 e^2-12 e^4+e^6\right ) x+93750000 \left (16873-7311 e^2+609 e^4-7 e^6\right ) x+2700000 \left (1353-1886 e^2+259 e^4-7 e^6\right ) x-11250000 \left (8471-6222 e^2+693 e^4-14 e^6\right ) x-13500 \left (1117-5304 e^2+861 e^4-28 e^6\right ) x-67500000 \left (1886-518 e^2+21 e^4\right ) x+8100000 \left (884-287 e^2+14 e^4\right ) x-194400 \left (337-126 e^2+7 e^4\right ) x+1687500000 \left (1037-231 e^2+7 e^4\right ) x-7031250000 \left (2437-406 e^2+7 e^4\right ) x-50 \left (109-e^4\right )^2 \left (13+24 e^2-e^4\right ) x-3000 e^2 \left (109-e^4\right ) \left (45+16 e^2-e^4\right ) x-60000 e^4 \left (77+8 e^2-e^4\right ) x+216000 e^2 \left (45+8 e^2-e^4\right ) x-194400 \left (13+8 e^2-e^4\right ) x-2 (2-e) (2+e) \left (109-e^4\right )^3 x-348 (2-e) e^2 (2+e) \left (109-e^4\right )^2 x-8784 (2-e) e^4 (2+e) \left (109-e^4\right ) x+388800 \left (28-e^2\right ) x-648000 e^2 \left (20-e^2\right ) x+360000 e^4 \left (12-e^2\right ) x+2460937500000 \left (10-e^2\right ) x+340200000 \left (9-e^2\right ) x-295312500000 \left (33-2 e^2\right ) x+23625000000 \left (37-3 e^2\right ) x-1417500000 \left (41-4 e^2\right ) x-453600 \left (49-6 e^2\right ) x-63424 (2-e) e^6 (2+e) x-400000 e^6 x+2160000 e^4 x-3888000 e^2 x-1638221760000 x+\frac {152587890625}{8} \log ^8(3-x)-12207031250 (3-x) \log ^7(3-x)+6103515625 \left (10-e^2\right ) \log ^7(3-x)+\frac {70000}{9} (3-x)^6+3417968750 (3-x)^2 \log ^6(3-x)-3417968750 \left (10-e^2\right ) (3-x) \log ^6(3-x)+\frac {244140625}{2} \left (575-140 e^2+7 e^4\right ) \log ^6(3-x)-33600 \left (9-e^2\right ) (3-x)^5-33600 (3-x)^5-546875000 (3-x)^3 \log ^5(3-x)+410156250 \left (33-2 e^2\right ) (3-x)^2 \log ^5(3-x)-5332031250 (3-x)^2 \log ^5(3-x)-58593750 \left (2437-406 e^2+7 e^4\right ) (3-x) \log ^5(3-x)+20507812500 \left (10-e^2\right ) (3-x) \log ^5(3-x)-2460937500 \left (33-2 e^2\right ) (3-x) \log ^5(3-x)-14765625000 (3-x) \log ^5(3-x)+9765625 \left (3250-1725 e^2+210 e^4-7 e^6\right ) \log ^5(3-x)+\frac {9375}{2} \left (884-287 e^2+14 e^4\right ) (3-x)^4+787500 \left (9-e^2\right ) (3-x)^4-\frac {1640625}{8} \left (41-4 e^2\right ) (3-x)^4+\frac {20540625}{8} (3-x)^4+54687500 (3-x)^4 \log ^4(3-x)-\frac {109375000}{3} \left (37-3 e^2\right ) (3-x)^3 \log ^4(3-x)+\frac {765625000}{3} (3-x)^3 \log ^4(3-x)+11718750 \left (1037-231 e^2+7 e^4\right ) (3-x)^2 \log ^4(3-x)-1025390625 \left (33-2 e^2\right ) (3-x)^2 \log ^4(3-x)+328125000 \left (37-3 e^2\right ) (3-x)^2 \log ^4(3-x)+16283203125 (3-x)^2 \log ^4(3-x)-3906250 \left (16873-7311 e^2+609 e^4-7 e^6\right ) (3-x) \log ^4(3-x)-70312500 \left (1037-231 e^2+7 e^4\right ) (3-x) \log ^4(3-x)+292968750 \left (2437-406 e^2+7 e^4\right ) (3-x) \log ^4(3-x)-102539062500 \left (10-e^2\right ) (3-x) \log ^4(3-x)+12304687500 \left (33-2 e^2\right ) (3-x) \log ^4(3-x)-984375000 \left (37-3 e^2\right ) (3-x) \log ^4(3-x)+67921875000 (3-x) \log ^4(3-x)+\frac {1953125}{4} \left (4375-13000 e^2+3450 e^4-280 e^6+7 e^8\right ) \log ^4(3-x)-\frac {100000}{9} \left (1353-1886 e^2+259 e^4-7 e^6\right ) (3-x)^3+\frac {2500000}{27} \left (1886-518 e^2+21 e^4\right ) (3-x)^3-100000 \left (884-287 e^2+14 e^4\right ) (3-x)^3-8400000 \left (9-e^2\right ) (3-x)^3-\frac {875000000}{81} \left (37-3 e^2\right ) (3-x)^3+\frac {17500000}{3} \left (41-4 e^2\right ) (3-x)^3+\frac {10434200000}{81} (3-x)^3-3500000 (3-x)^5 \log ^3(3-x)+2187500 \left (41-4 e^2\right ) (3-x)^4 \log ^3(3-x)-2187500 (3-x)^4 \log ^3(3-x)-\frac {1250000}{3} \left (1886-518 e^2+21 e^4\right ) (3-x)^3 \log ^3(3-x)+\frac {437500000}{9} \left (37-3 e^2\right ) (3-x)^3 \log ^3(3-x)-26250000 \left (41-4 e^2\right ) (3-x)^3 \log ^3(3-x)-\frac {5897500000}{9} (3-x)^3 \log ^3(3-x)+312500 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x)^2 \log ^3(3-x)+3750000 \left (1886-518 e^2+21 e^4\right ) (3-x)^2 \log ^3(3-x)-23437500 \left (1037-231 e^2+7 e^4\right ) (3-x)^2 \log ^3(3-x)+2050781250 \left (33-2 e^2\right ) (3-x)^2 \log ^3(3-x)-656250000 \left (37-3 e^2\right ) (3-x)^2 \log ^3(3-x)+118125000 \left (41-4 e^2\right ) (3-x)^2 \log ^3(3-x)-31621406250 (3-x)^2 \log ^3(3-x)-156250 \left (20867-67492 e^2+14622 e^4-812 e^6+7 e^8\right ) (3-x) \log ^3(3-x)+15625000 \left (16873-7311 e^2+609 e^4-7 e^6\right ) (3-x) \log ^3(3-x)-1875000 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x) \log ^3(3-x)-11250000 \left (1886-518 e^2+21 e^4\right ) (3-x) \log ^3(3-x)+281250000 \left (1037-231 e^2+7 e^4\right ) (3-x) \log ^3(3-x)-1171875000 \left (2437-406 e^2+7 e^4\right ) (3-x) \log ^3(3-x)+410156250000 \left (10-e^2\right ) (3-x) \log ^3(3-x)-49218750000 \left (33-2 e^2\right ) (3-x) \log ^3(3-x)+3937500000 \left (37-3 e^2\right ) (3-x) \log ^3(3-x)-236250000 \left (41-4 e^2\right ) (3-x) \log ^3(3-x)-273105000000 (3-x) \log ^3(3-x)-15625 \left (81250+21875 e^2-32500 e^4+5750 e^6-350 e^8+7 e^{10}\right ) \log ^3(3-x)-9375 \left (24573+16942 e^2-6222 e^4+462 e^6-7 e^8\right ) (3-x)^2+225000 \left (1353-1886 e^2+259 e^4-7 e^6\right ) (3-x)^2-234375 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x)^2-2812500 \left (1886-518 e^2+21 e^4\right ) (3-x)^2+1012500 \left (884-287 e^2+14 e^4\right ) (3-x)^2+17578125 \left (1037-231 e^2+7 e^4\right ) (3-x)^2+56700000 \left (9-e^2\right ) (3-x)^2-\frac {3076171875}{2} \left (33-2 e^2\right ) (3-x)^2+492187500 \left (37-3 e^2\right ) (3-x)^2-88593750 \left (41-4 e^2\right ) (3-x)^2+\frac {47602209375}{2} (3-x)^2+2100000 (3-x)^5 \log ^2(3-x)-1640625 \left (41-4 e^2\right ) (3-x)^4 \log ^2(3-x)+1640625 (3-x)^4 \log ^2(3-x)+\frac {1250000}{3} \left (1886-518 e^2+21 e^4\right ) (3-x)^3 \log ^2(3-x)-\frac {437500000}{9} \left (37-3 e^2\right ) (3-x)^3 \log ^2(3-x)+26250000 \left (41-4 e^2\right ) (3-x)^3 \log ^2(3-x)+\frac {5897500000}{9} (3-x)^3 \log ^2(3-x)-18750 \left (24573+16942 e^2-6222 e^4+462 e^6-7 e^8\right ) (3-x)^2 \log ^2(3-x)-468750 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x)^2 \log ^2(3-x)-5625000 \left (1886-518 e^2+21 e^4\right ) (3-x)^2 \log ^2(3-x)+35156250 \left (1037-231 e^2+7 e^4\right ) (3-x)^2 \log ^2(3-x)-3076171875 \left (33-2 e^2\right ) (3-x)^2 \log ^2(3-x)+984375000 \left (37-3 e^2\right ) (3-x)^2 \log ^2(3-x)-177187500 \left (41-4 e^2\right ) (3-x)^2 \log ^2(3-x)+47432109375 (3-x)^2 \log ^2(3-x)+3750 \left (701657+104335 e^2-168730 e^4+24370 e^6-1015 e^8+7 e^{10}\right ) (3-x) \log ^2(3-x)+468750 \left (20867-67492 e^2+14622 e^4-812 e^6+7 e^8\right ) (3-x) \log ^2(3-x)+112500 \left (24573+16942 e^2-6222 e^4+462 e^6-7 e^8\right ) (3-x) \log ^2(3-x)-46875000 \left (16873-7311 e^2+609 e^4-7 e^6\right ) (3-x) \log ^2(3-x)+5625000 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x) \log ^2(3-x)+33750000 \left (1886-518 e^2+21 e^4\right ) (3-x) \log ^2(3-x)-843750000 \left (1037-231 e^2+7 e^4\right ) (3-x) \log ^2(3-x)+3515625000 \left (2437-406 e^2+7 e^4\right ) (3-x) \log ^2(3-x)-1230468750000 \left (10-e^2\right ) (3-x) \log ^2(3-x)+147656250000 \left (33-2 e^2\right ) (3-x) \log ^2(3-x)-11812500000 \left (37-3 e^2\right ) (3-x) \log ^2(3-x)+708750000 \left (41-4 e^2\right ) (3-x) \log ^2(3-x)+819315000000 (3-x) \log ^2(3-x)-1350000 \left (1353-1886 e^2+259 e^4-7 e^6\right ) \log ^2(3-x)-3037500 \left (884-287 e^2+14 e^4\right ) \log ^2(3-x)+\frac {625}{2} \left (25+20 e^2-e^4\right )^2 \left (575-140 e^2+7 e^4\right ) \log ^2(3-x)-102060000 \left (9-e^2\right ) \log ^2(3-x)-102060000 \log ^2(3-x)-\frac {140000}{3} (3-x)^6 \log (3-x)+168000 \left (9-e^2\right ) (3-x)^5 \log (3-x)+168000 (3-x)^5 \log (3-x)-18750 \left (884-287 e^2+14 e^4\right ) (3-x)^4 \log (3-x)-3150000 \left (9-e^2\right ) (3-x)^4 \log (3-x)+\frac {1640625}{2} \left (41-4 e^2\right ) (3-x)^4 \log (3-x)-\frac {20540625}{2} (3-x)^4 \log (3-x)+\frac {100000}{3} \left (1353-1886 e^2+259 e^4-7 e^6\right ) (3-x)^3 \log (3-x)-\frac {2500000}{9} \left (1886-518 e^2+21 e^4\right ) (3-x)^3 \log (3-x)+300000 \left (884-287 e^2+14 e^4\right ) (3-x)^3 \log (3-x)+25200000 \left (9-e^2\right ) (3-x)^3 \log (3-x)+\frac {875000000}{27} \left (37-3 e^2\right ) (3-x)^3 \log (3-x)-17500000 \left (41-4 e^2\right ) (3-x)^3 \log (3-x)-\frac {10434200000}{27} (3-x)^3 \log (3-x)+18750 \left (24573+16942 e^2-6222 e^4+462 e^6-7 e^8\right ) (3-x)^2 \log (3-x)-450000 \left (1353-1886 e^2+259 e^4-7 e^6\right ) (3-x)^2 \log (3-x)+468750 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x)^2 \log (3-x)+5625000 \left (1886-518 e^2+21 e^4\right ) (3-x)^2 \log (3-x)-2025000 \left (884-287 e^2+14 e^4\right ) (3-x)^2 \log (3-x)-35156250 \left (1037-231 e^2+7 e^4\right ) (3-x)^2 \log (3-x)-113400000 \left (9-e^2\right ) (3-x)^2 \log (3-x)+3076171875 \left (33-2 e^2\right ) (3-x)^2 \log (3-x)-984375000 \left (37-3 e^2\right ) (3-x)^2 \log (3-x)+177187500 \left (41-4 e^2\right ) (3-x)^2 \log (3-x)-47602209375 (3-x)^2 \log (3-x)-50 \left (1986497+4209942 e^2+313005 e^4-337460 e^6+36555 e^8-1218 e^{10}+7 e^{12}\right ) (3-x) \log (3-x)-7500 \left (701657+104335 e^2-168730 e^4+24370 e^6-1015 e^8+7 e^{10}\right ) (3-x) \log (3-x)-937500 \left (20867-67492 e^2+14622 e^4-812 e^6+7 e^8\right ) (3-x) \log (3-x)-225000 \left (24573+16942 e^2-6222 e^4+462 e^6-7 e^8\right ) (3-x) \log (3-x)+93750000 \left (16873-7311 e^2+609 e^4-7 e^6\right ) (3-x) \log (3-x)+2700000 \left (1353-1886 e^2+259 e^4-7 e^6\right ) (3-x) \log (3-x)-11250000 \left (8471-6222 e^2+693 e^4-14 e^6\right ) (3-x) \log (3-x)-67500000 \left (1886-518 e^2+21 e^4\right ) (3-x) \log (3-x)+8100000 \left (884-287 e^2+14 e^4\right ) (3-x) \log (3-x)+1687500000 \left (1037-231 e^2+7 e^4\right ) (3-x) \log (3-x)-7031250000 \left (2437-406 e^2+7 e^4\right ) (3-x) \log (3-x)+2460937500000 \left (10-e^2\right ) (3-x) \log (3-x)+340200000 \left (9-e^2\right ) (3-x) \log (3-x)-295312500000 \left (33-2 e^2\right ) (3-x) \log (3-x)+23625000000 \left (37-3 e^2\right ) (3-x) \log (3-x)-1417500000 \left (41-4 e^2\right ) (3-x) \log (3-x)-1638221760000 (3-x) \log (3-x)+1350 \left (607289-245730 e^2-84710 e^4+20740 e^6-1155 e^8+14 e^{10}\right ) \log (3-x)-5400 \left (4165-4720 e^2+270 e^4+48 e^6-3 e^8\right ) \log (3-x)+9000 \left (75749+16236 e^2-11316 e^4+1036 e^6-21 e^8\right ) \log (3-x)-32400 \left (5260-135 e^2-60 e^4+3 e^6\right ) \log (3-x)+2700 \left (109-e^4\right ) \left (1052-45 e^2-12 e^4+e^6\right ) \log (3-x)+108000 e^2 \left (1180-77 e^2-12 e^4+e^6\right ) \log (3-x)-40500 \left (1117-5304 e^2+861 e^4-28 e^6\right ) \log (3-x)-583200 \left (337-126 e^2+7 e^4\right ) \log (3-x)-150 \left (109-e^4\right )^2 \left (13+24 e^2-e^4\right ) \log (3-x)-9000 e^2 \left (109-e^4\right ) \left (45+16 e^2-e^4\right ) \log (3-x)-180000 e^4 \left (77+8 e^2-e^4\right ) \log (3-x)+648000 e^2 \left (45+8 e^2-e^4\right ) \log (3-x)-583200 \left (13+8 e^2-e^4\right ) \log (3-x)-25 (2-e) (2+e) \left (109-e^4\right )^3 \log (3-x)-1500 (2-e) e^2 (2+e) \left (109-e^4\right )^2 \log (3-x)-30000 (2-e) e^4 (2+e) \left (109-e^4\right ) \log (3-x)+1166400 \left (28-e^2\right ) \log (3-x)-1944000 e^2 \left (20-e^2\right ) \log (3-x)+1080000 e^4 \left (12-e^2\right ) \log (3-x)-1360800 \left (49-6 e^2\right ) \log (3-x)-200000 (2-e) e^6 (2+e) \log (3-x)-1200000 e^6 \log (3-x)+6480000 e^4 \log (3-x)-11664000 e^2 \log (3-x)\right )}{390625}\) |
Int[(-787377632 + E^14*(-152 - 16*x) - 129835568*x + 204211936*x^2 + 16951 616*x^3 - 13325440*x^4 - 1536256*x^5 + 252416*x^6 + 48128*x^7 + 2048*x^8 + E^12*(4256 + 2576*x + 224*x^2) + E^10*(5928 - 50448*x - 18144*x^2 - 1344* x^3) + E^8*(-799520 - 143440*x + 249120*x^2 + 69440*x^3 + 4480*x^4) + E^6* (633080 + 6462800*x + 910400*x^2 - 656000*x^3 - 156800*x^4 - 8960*x^5) + E ^4*(52288608 + 1705584*x - 19588320*x^2 - 2494080*x^3 + 971520*x^4 + 20966 4*x^5 + 10752*x^6) + E^2*(23476856 - 206683184*x - 14419296*x^2 + 26384320 *x^3 + 3167360*x^4 - 767232*x^5 - 154112*x^6 - 7168*x^7) + (-586921400 + 5 167079600*x + 360482400*x^2 - 659608000*x^3 - 79184000*x^4 + 19180800*x^5 + 3852800*x^6 + 179200*x^7 + E^12*(26600 + 2800*x) + E^10*(-638400 - 38640 0*x - 33600*x^2) + E^8*(-741000 + 6306000*x + 2268000*x^2 + 168000*x^3) + E^6*(79952000 + 14344000*x - 24912000*x^2 - 6944000*x^3 - 448000*x^4) + E^ 4*(-47481000 - 484710000*x - 68280000*x^2 + 49200000*x^3 + 11760000*x^4 + 672000*x^5) + E^2*(-2614430400 - 85279200*x + 979416000*x^2 + 124704000*x^ 3 - 48576000*x^4 - 10483200*x^5 - 537600*x^6))*Log[3 - x] + (32680380000 + E^10*(-1995000 - 210000*x) + 1065990000*x - 12242700000*x^2 - 1558800000* x^3 + 607200000*x^4 + 131040000*x^5 + 6720000*x^6 + E^8*(39900000 + 241500 00*x + 2100000*x^2) + E^6*(37050000 - 315300000*x - 113400000*x^2 - 840000 0*x^3) + E^4*(-2998200000 - 537900000*x + 934200000*x^2 + 260400000*x^3 + 16800000*x^4) + E^2*(1187025000 + 12117750000*x + 1707000000*x^2 - 1230000 000*x^3 - 294000000*x^4 - 16800000*x^5))*Log[3 - x]^2 + (-9891875000 - 100 981250000*x - 14225000000*x^2 + 10250000000*x^3 + 2450000000*x^4 + 1400000 00*x^5 + E^8*(83125000 + 8750000*x) + E^6*(-1330000000 - 805000000*x - 700 00000*x^2) + E^4*(-926250000 + 7882500000*x + 2835000000*x^2 + 210000000*x ^3) + E^2*(49970000000 + 8965000000*x - 15570000000*x^2 - 4340000000*x^3 - 280000000*x^4))*Log[3 - x]^3 + (-312312500000 + E^6*(-2078125000 - 218750 000*x) - 56031250000*x + 97312500000*x^2 + 27125000000*x^3 + 1750000000*x^ 4 + E^4*(24937500000 + 15093750000*x + 1312500000*x^2) + E^2*(11578125000 - 98531250000*x - 35437500000*x^2 - 2625000000*x^3))*Log[3 - x]^4 + (-5789 0625000 + 492656250000*x + 177187500000*x^2 + 13125000000*x^3 + E^4*(31171 875000 + 3281250000*x) + E^2*(-249375000000 - 150937500000*x - 13125000000 *x^2))*Log[3 - x]^5 + (1039062500000 + E^2*(-259765625000 - 27343750000*x) + 628906250000*x + 54687500000*x^2)*Log[3 - x]^6 + (927734375000 + 976562 50000*x)*Log[3 - x]^7)/(-1171875 + 390625*x),x]
(8*((47602209375*(3 - x)^2)/2 - 88593750*(41 - 4*E^2)*(3 - x)^2 + 49218750 0*(37 - 3*E^2)*(3 - x)^2 - (3076171875*(33 - 2*E^2)*(3 - x)^2)/2 + 5670000 0*(9 - E^2)*(3 - x)^2 + 17578125*(1037 - 231*E^2 + 7*E^4)*(3 - x)^2 + 1012 500*(884 - 287*E^2 + 14*E^4)*(3 - x)^2 - 2812500*(1886 - 518*E^2 + 21*E^4) *(3 - x)^2 - 234375*(8471 - 6222*E^2 + 693*E^4 - 14*E^6)*(3 - x)^2 + 22500 0*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*(3 - x)^2 - 9375*(24573 + 16942*E^2 - 6222*E^4 + 462*E^6 - 7*E^8)*(3 - x)^2 + (10434200000*(3 - x)^3)/81 + (17 500000*(41 - 4*E^2)*(3 - x)^3)/3 - (875000000*(37 - 3*E^2)*(3 - x)^3)/81 - 8400000*(9 - E^2)*(3 - x)^3 - 100000*(884 - 287*E^2 + 14*E^4)*(3 - x)^3 + (2500000*(1886 - 518*E^2 + 21*E^4)*(3 - x)^3)/27 - (100000*(1353 - 1886*E ^2 + 259*E^4 - 7*E^6)*(3 - x)^3)/9 + (20540625*(3 - x)^4)/8 - (1640625*(41 - 4*E^2)*(3 - x)^4)/8 + 787500*(9 - E^2)*(3 - x)^4 + (9375*(884 - 287*E^2 + 14*E^4)*(3 - x)^4)/2 - 33600*(3 - x)^5 - 33600*(9 - E^2)*(3 - x)^5 + (7 0000*(3 - x)^6)/9 - 1638221760000*x - 3888000*E^2*x + 2160000*E^4*x - 4000 00*E^6*x - 63424*(2 - E)*E^6*(2 + E)*x - 453600*(49 - 6*E^2)*x - 141750000 0*(41 - 4*E^2)*x + 23625000000*(37 - 3*E^2)*x - 295312500000*(33 - 2*E^2)* x + 340200000*(9 - E^2)*x + 2460937500000*(10 - E^2)*x + 360000*E^4*(12 - E^2)*x - 648000*E^2*(20 - E^2)*x + 388800*(28 - E^2)*x - 8784*(2 - E)*E^4* (2 + E)*(109 - E^4)*x - 348*(2 - E)*E^2*(2 + E)*(109 - E^4)^2*x - 2*(2 - E )*(2 + E)*(109 - E^4)^3*x - 194400*(13 + 8*E^2 - E^4)*x + 216000*E^2*(4...
3.8.35.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
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. \(960\) vs. \(2(25)=50\).
Time = 1.60 (sec) , antiderivative size = 961, normalized size of antiderivative = 31.00
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(961\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(1909\) |
| parts | \(\text {Expression too large to display}\) | \(3747\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(3929\) |
| default | \(\text {Expression too large to display}\) | \(3929\) |
int(((97656250000*x+927734375000)*ln(-x+3)^7+((-27343750000*x-259765625000 )*exp(2)+54687500000*x^2+628906250000*x+1039062500000)*ln(-x+3)^6+((328125 0000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-249375000000 )*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-57890625000)*ln(- x+3)^5+((-218750000*x-2078125000)*exp(2)^3+(1312500000*x^2+15093750000*x+2 4937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-98531250000*x+115781 25000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-56031250000*x -312312500000)*ln(-x+3)^4+((8750000*x+83125000)*exp(2)^4+(-70000000*x^2-80 5000000*x-1330000000)*exp(2)^3+(210000000*x^3+2835000000*x^2+7882500000*x- 926250000)*exp(2)^2+(-280000000*x^4-4340000000*x^3-15570000000*x^2+8965000 000*x+49970000000)*exp(2)+140000000*x^5+2450000000*x^4+10250000000*x^3-142 25000000*x^2-100981250000*x-9891875000)*ln(-x+3)^3+((-210000*x-1995000)*ex p(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3-113400000* x^2-315300000*x+37050000)*exp(2)^3+(16800000*x^4+260400000*x^3+934200000*x ^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-294000000*x^4-123000000 0*x^3+1707000000*x^2+12117750000*x+1187025000)*exp(2)+6720000*x^6+13104000 0*x^5+607200000*x^4-1558800000*x^3-12242700000*x^2+1065990000*x+3268038000 0)*ln(-x+3)^2+((2800*x+26600)*exp(2)^6+(-33600*x^2-386400*x-638400)*exp(2) ^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000*x^4-6944000 *x^3-24912000*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11760000*x^4+4 9200000*x^3-68280000*x^2-484710000*x-47481000)*exp(2)^2+(-537600*x^6-10483 200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-2614430400)*ex p(2)+179200*x^7+3852800*x^6+19180800*x^5-79184000*x^4-659608000*x^3+360482 400*x^2+5167079600*x-586921400)*ln(-x+3)+(-16*x-152)*exp(2)^7+(224*x^2+257 6*x+4256)*exp(2)^6+(-1344*x^3-18144*x^2-50448*x+5928)*exp(2)^5+(4480*x^4+6 9440*x^3+249120*x^2-143440*x-799520)*exp(2)^4+(-8960*x^5-156800*x^4-656000 *x^3+910400*x^2+6462800*x+633080)*exp(2)^3+(10752*x^6+209664*x^5+971520*x^ 4-2494080*x^3-19588320*x^2+1705584*x+52288608)*exp(2)^2+(-7168*x^7-154112* x^6-767232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-206683184*x+23476856) *exp(2)+2048*x^8+48128*x^7+252416*x^6-1536256*x^5-13325440*x^4+16951616*x^ 3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x,method=_RETURN VERBOSE)
112/390625*x^2*exp(12)-16/390625*x*exp(14)-82881856/390625*x+624/390625*x* exp(10)-14336/390625*x^6*exp(2)-134656/78125*x^3*exp(4)-39984/78125*x^2*ex p(4)+13328/78125*x*exp(6)+53312/78125*x^3*exp(2)-11008128/390625*x^2*exp(2 )+134656/78125*x^4*exp(2)-32/390625*exp(14)-2688/390625*x^2*exp(10)-448/39 0625*x^3*exp(10)-52/390625*exp(12)-2496/78125*x^4*exp(4)+21504/390625*x^5* exp(4)-1666/78125*exp(8)-41440928/15625*ln(-3+x)+1792/390625*x^6*exp(4)+1/ 390625*exp(16)-917344/390625*exp(6)+8416/390625*exp(10)+5504064/390625*x*e xp(4)-624/78125*x^2*exp(8)-617812/390625*exp(4)+4096/390625*x^7+256/390625 *x^8+41440928/390625*exp(2)-3328/390625*x^6-269312/390625*x^5-26656/78125* x^4+7338752/390625*x^3-2471248/390625*x^2+9984/390625*exp(2)*x^5+2471248/3 90625*exp(2)*x+1664/78125*x^3*exp(6)+67328/78125*x^2*exp(6)-16832/78125*x* exp(8)+390625*ln(-x+3)^8+(5504064/625*x-336/625*x*exp(10)+10752/125*x^3*ex p(4)-3744/125*x^2*exp(4)+1248/125*x*exp(6)+4992/125*x^3*exp(2)+201984/125* x^2*exp(2)-10752/125*x^4*exp(2)+28/625*exp(12)+1344/125*x^4*exp(4)-156/125 *exp(8)+16832/125*exp(6)-672/625*exp(10)-100992/125*x*exp(4)+336/125*x^2*e xp(8)-9996/125*exp(4)-2752032/625*exp(2)+1792/625*x^6+21504/625*x^5-2496/1 25*x^4-134656/125*x^3-39984/125*x^2-5376/625*exp(2)*x^5+39984/125*exp(2)*x -896/125*x^3*exp(6)-5376/125*x^2*exp(6)+1344/125*x*exp(8)-617812/625)*ln(- x+3)^2+(-1400*exp(6)+8400*x*exp(4)-16800*x^2*exp(2)+11200*x^3+16800*exp(4) -67200*exp(2)*x+67200*x^2+7800*exp(2)-15600*x-210400)*ln(-x+3)^5+(-2471...
Leaf count of result is larger than twice the leaf count of optimal. 793 vs. \(2 (25) = 50\).
Time = 0.29 (sec) , antiderivative size = 793, normalized size of antiderivative = 25.58 \begin {dmath*} \text {the integral} =\text {Too large to display} \end {dmath*}
integrate(((97656250000*x+927734375000)*log(-x+3)^7+((-27343750000*x-25976 5625000)*exp(2)+54687500000*x^2+628906250000*x+1039062500000)*log(-x+3)^6+ ((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-2493 75000000)*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-578906250 00)*log(-x+3)^5+((-218750000*x-2078125000)*exp(2)^3+(1312500000*x^2+150937 50000*x+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-98531250000 *x+11578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-5603 1250000*x-312312500000)*log(-x+3)^4+((8750000*x+83125000)*exp(2)^4+(-70000 000*x^2-805000000*x-1330000000)*exp(2)^3+(210000000*x^3+2835000000*x^2+788 2500000*x-926250000)*exp(2)^2+(-280000000*x^4-4340000000*x^3-15570000000*x ^2+8965000000*x+49970000000)*exp(2)+140000000*x^5+2450000000*x^4+102500000 00*x^3-14225000000*x^2-100981250000*x-9891875000)*log(-x+3)^3+((-210000*x- 1995000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3 -113400000*x^2-315300000*x+37050000)*exp(2)^3+(16800000*x^4+260400000*x^3+ 934200000*x^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-294000000*x^ 4-1230000000*x^3+1707000000*x^2+12117750000*x+1187025000)*exp(2)+6720000*x ^6+131040000*x^5+607200000*x^4-1558800000*x^3-12242700000*x^2+1065990000*x +32680380000)*log(-x+3)^2+((2800*x+26600)*exp(2)^6+(-33600*x^2-386400*x-63 8400)*exp(2)^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000 *x^4-6944000*x^3-24912000*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11 760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*exp(2)^2+(-5376 00*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-26 14430400)*exp(2)+179200*x^7+3852800*x^6+19180800*x^5-79184000*x^4-65960800 0*x^3+360482400*x^2+5167079600*x-586921400)*log(-x+3)+(-16*x-152)*exp(2)^7 +(224*x^2+2576*x+4256)*exp(2)^6+(-1344*x^3-18144*x^2-50448*x+5928)*exp(2)^ 5+(4480*x^4+69440*x^3+249120*x^2-143440*x-799520)*exp(2)^4+(-8960*x^5-1568 00*x^4-656000*x^3+910400*x^2+6462800*x+633080)*exp(2)^3+(10752*x^6+209664* x^5+971520*x^4-2494080*x^3-19588320*x^2+1705584*x+52288608)*exp(2)^2+(-716 8*x^7-154112*x^6-767232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-20668318 4*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-1536256*x^5-13325440*x^ 4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x, algorithm=\
256/390625*x^8 + 125000*(2*x - e^2 + 4)*log(-x + 3)^7 + 390625*log(-x + 3) ^8 + 4096/390625*x^7 + 2500*(28*x^2 - 28*(x + 2)*e^2 + 112*x + 7*e^4 - 13) *log(-x + 3)^6 - 3328/390625*x^6 + 200*(56*x^3 + 336*x^2 + 42*(x + 2)*e^4 - 3*(28*x^2 + 112*x - 13)*e^2 - 78*x - 7*e^6 - 1052)*log(-x + 3)^5 - 26931 2/390625*x^5 + 10*(112*x^4 + 896*x^3 - 312*x^2 - 56*(x + 2)*e^6 + 6*(28*x^ 2 + 112*x - 13)*e^4 - 8*(28*x^3 + 168*x^2 - 39*x - 526)*e^2 - 8416*x + 7*e ^8 - 833)*log(-x + 3)^4 - 26656/78125*x^4 + 8/25*(224*x^5 + 2240*x^4 - 104 0*x^3 - 42080*x^2 + 70*(x + 2)*e^8 - 10*(28*x^2 + 112*x - 13)*e^6 + 20*(28 *x^3 + 168*x^2 - 39*x - 526)*e^4 - 5*(112*x^4 + 896*x^3 - 312*x^2 - 8416*x - 833)*e^2 - 8330*x - 7*e^10 + 114668)*log(-x + 3)^3 + 7338752/390625*x^3 + 4/625*(448*x^6 + 5376*x^5 - 3120*x^4 - 168320*x^3 - 49980*x^2 - 84*(x + 2)*e^10 + 15*(28*x^2 + 112*x - 13)*e^8 - 40*(28*x^3 + 168*x^2 - 39*x - 52 6)*e^6 + 15*(112*x^4 + 896*x^3 - 312*x^2 - 8416*x - 833)*e^4 - 12*(112*x^5 + 1120*x^4 - 520*x^3 - 21040*x^2 - 4165*x + 57334)*e^2 + 1376016*x + 7*e^ 12 - 154453)*log(-x + 3)^2 - 2471248/390625*x^2 - 16/390625*x*e^14 + 112/3 90625*(x^2 + 4*x)*e^12 - 16/390625*(28*x^3 + 168*x^2 - 39*x)*e^10 + 16/781 25*(14*x^4 + 112*x^3 - 39*x^2 - 1052*x)*e^8 - 16/390625*(112*x^5 + 1120*x^ 4 - 520*x^3 - 21040*x^2 - 4165*x)*e^6 + 16/390625*(112*x^6 + 1344*x^5 - 78 0*x^4 - 42080*x^3 - 12495*x^2 + 344004*x)*e^4 - 16/390625*(64*x^7 + 896*x^ 6 - 624*x^5 - 42080*x^4 - 16660*x^3 + 688008*x^2 - 154453*x)*e^2 + 8/15...
Leaf count of result is larger than twice the leaf count of optimal. 1146 vs. \(2 (24) = 48\).
Time = 2.33 (sec) , antiderivative size = 1146, normalized size of antiderivative = 36.97 \begin {dmath*} \text {the integral} =\text {Too large to display} \end {dmath*}
integrate(((97656250000*x+927734375000)*ln(-x+3)**7+((-27343750000*x-25976 5625000)*exp(2)+54687500000*x**2+628906250000*x+1039062500000)*ln(-x+3)**6 +((3281250000*x+31171875000)*exp(2)**2+(-13125000000*x**2-150937500000*x-2 49375000000)*exp(2)+13125000000*x**3+177187500000*x**2+492656250000*x-5789 0625000)*ln(-x+3)**5+((-218750000*x-2078125000)*exp(2)**3+(1312500000*x**2 +15093750000*x+24937500000)*exp(2)**2+(-2625000000*x**3-35437500000*x**2-9 8531250000*x+11578125000)*exp(2)+1750000000*x**4+27125000000*x**3+97312500 000*x**2-56031250000*x-312312500000)*ln(-x+3)**4+((8750000*x+83125000)*exp (2)**4+(-70000000*x**2-805000000*x-1330000000)*exp(2)**3+(210000000*x**3+2 835000000*x**2+7882500000*x-926250000)*exp(2)**2+(-280000000*x**4-43400000 00*x**3-15570000000*x**2+8965000000*x+49970000000)*exp(2)+140000000*x**5+2 450000000*x**4+10250000000*x**3-14225000000*x**2-100981250000*x-9891875000 )*ln(-x+3)**3+((-210000*x-1995000)*exp(2)**5+(2100000*x**2+24150000*x+3990 0000)*exp(2)**4+(-8400000*x**3-113400000*x**2-315300000*x+37050000)*exp(2) **3+(16800000*x**4+260400000*x**3+934200000*x**2-537900000*x-2998200000)*e xp(2)**2+(-16800000*x**5-294000000*x**4-1230000000*x**3+1707000000*x**2+12 117750000*x+1187025000)*exp(2)+6720000*x**6+131040000*x**5+607200000*x**4- 1558800000*x**3-12242700000*x**2+1065990000*x+32680380000)*ln(-x+3)**2+((2 800*x+26600)*exp(2)**6+(-33600*x**2-386400*x-638400)*exp(2)**5+(168000*x** 3+2268000*x**2+6306000*x-741000)*exp(2)**4+(-448000*x**4-6944000*x**3-2491 2000*x**2+14344000*x+79952000)*exp(2)**3+(672000*x**5+11760000*x**4+492000 00*x**3-68280000*x**2-484710000*x-47481000)*exp(2)**2+(-537600*x**6-104832 00*x**5-48576000*x**4+124704000*x**3+979416000*x**2-85279200*x-2614430400) *exp(2)+179200*x**7+3852800*x**6+19180800*x**5-79184000*x**4-659608000*x** 3+360482400*x**2+5167079600*x-586921400)*ln(-x+3)+(-16*x-152)*exp(2)**7+(2 24*x**2+2576*x+4256)*exp(2)**6+(-1344*x**3-18144*x**2-50448*x+5928)*exp(2) **5+(4480*x**4+69440*x**3+249120*x**2-143440*x-799520)*exp(2)**4+(-8960*x* *5-156800*x**4-656000*x**3+910400*x**2+6462800*x+633080)*exp(2)**3+(10752* x**6+209664*x**5+971520*x**4-2494080*x**3-19588320*x**2+1705584*x+52288608 )*exp(2)**2+(-7168*x**7-154112*x**6-767232*x**5+3167360*x**4+26384320*x**3 -14419296*x**2-206683184*x+23476856)*exp(2)+2048*x**8+48128*x**7+252416*x* *6-1536256*x**5-13325440*x**4+16951616*x**3+204211936*x**2-129835568*x-787 377632)/(390625*x-1171875),x)
256*x**8/390625 + x**7*(4096/390625 - 1024*exp(2)/390625) + x**6*(-14336*e xp(2)/390625 - 3328/390625 + 1792*exp(4)/390625) + x**5*(-1792*exp(6)/3906 25 - 269312/390625 + 9984*exp(2)/390625 + 21504*exp(4)/390625) + x**4*(-35 84*exp(6)/78125 - 2496*exp(4)/78125 - 26656/78125 + 224*exp(8)/78125 + 134 656*exp(2)/78125) + x**3*(-134656*exp(4)/78125 - 448*exp(10)/390625 + 5331 2*exp(2)/78125 + 1664*exp(6)/78125 + 7338752/390625 + 1792*exp(8)/78125) + x**2*(-11008128*exp(2)/390625 - 2688*exp(10)/390625 - 39984*exp(4)/78125 - 624*exp(8)/78125 - 2471248/390625 + 112*exp(12)/390625 + 67328*exp(6)/78 125) + x*(-16832*exp(8)/78125 - 82881856/390625 - 16*exp(14)/390625 + 624* exp(10)/390625 + 2471248*exp(2)/390625 + 13328*exp(6)/78125 + 448*exp(12)/ 390625 + 5504064*exp(4)/390625) + (250000*x - 125000*exp(2) + 500000)*log( 3 - x)**7 + (70000*x**2 - 70000*x*exp(2) + 280000*x - 140000*exp(2) - 3250 0 + 17500*exp(4))*log(3 - x)**6 + (11200*x**3 - 16800*x**2*exp(2) + 67200* x**2 - 67200*x*exp(2) - 15600*x + 8400*x*exp(4) - 1400*exp(6) - 210400 + 7 800*exp(2) + 16800*exp(4))*log(3 - x)**5 + (1120*x**4 - 2240*x**3*exp(2) + 8960*x**3 - 13440*x**2*exp(2) - 3120*x**2 + 1680*x**2*exp(4) - 560*x*exp( 6) - 84160*x + 3120*x*exp(2) + 6720*x*exp(4) - 1120*exp(6) - 780*exp(4) - 8330 + 70*exp(8) + 42080*exp(2))*log(3 - x)**4 + (1792*x**5/25 - 896*x**4* exp(2)/5 + 3584*x**4/5 - 7168*x**3*exp(2)/5 - 1664*x**3/5 + 896*x**3*exp(4 )/5 - 448*x**2*exp(6)/5 - 67328*x**2/5 + 2496*x**2*exp(2)/5 + 5376*x**2...
Leaf count of result is larger than twice the leaf count of optimal. 6363 vs. \(2 (25) = 50\).
Time = 0.41 (sec) , antiderivative size = 6363, normalized size of antiderivative = 205.26 \begin {dmath*} \text {the integral} =\text {Too large to display} \end {dmath*}
integrate(((97656250000*x+927734375000)*log(-x+3)^7+((-27343750000*x-25976 5625000)*exp(2)+54687500000*x^2+628906250000*x+1039062500000)*log(-x+3)^6+ ((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-2493 75000000)*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-578906250 00)*log(-x+3)^5+((-218750000*x-2078125000)*exp(2)^3+(1312500000*x^2+150937 50000*x+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-98531250000 *x+11578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-5603 1250000*x-312312500000)*log(-x+3)^4+((8750000*x+83125000)*exp(2)^4+(-70000 000*x^2-805000000*x-1330000000)*exp(2)^3+(210000000*x^3+2835000000*x^2+788 2500000*x-926250000)*exp(2)^2+(-280000000*x^4-4340000000*x^3-15570000000*x ^2+8965000000*x+49970000000)*exp(2)+140000000*x^5+2450000000*x^4+102500000 00*x^3-14225000000*x^2-100981250000*x-9891875000)*log(-x+3)^3+((-210000*x- 1995000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3 -113400000*x^2-315300000*x+37050000)*exp(2)^3+(16800000*x^4+260400000*x^3+ 934200000*x^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-294000000*x^ 4-1230000000*x^3+1707000000*x^2+12117750000*x+1187025000)*exp(2)+6720000*x ^6+131040000*x^5+607200000*x^4-1558800000*x^3-12242700000*x^2+1065990000*x +32680380000)*log(-x+3)^2+((2800*x+26600)*exp(2)^6+(-33600*x^2-386400*x-63 8400)*exp(2)^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000 *x^4-6944000*x^3-24912000*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11 760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*exp(2)^2+(-5376 00*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-26 14430400)*exp(2)+179200*x^7+3852800*x^6+19180800*x^5-79184000*x^4-65960800 0*x^3+360482400*x^2+5167079600*x-586921400)*log(-x+3)+(-16*x-152)*exp(2)^7 +(224*x^2+2576*x+4256)*exp(2)^6+(-1344*x^3-18144*x^2-50448*x+5928)*exp(2)^ 5+(4480*x^4+69440*x^3+249120*x^2-143440*x-799520)*exp(2)^4+(-8960*x^5-1568 00*x^4-656000*x^3+910400*x^2+6462800*x+633080)*exp(2)^3+(10752*x^6+209664* x^5+971520*x^4-2494080*x^3-19588320*x^2+1705584*x+52288608)*exp(2)^2+(-716 8*x^7-154112*x^6-767232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-20668318 4*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-1536256*x^5-13325440*x^ 4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x, algorithm=\
256/390625*x^8 - 95000*e^2*log(-x + 3)^7 + 390625*log(-x + 3)^8 + 896/5625 *(18*log(-x + 3)^2 - 6*log(-x + 3) + 1)*(x - 3)^6 + 4096/390625*x^7 + 1330 0*e^4*log(-x + 3)^6 - 106400*e^2*log(-x + 3)^6 + 1250000*log(-x + 3)^7 + 1 792/3125*(125*log(-x + 3)^3 - 75*log(-x + 3)^2 + 30*log(-x + 3) - 6)*(x - 3)^5 + 16128/3125*(25*log(-x + 3)^2 - 10*log(-x + 3) + 2)*(x - 3)^5 - 5899 52/3515625*x^6 - 1064*e^6*log(-x + 3)^5 + 12768*e^4*log(-x + 3)^5 + 5928*e ^2*log(-x + 3)^5 + 1437500*log(-x + 3)^6 + 35*(32*log(-x + 3)^4 - 32*log(- x + 3)^3 + 24*log(-x + 3)^2 - 12*log(-x + 3) + 3)*(x - 3)^4 + 91*(32*log(- x + 3)^3 - 24*log(-x + 3)^2 + 12*log(-x + 3) - 3)*(x - 3)^4 + 1392/5*(8*lo g(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4 - 1837312/390625*x^5 + 266/5*e^ 8*log(-x + 3)^4 - 4256/5*e^6*log(-x + 3)^4 - 2964/5*e^4*log(-x + 3)^4 + 15 9904/5*e^2*log(-x + 3)^4 + 650000*log(-x + 3)^5 + 11200/81*(81*log(-x + 3) ^5 - 135*log(-x + 3)^4 + 180*log(-x + 3)^3 - 180*log(-x + 3)^2 + 120*log(- x + 3) - 40)*(x - 3)^3 + 123200/81*(27*log(-x + 3)^4 - 36*log(-x + 3)^3 + 36*log(-x + 3)^2 - 24*log(-x + 3) + 8)*(x - 3)^3 + 133760/27*(9*log(-x + 3 )^3 - 9*log(-x + 3)^2 + 6*log(-x + 3) - 2)*(x - 3)^3 + 6016/3*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 - 2267656/78125*x^4 - 1064/625*e^10*lo g(-x + 3)^3 + 4256/125*e^8*log(-x + 3)^3 + 3952/125*e^6*log(-x + 3)^3 - 31 9808/125*e^4*log(-x + 3)^3 + 126616/125*e^2*log(-x + 3)^3 + 43750*log(-x + 3)^4 + 17500*(4*log(-x + 3)^6 - 12*log(-x + 3)^5 + 30*log(-x + 3)^4 - ...
Leaf count of result is larger than twice the leaf count of optimal. 1952 vs. \(2 (25) = 50\).
Time = 0.39 (sec) , antiderivative size = 1952, normalized size of antiderivative = 62.97 \begin {dmath*} \text {the integral} =\text {Too large to display} \end {dmath*}
integrate(((97656250000*x+927734375000)*log(-x+3)^7+((-27343750000*x-25976 5625000)*exp(2)+54687500000*x^2+628906250000*x+1039062500000)*log(-x+3)^6+ ((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-2493 75000000)*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-578906250 00)*log(-x+3)^5+((-218750000*x-2078125000)*exp(2)^3+(1312500000*x^2+150937 50000*x+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-98531250000 *x+11578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-5603 1250000*x-312312500000)*log(-x+3)^4+((8750000*x+83125000)*exp(2)^4+(-70000 000*x^2-805000000*x-1330000000)*exp(2)^3+(210000000*x^3+2835000000*x^2+788 2500000*x-926250000)*exp(2)^2+(-280000000*x^4-4340000000*x^3-15570000000*x ^2+8965000000*x+49970000000)*exp(2)+140000000*x^5+2450000000*x^4+102500000 00*x^3-14225000000*x^2-100981250000*x-9891875000)*log(-x+3)^3+((-210000*x- 1995000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3 -113400000*x^2-315300000*x+37050000)*exp(2)^3+(16800000*x^4+260400000*x^3+ 934200000*x^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-294000000*x^ 4-1230000000*x^3+1707000000*x^2+12117750000*x+1187025000)*exp(2)+6720000*x ^6+131040000*x^5+607200000*x^4-1558800000*x^3-12242700000*x^2+1065990000*x +32680380000)*log(-x+3)^2+((2800*x+26600)*exp(2)^6+(-33600*x^2-386400*x-63 8400)*exp(2)^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000 *x^4-6944000*x^3-24912000*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11 760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*exp(2)^2+(-5376 00*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-26 14430400)*exp(2)+179200*x^7+3852800*x^6+19180800*x^5-79184000*x^4-65960800 0*x^3+360482400*x^2+5167079600*x-586921400)*log(-x+3)+(-16*x-152)*exp(2)^7 +(224*x^2+2576*x+4256)*exp(2)^6+(-1344*x^3-18144*x^2-50448*x+5928)*exp(2)^ 5+(4480*x^4+69440*x^3+249120*x^2-143440*x-799520)*exp(2)^4+(-8960*x^5-1568 00*x^4-656000*x^3+910400*x^2+6462800*x+633080)*exp(2)^3+(10752*x^6+209664* x^5+971520*x^4-2494080*x^3-19588320*x^2+1705584*x+52288608)*exp(2)^2+(-716 8*x^7-154112*x^6-767232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-20668318 4*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-1536256*x^5-13325440*x^ 4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x, algorithm=\
256/390625*(x - 3)^8 - 1024/390625*(x - 3)^7*e^2 + 1024/15625*(x - 3)^7*lo g(-x + 3) - 3584/15625*(x - 3)^6*e^2*log(-x + 3) + 1792/625*(x - 3)^6*log( -x + 3)^2 - 5376/625*(x - 3)^5*e^2*log(-x + 3)^2 + 1792/25*(x - 3)^5*log(- x + 3)^3 - 896/5*(x - 3)^4*e^2*log(-x + 3)^3 + 1120*(x - 3)^4*log(-x + 3)^ 4 - 2240*(x - 3)^3*e^2*log(-x + 3)^4 + 11200*(x - 3)^3*log(-x + 3)^5 - 168 00*(x - 3)^2*e^2*log(-x + 3)^5 + 70000*(x - 3)^2*log(-x + 3)^6 - 70000*(x - 3)*e^2*log(-x + 3)^6 + 250000*(x - 3)*log(-x + 3)^7 - 125000*e^2*log(-x + 3)^7 + 390625*log(-x + 3)^8 + 2048/78125*(x - 3)^7 + 1792/390625*(x - 3) ^6*e^4 - 7168/78125*(x - 3)^6*e^2 + 7168/3125*(x - 3)^6*log(-x + 3) + 5376 /15625*(x - 3)^5*e^4*log(-x + 3) - 21504/3125*(x - 3)^5*e^2*log(-x + 3) + 10752/125*(x - 3)^5*log(-x + 3)^2 + 1344/125*(x - 3)^4*e^4*log(-x + 3)^2 - 5376/25*(x - 3)^4*e^2*log(-x + 3)^2 + 1792*(x - 3)^4*log(-x + 3)^3 + 896/ 5*(x - 3)^3*e^4*log(-x + 3)^3 - 3584*(x - 3)^3*e^2*log(-x + 3)^3 + 22400*( x - 3)^3*log(-x + 3)^4 + 1680*(x - 3)^2*e^4*log(-x + 3)^4 - 33600*(x - 3)^ 2*e^2*log(-x + 3)^4 + 168000*(x - 3)^2*log(-x + 3)^5 + 8400*(x - 3)*e^4*lo g(-x + 3)^5 - 168000*(x - 3)*e^2*log(-x + 3)^5 + 700000*(x - 3)*log(-x + 3 )^6 + 17500*e^4*log(-x + 3)^6 - 350000*e^2*log(-x + 3)^6 + 1250000*log(-x + 3)^7 + 5888/15625*(x - 3)^6 - 1792/390625*(x - 3)^5*e^6 + 10752/78125*(x - 3)^5*e^4 - 17664/15625*(x - 3)^5*e^2 + 17664/625*(x - 3)^5*log(-x + 3) - 896/3125*(x - 3)^4*e^6*log(-x + 3) + 5376/625*(x - 3)^4*e^4*log(-x + ...
Time = 18.69 (sec) , antiderivative size = 772, normalized size of antiderivative = 24.90 \begin {dmath*} \text {the integral} =\text {Too large to display} \end {dmath*}
int((log(3 - x)^2*(1065990000*x + exp(8)*(24150000*x + 2100000*x^2 + 39900 000) - exp(6)*(315300000*x + 113400000*x^2 + 8400000*x^3 - 37050000) + exp (2)*(12117750000*x + 1707000000*x^2 - 1230000000*x^3 - 294000000*x^4 - 168 00000*x^5 + 1187025000) + exp(4)*(934200000*x^2 - 537900000*x + 260400000* x^3 + 16800000*x^4 - 2998200000) - 12242700000*x^2 - 1558800000*x^3 + 6072 00000*x^4 + 131040000*x^5 + 6720000*x^6 - exp(10)*(210000*x + 1995000) + 3 2680380000) - 129835568*x + exp(4)*(1705584*x - 19588320*x^2 - 2494080*x^3 + 971520*x^4 + 209664*x^5 + 10752*x^6 + 52288608) + exp(12)*(2576*x + 224 *x^2 + 4256) + log(3 - x)*(5167079600*x - exp(10)*(386400*x + 33600*x^2 + 638400) + exp(8)*(6306000*x + 2268000*x^2 + 168000*x^3 - 741000) - exp(6)* (24912000*x^2 - 14344000*x + 6944000*x^3 + 448000*x^4 - 79952000) + 360482 400*x^2 - 659608000*x^3 - 79184000*x^4 + 19180800*x^5 + 3852800*x^6 + 1792 00*x^7 - exp(2)*(85279200*x - 979416000*x^2 - 124704000*x^3 + 48576000*x^4 + 10483200*x^5 + 537600*x^6 + 2614430400) + exp(12)*(2800*x + 26600) - ex p(4)*(484710000*x + 68280000*x^2 - 49200000*x^3 - 11760000*x^4 - 672000*x^ 5 + 47481000) - 586921400) - exp(2)*(206683184*x + 14419296*x^2 - 26384320 *x^3 - 3167360*x^4 + 767232*x^5 + 154112*x^6 + 7168*x^7 - 23476856) + log( 3 - x)^7*(97656250000*x + 927734375000) - exp(10)*(50448*x + 18144*x^2 + 1 344*x^3 - 5928) - log(3 - x)^3*(100981250000*x - exp(8)*(8750000*x + 83125 000) + exp(2)*(15570000000*x^2 - 8965000000*x + 4340000000*x^3 + 280000000 *x^4 - 49970000000) - exp(4)*(7882500000*x + 2835000000*x^2 + 210000000*x^ 3 - 926250000) + exp(6)*(805000000*x + 70000000*x^2 + 1330000000) + 142250 00000*x^2 - 10250000000*x^3 - 2450000000*x^4 - 140000000*x^5 + 9891875000) + exp(8)*(249120*x^2 - 143440*x + 69440*x^3 + 4480*x^4 - 799520) - log(3 - x)^4*(56031250000*x + exp(6)*(218750000*x + 2078125000) - exp(4)*(150937 50000*x + 1312500000*x^2 + 24937500000) - 97312500000*x^2 - 27125000000*x^ 3 - 1750000000*x^4 + exp(2)*(98531250000*x + 35437500000*x^2 + 2625000000* x^3 - 11578125000) + 312312500000) + log(3 - x)^6*(628906250000*x - exp(2) *(27343750000*x + 259765625000) + 54687500000*x^2 + 1039062500000) + 20421 1936*x^2 + 16951616*x^3 - 13325440*x^4 - 1536256*x^5 + 252416*x^6 + 48128* x^7 + 2048*x^8 + exp(6)*(6462800*x + 910400*x^2 - 656000*x^3 - 156800*x^4 - 8960*x^5 + 633080) - exp(14)*(16*x + 152) + log(3 - x)^5*(492656250000*x + exp(4)*(3281250000*x + 31171875000) - exp(2)*(150937500000*x + 13125000 000*x^2 + 249375000000) + 177187500000*x^2 + 13125000000*x^3 - 57890625000 ) - 787377632)/(390625*x - 1171875),x)
390625*log(3 - x)^8 - log(3 - x)^4*(780*exp(4) - 42080*exp(2) + 1120*exp(6 ) - 70*exp(8) + x^2*(13440*exp(2) - 1680*exp(4) + 3120) + x^3*(2240*exp(2) - 8960) - x*(3120*exp(2) + 6720*exp(4) - 560*exp(6) - 84160) - 1120*x^4 + 8330) - x^6*((14336*exp(2))/390625 - (1792*exp(4))/390625 + 3328/390625) - x^2*((11008128*exp(2))/390625 + (39984*exp(4))/78125 - (67328*exp(6))/78 125 + (624*exp(8))/78125 + (2688*exp(10))/390625 - (112*exp(12))/390625 + 2471248/390625) - x^7*((1024*exp(2))/390625 - 4096/390625) + log(3 - x)^7* (250000*x - 125000*exp(2) + 500000) - log(3 - x)^5*(1400*exp(6) - 16800*ex p(4) - 7800*exp(2) + x^2*(16800*exp(2) - 67200) + x*(67200*exp(2) - 8400*e xp(4) + 15600) - 11200*x^3 + 210400) + log(x - 3)*((1235624*exp(2))/15625 + (2752032*exp(4))/15625 + (6664*exp(6))/3125 - (8416*exp(8))/3125 + (312* exp(10))/15625 + (224*exp(12))/15625 - (8*exp(14))/15625 - 41440928/15625) + x^3*((53312*exp(2))/78125 - (134656*exp(4))/78125 + (1664*exp(6))/78125 + (1792*exp(8))/78125 - (448*exp(10))/390625 + 7338752/390625) + log(3 - x)^3*((6664*exp(2))/5 - (16832*exp(4))/5 + (208*exp(6))/5 + (224*exp(8))/5 - (56*exp(10))/25 - x^3*((7168*exp(2))/5 - (896*exp(4))/5 + 1664/5) - x*( (1248*exp(4))/5 - (67328*exp(2))/5 + (1792*exp(6))/5 - (112*exp(8))/5 + 13 328/5) - x^4*((896*exp(2))/5 - 3584/5) + (1792*x^5)/25 + x^2*((2496*exp(2) )/5 + (5376*exp(4))/5 - (448*exp(6))/5 - 67328/5) + 917344/25) - log(3 - x )^6*(140000*exp(2) - 17500*exp(4) - 70000*x^2 + x*(70000*exp(2) - 28000...