\(\int \frac {-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+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7)+(-586921400+5167079600 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} (-638400-386400 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+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+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^2-1230000000 x^3-294000000 x^4-16800000 x^5)) \log ^2(3-x)+(-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 (-1330000000-805000000 x-70000000 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(3-x)+(-312312500000+e^6 (-2078125000-218750000 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 ^4(3-x)+(-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 (-249375000000-150937500000 x-13125000000 x^2)) \log ^5(3-x)+(1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx\) [9735]
Optimal result
Integrand size = 781, antiderivative size = 31 \[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx=\left (5-\left (\frac {1}{5} \left (4-e^2+2 x\right )+5 \log (3-x)\right )^2\right )^4
\]
[Out]
(5-(5*ln(-x+3)-1/5*exp(2)+2/5*x+4/5)^2)^4
Rubi [B] (verified)
Leaf count is larger than twice the leaf count of optimal. \(6930\) vs. \(2(31)=62\).
Time = 63.54 (sec) , antiderivative size = 6930, normalized size of antiderivative = 223.55,
number of steps used = 322, number of rules used = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6820, 12, 6874,
45, 78, 147, 153, 2465, 2436, 2332, 2437, 2338, 2442, 2333, 2339, 30, 2448, 2342, 2341, 2445, 2458,
2372, 2388} \[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx =\text {Too large to display}
\]
[In]
Int[(-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 - 134
4*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 + 2
09664*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 + 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*(-74100
0 + 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*(-26144304
00 - 85279200*x + 979416000*x^2 + 124704000*x^3 - 48576000*x^4 - 10483200*x^5 - 537600*x^6))*Log[3 - x] + (326
80380000 + E^10*(-1995000 - 210000*x) + 1065990000*x - 12242700000*x^2 - 1558800000*x^3 + 607200000*x^4 + 1310
40000*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*(118
7025000 + 12117750000*x + 1707000000*x^2 - 1230000000*x^3 - 294000000*x^4 - 16800000*x^5))*Log[3 - x]^2 + (-98
91875000 - 100981250000*x - 14225000000*x^2 + 10250000000*x^3 + 2450000000*x^4 + 140000000*x^5 + E^8*(83125000
+ 8750000*x) + E^6*(-1330000000 - 805000000*x - 70000000*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 - 218750000*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 + (-57890625000 + 492656250000*x + 177187500000*x^2 + 13125000
000*x^3 + E^4*(31171875000 + 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 + 97656250000*x)*Log[3 - x]^7)/(-1171875 + 390625*x),x]
[Out]
(60930828*(3 - x)^2)/125 - (9072*(41 - 4*E^2)*(3 - x)^2)/5 + 10080*(37 - 3*E^2)*(3 - x)^2 - 31500*(33 - 2*E^2)
*(3 - x)^2 + (145152*(9 - E^2)*(3 - x)^2)/125 + 360*(1037 - 231*E^2 + 7*E^4)*(3 - x)^2 + (2592*(884 - 287*E^2
+ 14*E^4)*(3 - x)^2)/125 - (288*(1886 - 518*E^2 + 21*E^4)*(3 - x)^2)/5 - (24*(8471 - 6222*E^2 + 693*E^4 - 14*E
^6)*(3 - x)^2)/5 + (576*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*(3 - x)^2)/125 - (24*(24573 + 16942*E^2 - 6222*E^4
+ 462*E^6 - 7*E^8)*(3 - x)^2)/125 + (26711552*(3 - x)^3)/10125 + (1792*(41 - 4*E^2)*(3 - x)^3)/15 - (17920*(3
7 - 3*E^2)*(3 - x)^3)/81 - (21504*(9 - E^2)*(3 - x)^3)/125 - (256*(884 - 287*E^2 + 14*E^4)*(3 - x)^3)/125 + (2
56*(1886 - 518*E^2 + 21*E^4)*(3 - x)^3)/135 - (256*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*(3 - x)^3)/1125 + (6573
*(3 - x)^4)/125 - (21*(41 - 4*E^2)*(3 - x)^4)/5 + (2016*(9 - E^2)*(3 - x)^4)/125 + (12*(884 - 287*E^2 + 14*E^4
)*(3 - x)^4)/125 - (10752*(3 - x)^5)/15625 - (10752*(9 - E^2)*(3 - x)^5)/15625 + (896*(3 - x)^6)/5625 - (20969
238528*x)/625 - (248832*E^2*x)/3125 + (27648*E^4*x)/625 - (1024*E^6*x)/125 - (507392*(2 - E)*E^6*(2 + E)*x)/39
0625 - (145152*(49 - 6*E^2)*x)/15625 - (145152*(41 - 4*E^2)*x)/5 + 483840*(37 - 3*E^2)*x - 6048000*(33 - 2*E^2
)*x + (870912*(9 - E^2)*x)/125 + 50400000*(10 - E^2)*x + (4608*E^4*(12 - E^2)*x)/625 - (41472*E^2*(20 - E^2)*x
)/3125 + (124416*(28 - E^2)*x)/15625 - (70272*(2 - E)*E^4*(2 + E)*(109 - E^4)*x)/390625 - (2784*(2 - E)*E^2*(2
+ E)*(109 - E^4)^2*x)/390625 - (16*(2 - E)*(2 + E)*(109 - E^4)^3*x)/390625 - (62208*(13 + 8*E^2 - E^4)*x)/156
25 + (13824*E^2*(45 + 8*E^2 - E^4)*x)/3125 - (768*E^4*(77 + 8*E^2 - E^4)*x)/625 - (192*E^2*(109 - E^4)*(45 + 1
6*E^2 - E^4)*x)/3125 - (16*(109 - E^4)^2*(13 + 24*E^2 - E^4)*x)/15625 - 144000*(2437 - 406*E^2 + 7*E^4)*x + 34
560*(1037 - 231*E^2 + 7*E^4)*x - (62208*(337 - 126*E^2 + 7*E^4)*x)/15625 + (20736*(884 - 287*E^2 + 14*E^4)*x)/
125 - (6912*(1886 - 518*E^2 + 21*E^4)*x)/5 - (864*(1117 - 5304*E^2 + 861*E^4 - 28*E^6)*x)/3125 - (1152*(8471 -
6222*E^2 + 693*E^4 - 14*E^6)*x)/5 + (6912*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*x)/125 + 1920*(16873 - 7311*E^2
+ 609*E^4 - 7*E^6)*x + (2304*E^2*(1180 - 77*E^2 - 12*E^4 + E^6)*x)/3125 + (288*(109 - E^4)*(1052 - 45*E^2 - 1
2*E^4 + E^6)*x)/15625 - (3456*(5260 - 135*E^2 - 60*E^4 + 3*E^6)*x)/15625 + (192*(75749 + 16236*E^2 - 11316*E^4
+ 1036*E^6 - 21*E^8)*x)/3125 - (576*(24573 + 16942*E^2 - 6222*E^4 + 462*E^6 - 7*E^8)*x)/125 - (576*(4165 - 47
20*E^2 + 270*E^4 + 48*E^6 - 3*E^8)*x)/15625 - (96*(20867 - 67492*E^2 + 14622*E^4 - 812*E^6 + 7*E^8)*x)/5 - (96
*(701657 + 104335*E^2 - 168730*E^4 + 24370*E^6 - 1015*E^8 + 7*E^10)*x)/625 + (144*(607289 - 245730*E^2 - 84710
*E^4 + 20740*E^6 - 1155*E^8 + 14*E^10)*x)/15625 - (16*(1986497 + 4209942*E^2 + 313005*E^4 - 337460*E^6 + 36555
*E^8 - 1218*E^10 + 7*E^12)*x)/15625 - (41472*E^2*x^2)/3125 + (4608*E^4*x^2)/625 - (507392*E^6*x^2)/390625 - (6
3744*(2 - E)*E^6*(2 + E)*x^2)/390625 - (24192*(49 - 6*E^2)*x^2)/15625 + (768*E^4*(12 - E^2)*x^2)/625 - (6912*E
^2*(20 - E^2)*x^2)/3125 + (20736*(28 - E^2)*x^2)/15625 - (6336*(2 - E)*E^4*(2 + E)*(109 - E^4)*x^2)/390625 - (
96*(2 - E)*E^2*(2 + E)*(109 - E^4)^2*x^2)/390625 - (10368*(13 + 8*E^2 - E^4)*x^2)/15625 + (2304*E^2*(45 + 8*E^
2 - E^4)*x^2)/3125 - (70272*E^4*(77 + 8*E^2 - E^4)*x^2)/390625 - (2784*E^2*(109 - E^4)*(45 + 16*E^2 - E^4)*x^2
)/390625 - (16*(109 - E^4)^2*(13 + 24*E^2 - E^4)*x^2)/390625 - (10368*(337 - 126*E^2 + 7*E^4)*x^2)/15625 - (14
4*(1117 - 5304*E^2 + 861*E^4 - 28*E^6)*x^2)/3125 + (384*E^2*(1180 - 77*E^2 - 12*E^4 + E^6)*x^2)/3125 + (48*(10
9 - E^4)*(1052 - 45*E^2 - 12*E^4 + E^6)*x^2)/15625 - (576*(5260 - 135*E^2 - 60*E^4 + 3*E^6)*x^2)/15625 + (32*(
75749 + 16236*E^2 - 11316*E^4 + 1036*E^6 - 21*E^8)*x^2)/3125 - (96*(4165 - 4720*E^2 + 270*E^4 + 48*E^6 - 3*E^8
)*x^2)/15625 + (24*(607289 - 245730*E^2 - 84710*E^4 + 20740*E^6 - 1155*E^8 + 14*E^10)*x^2)/15625 - (9216*E^2*x
^3)/3125 + (1024*E^4*x^3)/625 - (84992*E^6*x^3)/390625 - (18944*(2 - E)*E^6*(2 + E)*x^3)/1171875 - (5376*(49 -
6*E^2)*x^3)/15625 + (93696*E^4*(12 - E^2)*x^3)/390625 - (1536*E^2*(20 - E^2)*x^3)/3125 + (4608*(28 - E^2)*x^3
)/15625 - (256*(2 - E)*E^4*(2 + E)*(109 - E^4)*x^3)/390625 - (2304*(13 + 8*E^2 - E^4)*x^3)/15625 + (512*E^2*(4
5 + 8*E^2 - E^4)*x^3)/3125 - (8448*E^4*(77 + 8*E^2 - E^4)*x^3)/390625 - (128*E^2*(109 - E^4)*(45 + 16*E^2 - E^
4)*x^3)/390625 - (2304*(337 - 126*E^2 + 7*E^4)*x^3)/15625 - (32*(1117 - 5304*E^2 + 861*E^4 - 28*E^6)*x^3)/3125
+ (7424*E^2*(1180 - 77*E^2 - 12*E^4 + E^6)*x^3)/390625 + (64*(109 - E^4)*(1052 - 45*E^2 - 12*E^4 + E^6)*x^3)/
390625 - (128*(5260 - 135*E^2 - 60*E^4 + 3*E^6)*x^3)/15625 + (64*(75749 + 16236*E^2 - 11316*E^4 + 1036*E^6 - 2
1*E^8)*x^3)/28125 - (64*(4165 - 4720*E^2 + 270*E^4 + 48*E^6 - 3*E^8)*x^3)/46875 - (2304*E^2*x^4)/3125 + (14054
4*E^4*x^4)/390625 - (9472*E^6*x^4)/390625 - (256*(2 - E)*E^6*(2 + E)*x^4)/390625 - (1344*(49 - 6*E^2)*x^4)/156
25 + (12672*E^4*(12 - E^2)*x^4)/390625 - (384*E^2*(20 - E^2)*x^4)/3125 + (1152*(28 - E^2)*x^4)/15625 - (576*(1
3 + 8*E^2 - E^4)*x^4)/15625 + (11136*E^2*(45 + 8*E^2 - E^4)*x^4)/390625 - (384*E^4*(77 + 8*E^2 - E^4)*x^4)/390
625 - (576*(337 - 126*E^2 + 7*E^4)*x^4)/15625 - (8*(1117 - 5304*E^2 + 861*E^4 - 28*E^6)*x^4)/3125 + (384*E^2*(
1180 - 77*E^2 - 12*E^4 + E^6)*x^4)/390625 - (32*(5260 - 135*E^2 - 60*E^4 + 3*E^6)*x^4)/15625 - (32*(4165 - 472
0*E^2 + 270*E^4 + 48*E^6 - 3*E^8)*x^4)/390625 - (3072*E^2*x^5)/15625 + (101376*E^4*x^5)/1953125 - (2048*E^6*x^
5)/1953125 - (1792*(49 - 6*E^2)*x^5)/78125 + (3072*E^4*(12 - E^2)*x^5)/1953125 - (44544*E^2*(20 - E^2)*x^5)/19
53125 + (1536*(28 - E^2)*x^5)/78125 - (768*(13 + 8*E^2 - E^4)*x^5)/78125 + (3072*E^2*(45 + 8*E^2 - E^4)*x^5)/1
953125 - (768*(337 - 126*E^2 + 7*E^4)*x^5)/78125 - (256*(5260 - 135*E^2 - 60*E^4 + 3*E^6)*x^5)/1953125 - (1484
8*E^2*x^6)/390625 + (1024*E^4*x^6)/390625 - (896*(49 - 6*E^2)*x^6)/140625 - (512*E^2*(20 - E^2)*x^6)/390625 +
(256*(28 - E^2)*x^6)/46875 - (256*(13 + 8*E^2 - E^4)*x^6)/390625 - (6144*E^2*x^7)/2734375 + (1024*(28 - E^2)*x
^7)/2734375 + (256*x^8)/390625 - (746496*E^2*Log[3 - x])/3125 + (82944*E^4*Log[3 - x])/625 - (3072*E^6*Log[3 -
x])/125 - (512*(2 - E)*E^6*(2 + E)*Log[3 - x])/125 - (435456*(49 - 6*E^2)*Log[3 - x])/15625 + (13824*E^4*(12
- E^2)*Log[3 - x])/625 - (124416*E^2*(20 - E^2)*Log[3 - x])/3125 + (373248*(28 - E^2)*Log[3 - x])/15625 - (384
*(2 - E)*E^4*(2 + E)*(109 - E^4)*Log[3 - x])/625 - (96*(2 - E)*E^2*(2 + E)*(109 - E^4)^2*Log[3 - x])/3125 - (8
*(2 - E)*(2 + E)*(109 - E^4)^3*Log[3 - x])/15625 - (186624*(13 + 8*E^2 - E^4)*Log[3 - x])/15625 + (41472*E^2*(
45 + 8*E^2 - E^4)*Log[3 - x])/3125 - (2304*E^4*(77 + 8*E^2 - E^4)*Log[3 - x])/625 - (576*E^2*(109 - E^4)*(45 +
16*E^2 - E^4)*Log[3 - x])/3125 - (48*(109 - E^4)^2*(13 + 24*E^2 - E^4)*Log[3 - x])/15625 - (186624*(337 - 126
*E^2 + 7*E^4)*Log[3 - x])/15625 - (2592*(1117 - 5304*E^2 + 861*E^4 - 28*E^6)*Log[3 - x])/3125 + (6912*E^2*(118
0 - 77*E^2 - 12*E^4 + E^6)*Log[3 - x])/3125 + (864*(109 - E^4)*(1052 - 45*E^2 - 12*E^4 + E^6)*Log[3 - x])/1562
5 - (10368*(5260 - 135*E^2 - 60*E^4 + 3*E^6)*Log[3 - x])/15625 + (576*(75749 + 16236*E^2 - 11316*E^4 + 1036*E^
6 - 21*E^8)*Log[3 - x])/3125 - (1728*(4165 - 4720*E^2 + 270*E^4 + 48*E^6 - 3*E^8)*Log[3 - x])/15625 + (432*(60
7289 - 245730*E^2 - 84710*E^4 + 20740*E^6 - 1155*E^8 + 14*E^10)*Log[3 - x])/15625 - (20969238528*(3 - x)*Log[3
- x])/625 - (145152*(41 - 4*E^2)*(3 - x)*Log[3 - x])/5 + 483840*(37 - 3*E^2)*(3 - x)*Log[3 - x] - 6048000*(33
- 2*E^2)*(3 - x)*Log[3 - x] + (870912*(9 - E^2)*(3 - x)*Log[3 - x])/125 + 50400000*(10 - E^2)*(3 - x)*Log[3 -
x] - 144000*(2437 - 406*E^2 + 7*E^4)*(3 - x)*Log[3 - x] + 34560*(1037 - 231*E^2 + 7*E^4)*(3 - x)*Log[3 - x] +
(20736*(884 - 287*E^2 + 14*E^4)*(3 - x)*Log[3 - x])/125 - (6912*(1886 - 518*E^2 + 21*E^4)*(3 - x)*Log[3 - x])
/5 - (1152*(8471 - 6222*E^2 + 693*E^4 - 14*E^6)*(3 - x)*Log[3 - x])/5 + (6912*(1353 - 1886*E^2 + 259*E^4 - 7*E
^6)*(3 - x)*Log[3 - x])/125 + 1920*(16873 - 7311*E^2 + 609*E^4 - 7*E^6)*(3 - x)*Log[3 - x] - (576*(24573 + 169
42*E^2 - 6222*E^4 + 462*E^6 - 7*E^8)*(3 - x)*Log[3 - x])/125 - (96*(20867 - 67492*E^2 + 14622*E^4 - 812*E^6 +
7*E^8)*(3 - x)*Log[3 - x])/5 - (96*(701657 + 104335*E^2 - 168730*E^4 + 24370*E^6 - 1015*E^8 + 7*E^10)*(3 - x)*
Log[3 - x])/625 - (16*(1986497 + 4209942*E^2 + 313005*E^4 - 337460*E^6 + 36555*E^8 - 1218*E^10 + 7*E^12)*(3 -
x)*Log[3 - x])/15625 - (121861656*(3 - x)^2*Log[3 - x])/125 + (18144*(41 - 4*E^2)*(3 - x)^2*Log[3 - x])/5 - 20
160*(37 - 3*E^2)*(3 - x)^2*Log[3 - x] + 63000*(33 - 2*E^2)*(3 - x)^2*Log[3 - x] - (290304*(9 - E^2)*(3 - x)^2*
Log[3 - x])/125 - 720*(1037 - 231*E^2 + 7*E^4)*(3 - x)^2*Log[3 - x] - (5184*(884 - 287*E^2 + 14*E^4)*(3 - x)^2
*Log[3 - x])/125 + (576*(1886 - 518*E^2 + 21*E^4)*(3 - x)^2*Log[3 - x])/5 + (48*(8471 - 6222*E^2 + 693*E^4 - 1
4*E^6)*(3 - x)^2*Log[3 - x])/5 - (1152*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*(3 - x)^2*Log[3 - x])/125 + (48*(24
573 + 16942*E^2 - 6222*E^4 + 462*E^6 - 7*E^8)*(3 - x)^2*Log[3 - x])/125 - (26711552*(3 - x)^3*Log[3 - x])/3375
- (1792*(41 - 4*E^2)*(3 - x)^3*Log[3 - x])/5 + (17920*(37 - 3*E^2)*(3 - x)^3*Log[3 - x])/27 + (64512*(9 - E^2
)*(3 - x)^3*Log[3 - x])/125 + (768*(884 - 287*E^2 + 14*E^4)*(3 - x)^3*Log[3 - x])/125 - (256*(1886 - 518*E^2 +
21*E^4)*(3 - x)^3*Log[3 - x])/45 + (256*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*(3 - x)^3*Log[3 - x])/375 - (2629
2*(3 - x)^4*Log[3 - x])/125 + (84*(41 - 4*E^2)*(3 - x)^4*Log[3 - x])/5 - (8064*(9 - E^2)*(3 - x)^4*Log[3 - x])
/125 - (48*(884 - 287*E^2 + 14*E^4)*(3 - x)^4*Log[3 - x])/125 + (10752*(3 - x)^5*Log[3 - x])/3125 + (10752*(9
- E^2)*(3 - x)^5*Log[3 - x])/3125 - (1792*(3 - x)^6*Log[3 - x])/1875 - (48*(607289 - 245730*E^2 - 84710*E^4 +
20740*E^6 - 1155*E^8 + 14*E^10)*x^2*Log[3 - x])/15625 - (64*(75749 + 16236*E^2 - 11316*E^4 + 1036*E^6 - 21*E^8
)*x^3*Log[3 - x])/9375 + (32*(1117 - 5304*E^2 + 861*E^4 - 28*E^6)*x^4*Log[3 - x])/3125 + (768*(337 - 126*E^2 +
7*E^4)*x^5*Log[3 - x])/15625 + (1792*(49 - 6*E^2)*x^6*Log[3 - x])/46875 + (1024*x^7*Log[3 - x])/15625 - (1306
368*Log[3 - x]^2)/625 - (1306368*(9 - E^2)*Log[3 - x]^2)/625 + (4*(25 + 20*E^2 - E^4)^2*(575 - 140*E^2 + 7*E^4
)*Log[3 - x]^2)/625 - (7776*(884 - 287*E^2 + 14*E^4)*Log[3 - x]^2)/125 - (3456*(1353 - 1886*E^2 + 259*E^4 - 7*
E^6)*Log[3 - x]^2)/125 + (83897856*(3 - x)*Log[3 - x]^2)/5 + (72576*(41 - 4*E^2)*(3 - x)*Log[3 - x]^2)/5 - 241
920*(37 - 3*E^2)*(3 - x)*Log[3 - x]^2 + 3024000*(33 - 2*E^2)*(3 - x)*Log[3 - x]^2 - 25200000*(10 - E^2)*(3 - x
)*Log[3 - x]^2 + 72000*(2437 - 406*E^2 + 7*E^4)*(3 - x)*Log[3 - x]^2 - 17280*(1037 - 231*E^2 + 7*E^4)*(3 - x)*
Log[3 - x]^2 + (3456*(1886 - 518*E^2 + 21*E^4)*(3 - x)*Log[3 - x]^2)/5 + (576*(8471 - 6222*E^2 + 693*E^4 - 14*
E^6)*(3 - x)*Log[3 - x]^2)/5 - 960*(16873 - 7311*E^2 + 609*E^4 - 7*E^6)*(3 - x)*Log[3 - x]^2 + (288*(24573 + 1
6942*E^2 - 6222*E^4 + 462*E^6 - 7*E^8)*(3 - x)*Log[3 - x]^2)/125 + (48*(20867 - 67492*E^2 + 14622*E^4 - 812*E^
6 + 7*E^8)*(3 - x)*Log[3 - x]^2)/5 + (48*(701657 + 104335*E^2 - 168730*E^4 + 24370*E^6 - 1015*E^8 + 7*E^10)*(3
- x)*Log[3 - x]^2)/625 + (4857048*(3 - x)^2*Log[3 - x]^2)/5 - (18144*(41 - 4*E^2)*(3 - x)^2*Log[3 - x]^2)/5 +
20160*(37 - 3*E^2)*(3 - x)^2*Log[3 - x]^2 - 63000*(33 - 2*E^2)*(3 - x)^2*Log[3 - x]^2 + 720*(1037 - 231*E^2 +
7*E^4)*(3 - x)^2*Log[3 - x]^2 - (576*(1886 - 518*E^2 + 21*E^4)*(3 - x)^2*Log[3 - x]^2)/5 - (48*(8471 - 6222*E
^2 + 693*E^4 - 14*E^6)*(3 - x)^2*Log[3 - x]^2)/5 - (48*(24573 + 16942*E^2 - 6222*E^4 + 462*E^6 - 7*E^8)*(3 - x
)^2*Log[3 - x]^2)/125 + (603904*(3 - x)^3*Log[3 - x]^2)/45 + (2688*(41 - 4*E^2)*(3 - x)^3*Log[3 - x]^2)/5 - (8
960*(37 - 3*E^2)*(3 - x)^3*Log[3 - x]^2)/9 + (128*(1886 - 518*E^2 + 21*E^4)*(3 - x)^3*Log[3 - x]^2)/15 + (168*
(3 - x)^4*Log[3 - x]^2)/5 - (168*(41 - 4*E^2)*(3 - x)^4*Log[3 - x]^2)/5 + (5376*(3 - x)^5*Log[3 - x]^2)/125 +
(128*(1353 - 1886*E^2 + 259*E^4 - 7*E^6)*x^3*Log[3 - x]^2)/125 + (96*(884 - 287*E^2 + 14*E^4)*x^4*Log[3 - x]^2
)/125 + (5376*(9 - E^2)*x^5*Log[3 - x]^2)/625 + (1792*x^6*Log[3 - x]^2)/625 - (8*(81250 + 21875*E^2 - 32500*E^
4 + 5750*E^6 - 350*E^8 + 7*E^10)*Log[3 - x]^3)/25 - (27965952*(3 - x)*Log[3 - x]^3)/5 - (24192*(41 - 4*E^2)*(3
- x)*Log[3 - x]^3)/5 + 80640*(37 - 3*E^2)*(3 - x)*Log[3 - x]^3 - 1008000*(33 - 2*E^2)*(3 - x)*Log[3 - x]^3 +
8400000*(10 - E^2)*(3 - x)*Log[3 - x]^3 - 24000*(2437 - 406*E^2 + 7*E^4)*(3 - x)*Log[3 - x]^3 + 5760*(1037 - 2
31*E^2 + 7*E^4)*(3 - x)*Log[3 - x]^3 - (1152*(1886 - 518*E^2 + 21*E^4)*(3 - x)*Log[3 - x]^3)/5 - (192*(8471 -
6222*E^2 + 693*E^4 - 14*E^6)*(3 - x)*Log[3 - x]^3)/5 + 320*(16873 - 7311*E^2 + 609*E^4 - 7*E^6)*(3 - x)*Log[3
- x]^3 - (16*(20867 - 67492*E^2 + 14622*E^4 - 812*E^6 + 7*E^8)*(3 - x)*Log[3 - x]^3)/5 - (3238032*(3 - x)^2*Lo
g[3 - x]^3)/5 + (12096*(41 - 4*E^2)*(3 - x)^2*Log[3 - x]^3)/5 - 13440*(37 - 3*E^2)*(3 - x)^2*Log[3 - x]^3 + 42
000*(33 - 2*E^2)*(3 - x)^2*Log[3 - x]^3 - 480*(1037 - 231*E^2 + 7*E^4)*(3 - x)^2*Log[3 - x]^3 + (384*(1886 - 5
18*E^2 + 21*E^4)*(3 - x)^2*Log[3 - x]^3)/5 + (32*(8471 - 6222*E^2 + 693*E^4 - 14*E^6)*(3 - x)^2*Log[3 - x]^3)/
5 - (603904*(3 - x)^3*Log[3 - x]^3)/45 - (2688*(41 - 4*E^2)*(3 - x)^3*Log[3 - x]^3)/5 + (8960*(37 - 3*E^2)*(3
- x)^3*Log[3 - x]^3)/9 - (128*(1886 - 518*E^2 + 21*E^4)*(3 - x)^3*Log[3 - x]^3)/15 - (224*(3 - x)^4*Log[3 - x]
^3)/5 + (224*(41 - 4*E^2)*(3 - x)^4*Log[3 - x]^3)/5 - (1792*(3 - x)^5*Log[3 - x]^3)/25 + 10*(4375 - 13000*E^2
+ 3450*E^4 - 280*E^6 + 7*E^8)*Log[3 - x]^4 + 1391040*(3 - x)*Log[3 - x]^4 - 20160*(37 - 3*E^2)*(3 - x)*Log[3 -
x]^4 + 252000*(33 - 2*E^2)*(3 - x)*Log[3 - x]^4 - 2100000*(10 - E^2)*(3 - x)*Log[3 - x]^4 + 6000*(2437 - 406*
E^2 + 7*E^4)*(3 - x)*Log[3 - x]^4 - 1440*(1037 - 231*E^2 + 7*E^4)*(3 - x)*Log[3 - x]^4 - 80*(16873 - 7311*E^2
+ 609*E^4 - 7*E^6)*(3 - x)*Log[3 - x]^4 + 333480*(3 - x)^2*Log[3 - x]^4 + 6720*(37 - 3*E^2)*(3 - x)^2*Log[3 -
x]^4 - 21000*(33 - 2*E^2)*(3 - x)^2*Log[3 - x]^4 + 240*(1037 - 231*E^2 + 7*E^4)*(3 - x)^2*Log[3 - x]^4 + (1568
0*(3 - x)^3*Log[3 - x]^4)/3 - (2240*(37 - 3*E^2)*(3 - x)^3*Log[3 - x]^4)/3 + 1120*(3 - x)^4*Log[3 - x]^4 + 200
*(3250 - 1725*E^2 + 210*E^4 - 7*E^6)*Log[3 - x]^5 - 302400*(3 - x)*Log[3 - x]^5 - 50400*(33 - 2*E^2)*(3 - x)*L
og[3 - x]^5 + 420000*(10 - E^2)*(3 - x)*Log[3 - x]^5 - 1200*(2437 - 406*E^2 + 7*E^4)*(3 - x)*Log[3 - x]^5 - 10
9200*(3 - x)^2*Log[3 - x]^5 + 8400*(33 - 2*E^2)*(3 - x)^2*Log[3 - x]^5 - 11200*(3 - x)^3*Log[3 - x]^5 + 2500*(
575 - 140*E^2 + 7*E^4)*Log[3 - x]^6 - 70000*(10 - E^2)*(3 - x)*Log[3 - x]^6 + 70000*(3 - x)^2*Log[3 - x]^6 + 1
25000*(10 - E^2)*Log[3 - x]^7 - 250000*(3 - x)*Log[3 - x]^7 + 390625*Log[3 - x]^8
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 30
Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]
Rule 45
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Rule 78
Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))
Rule 147
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_) + (f_.)*(x_))*((g_.) + (h_.)*(x_)), x_Symbol]
:> Int[ExpandIntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)*(g + h*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, h},
x] && (IGtQ[m, 0] || IntegersQ[m, n])
Rule 153
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p*(g + h*x), x], x] /; FreeQ[{a, b, c, d, e, f, g
, h, m}, x] && (IntegersQ[m, n, p] || (IGtQ[n, 0] && IGtQ[p, 0]))
Rule 2332
Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]
Rule 2333
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]
Rule 2338
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]
Rule 2339
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, x]
Rule 2341
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]
Rule 2342
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Lo
g[c*x^n])^p/(d*(m + 1))), x] - Dist[b*n*(p/(m + 1)), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]
Rule 2372
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*(x_)^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = I
ntHide[x^m*(d + e*x^r)^q, x]}, Dist[a + b*Log[c*x^n], u, x] - Dist[b*n, Int[SimplifyIntegrand[u/x, x], x], x]]
/; FreeQ[{a, b, c, d, e, n, r}, x] && IGtQ[q, 0] && IntegerQ[m] && !(EqQ[q, 1] && EqQ[m, -1])
Rule 2388
Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_.))/(x_), x_Symbol] :> Dist[d, Int[(d
+ e*x)^(q - 1)*((a + b*Log[c*x^n])^p/x), x], x] + Dist[e, Int[(d + e*x)^(q - 1)*(a + b*Log[c*x^n])^p, x], x] /
; FreeQ[{a, b, c, d, e, n}, x] && IGtQ[p, 0] && GtQ[q, 0] && IntegerQ[2*q]
Rule 2436
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.), x_Symbol] :> Dist[1/e, Subst[Int[(a + b*Log[c*
x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, n, p}, x]
Rule 2437
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_) + (g_.)*(x_))^(q_.), x_Symbol] :> Dist[1/
e, Subst[Int[(f*(x/d))^q*(a + b*Log[c*x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p, q}, x]
&& EqQ[e*f - d*g, 0]
Rule 2442
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[(f + g*
x)^(q + 1)*((a + b*Log[c*(d + e*x)^n])/(g*(q + 1))), x] - Dist[b*e*(n/(g*(q + 1))), Int[(f + g*x)^(q + 1)/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*f - d*g, 0] && NeQ[q, -1]
Rule 2445
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[(f
+ g*x)^(q + 1)*((a + b*Log[c*(d + e*x)^n])^p/(g*(q + 1))), x] - Dist[b*e*n*(p/(g*(q + 1))), Int[(f + g*x)^(q
+ 1)*((a + b*Log[c*(d + e*x)^n])^(p - 1)/(d + e*x)), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*
f - d*g, 0] && GtQ[p, 0] && NeQ[q, -1] && IntegersQ[2*p, 2*q] && ( !IGtQ[q, 0] || (EqQ[p, 2] && NeQ[q, 1]))
Rule 2448
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Int[Exp
andIntegrand[(f + g*x)^q*(a + b*Log[c*(d + e*x)^n])^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p}, x] && NeQ[
e*f - d*g, 0] && IGtQ[q, 0]
Rule 2458
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + (g_.)*(x_))^(q_.)*((h_.) + (i_.)*(x_))
^(r_.), x_Symbol] :> Dist[1/e, Subst[Int[(g*(x/e))^q*((e*h - d*i)/e + i*(x/e))^r*(a + b*Log[c*x^n])^p, x], x,
d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, h, i, n, p, q, r}, x] && EqQ[e*f - d*g, 0] && (IGtQ[p, 0] || IGtQ[
r, 0]) && IntegerQ[2*r]
Rule 2465
Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[
(a + b*Log[c*(d + e*x)^n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, d, e, n}, x] && RationalFunct
ionQ[RFx, x] && IntegerQ[p]
Rule 6820
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rule 6874
Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]
Rubi steps \begin{align*}
\text {integral}& = \int \frac {8 (19+2 x) \left (4 \left (1-\frac {e^2}{4}\right )+2 x+25 \log (3-x)\right ) \left (109 \left (1-\frac {e^4}{109}\right )-16 x-4 x^2+4 e^2 (2+x)+50 \left (e^2-2 (2+x)\right ) \log (3-x)-625 \log ^2(3-x)\right )^3}{390625 (3-x)} \, dx \\ & = \frac {8 \int \frac {(19+2 x) \left (4 \left (1-\frac {e^2}{4}\right )+2 x+25 \log (3-x)\right ) \left (109 \left (1-\frac {e^4}{109}\right )-16 x-4 x^2+4 e^2 (2+x)+50 \left (e^2-2 (2+x)\right ) \log (3-x)-625 \log ^2(3-x)\right )^3}{3-x} \, dx}{390625} \\ & = \frac {8 \int \left (-\frac {(-2+e) (2+e) \left (-109+e^4\right )^3 (19+2 x)}{-3+x}-\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 ) x (19+2 x)}{-3+x}-\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 ) x^2 (19+2 x)}{-3+x}-\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 ) x^3 (19+2 x)}{-3+x}+\frac {8192 \left (1-\frac {3}{512} \left (1924-45 e^2-20 e^4+e^6\right )\right ) x^4 (19+2 x)}{-3+x}+\frac {6144 \left (1+\frac {1}{64} \left (-77-8 e^2+e^4\right )\right ) x^5 (19+2 x)}{-3+x}+\frac {1536 \left (1-\frac {1}{24} (-2+e) (2+e)\right ) x^6 (19+2 x)}{-3+x}+\frac {128 x^7 (19+2 x)}{-3+x}+\frac {12 (-2+e) e^2 (2+e) \left (-109+e^4\right )^2 (2+x) (19+2 x)}{-3+x}+\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+x) (19+2 x)}{-3+x}+\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+2 x)}{-3+x}-\frac {6144 e^2 \left (1+\frac {1}{32} \left (-77-8 e^2+e^4\right )\right ) x^3 (2+x) (19+2 x)}{-3+x}-\frac {3072 e^2 \left (1-\frac {1}{16} (-2+e) (2+e)\right ) x^4 (2+x) (19+2 x)}{-3+x}-\frac {384 e^2 x^5 (2+x) (19+2 x)}{-3+x}-\frac {48 (-2+e) e^4 (2+e) \left (-109+e^4\right ) (2+x)^2 (19+2 x)}{-3+x}-\frac {768 (-2+e) e^4 (2+e) \left (1-\frac {-109+e^4}{8 \left (-4+e^2\right )}\right ) x (2+x)^2 (19+2 x)}{-3+x}+\frac {1536 e^4 \left (1-\frac {1}{8} (-2+e) (2+e)\right ) x^2 (2+x)^2 (19+2 x)}{-3+x}+\frac {384 e^4 x^3 (2+x)^2 (19+2 x)}{-3+x}+\frac {64 (-2+e) e^6 (2+e) (2+x)^3 (19+2 x)}{-3+x}-\frac {128 e^6 x (2+x)^3 (19+2 x)}{-3+x}+\frac {25 (19+2 x) \left (13+56 e^2-7 e^4-28 \left (4-e^2\right ) x-28 x^2\right ) \left (109+8 e^2-e^4-4 \left (4-e^2\right ) x-4 x^2\right )^2 \log (3-x)}{3-x}+\frac {1875 (19+2 x) \left (-114668 \left (1-\frac {e^2 \left (-4165+10520 e^2-130 e^4-140 e^6+7 e^8\right )}{114668}\right )+8330 \left (1-\frac {1}{833} e^2 \left (4208-78 e^2-112 e^4+7 e^6\right )\right ) x+42080 \left (1+\frac {e^2 \left (-39-84 e^2+7 e^4\right )}{1052}\right ) x^2+1040 \left (1-\frac {7}{13} e^2 \left (-8+e^2\right )\right ) x^3-2240 \left (1-\frac {e^2}{4}\right ) x^4-224 x^5\right ) \log ^2(3-x)}{3-x}+\frac {78125 (19+2 x) \left (833-4208 e^2+78 e^4+112 e^6-7 e^8+8 \left (1052-39 e^2-84 e^4+7 e^6\right ) x+24 \left (13+56 e^2-7 e^4\right ) x^2-224 \left (4-e^2\right ) x^3-112 x^4\right ) \log ^3(3-x)}{3-x}+\frac {1953125 (19+2 x) \left (1052-39 e^2-84 e^4+7 e^6+6 \left (13+56 e^2-7 e^4\right ) x-84 \left (4-e^2\right ) x^2-56 x^3\right ) \log ^4(3-x)}{3-x}+\frac {29296875 (19+2 x) \left (13+56 e^2-7 e^4-28 \left (4-e^2\right ) x-28 x^2\right ) \log ^5(3-x)}{3-x}+\frac {1708984375 (19+2 x) \left (4-e^2+2 x\right ) \log ^6(3-x)}{-3+x}+\frac {6103515625 (19+2 x) \log ^7(3-x)}{-3+x}\right ) \, dx}{390625} \\ & = \text {Too large to display} \\
\end{align*}
Mathematica [B] (verified)
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
\[
\text {integral}=\frac {8 \left (\frac {390625}{8}+\frac {e^{16}}{8}-10360232 x-308906 x^2+917344 x^3-16660 x^4-33664 x^5-416 x^6+512 x^7+32 x^8-2 e^{14} (5+x)+e^{12} \left (\frac {575}{2}+56 x+14 x^2\right )-2 e^{10} \left (1625-39 x+168 x^2+28 x^3\right )+\frac {5}{4} e^8 \left (4375-8416 x-312 x^2+896 x^3+112 x^4\right )+e^6 \left (81250+8330 x+42080 x^2+1040 x^3-2240 x^4-224 x^5\right )+e^4 \left (\frac {359375}{2}+688008 x-24990 x^2-84160 x^3-1560 x^4+2688 x^5+224 x^6\right )-2 e^2 \left (-78125-154453 x+688008 x^2-16660 x^3-42080 x^4-624 x^5+896 x^6+64 x^7\right )-25 \left (e^2-2 (2+x)\right ) \left (-109+e^4+16 x+4 x^2-4 e^2 (2+x)\right )^3 \log (3-x)+\frac {625}{2} \left (-13+7 e^4+112 x+28 x^2-28 e^2 (2+x)\right ) \left (-109+e^4+16 x+4 x^2-4 e^2 (2+x)\right )^2 \log ^2(3-x)-15625 \left (-114668+7 e^{10}+8330 x+42080 x^2+1040 x^3-2240 x^4-224 x^5-70 e^8 (2+x)+10 e^6 \left (-13+112 x+28 x^2\right )-20 e^4 \left (-526-39 x+168 x^2+28 x^3\right )+5 e^2 \left (-833-8416 x-312 x^2+896 x^3+112 x^4\right )\right ) \log ^3(3-x)+\frac {1953125}{4} \left (-833+7 e^8-8416 x-312 x^2+896 x^3+112 x^4-56 e^6 (2+x)+6 e^4 \left (-13+112 x+28 x^2\right )-8 e^2 \left (-526-39 x+168 x^2+28 x^3\right )\right ) \log ^4(3-x)-9765625 \left (1052+7 e^6+78 x-336 x^2-56 x^3-42 e^4 (2+x)+e^2 \left (-39+336 x+84 x^2\right )\right ) \log ^5(3-x)+\frac {244140625}{2} \left (-13+7 e^4+112 x+28 x^2-28 e^2 (2+x)\right ) \log ^6(3-x)-6103515625 \left (e^2-2 (2+x)\right ) \log ^7(3-x)+\frac {152587890625}{8} \log ^8(3-x)\right )}{390625}
\]
[In]
Integrate[(-787377632 + E^14*(-152 - 16*x) - 129835568*x + 204211936*x^2 + 16951616*x^3 - 13325440*x^4 - 15362
56*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 + 26384320*x^3 + 3167360*x^4 - 76723
2*x^5 - 154112*x^6 - 7168*x^7) + (-586921400 + 5167079600*x + 360482400*x^2 - 659608000*x^3 - 79184000*x^4 + 1
9180800*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 - 44
8000*x^4) + E^4*(-47481000 - 484710000*x - 68280000*x^2 + 49200000*x^3 + 11760000*x^4 + 672000*x^5) + E^2*(-26
14430400 - 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 + 24150000*x + 2100000*x^2) + E^6*(37050000 - 315300000*x - 1134
00000*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 - 1230000000*x^3 - 294000000*x^4 - 16800000*x^5))*Log[3 - x]^2
+ (-9891875000 - 100981250000*x - 14225000000*x^2 + 10250000000*x^3 + 2450000000*x^4 + 140000000*x^5 + E^8*(83
125000 + 8750000*x) + E^6*(-1330000000 - 805000000*x - 70000000*x^2) + E^4*(-926250000 + 7882500000*x + 283500
0000*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 - 218750000*x) - 56031250000*x + 97312500000*x^2 + 2712500
0000*x^3 + 1750000000*x^4 + E^4*(24937500000 + 15093750000*x + 1312500000*x^2) + E^2*(11578125000 - 9853125000
0*x - 35437500000*x^2 - 2625000000*x^3))*Log[3 - x]^4 + (-57890625000 + 492656250000*x + 177187500000*x^2 + 13
125000000*x^3 + E^4*(31171875000 + 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 + 97656250000*x)*Log[3 - x]^7)/(-1171875 + 390625*x),x]
[Out]
(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 + 56*x + 14*x^2) - 2*E^10*(1625 - 39*x + 168*x^2 + 28*x^3) + (5*E^8*(4375 -
8416*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
+ 688008*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] + (625*(-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 + 89
6*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))*L
og[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))*Log[3 - x]^7 + (152587890625*Log[3 - x]^8)/8))/390625
Maple [B] (verified)
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 |
\(\text {Expression too large to display}\) |
\(3929\) |
| | |
|
|
|
|
[In]
int(((97656250000*x+927734375000)*ln(-x+3)^7+((-27343750000*x-259765625000)*exp(2)+54687500000*x^2+62890625000
0*x+1039062500000)*ln(-x+3)^6+((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-2493750000
00)*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+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-98531250000*x+11
578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-56031250000*x-312312500000)*ln(-x+3)^4+((8750
000*x+83125000)*exp(2)^4+(-70000000*x^2-805000000*x-1330000000)*exp(2)^3+(210000000*x^3+2835000000*x^2+7882500
000*x-926250000)*exp(2)^2+(-280000000*x^4-4340000000*x^3-15570000000*x^2+8965000000*x+49970000000)*exp(2)+1400
00000*x^5+2450000000*x^4+10250000000*x^3-14225000000*x^2-100981250000*x-9891875000)*ln(-x+3)^3+((-210000*x-199
5000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3-113400000*x^2-315300000*x+37050000)*ex
p(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^4-155880
0000*x^3-12242700000*x^2+1065990000*x+32680380000)*ln(-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+143440
00*x+79952000)*exp(2)^3+(672000*x^5+11760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*exp(2)^2+(-53
7600*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-2614430400)*exp(2)+179200*x^7+385280
0*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+(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^5-156800*x^4-656000*x^3+910400*x^2+6462800*x+633080)*exp(2)^3+(10752*x^6+20
9664*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+316
7360*x^4+26384320*x^3-14419296*x^2-206683184*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-1536256*x^5-1332
5440*x^4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x,method=_RETURNVERBOSE)
[Out]
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)-1346
56/78125*x^3*exp(4)-39984/78125*x^2*exp(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)-448/390625*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*exp(4)-624/78125*x^2*exp(8)-61781
2/390625*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+2471248/390625*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)+10752/12
5*x^3*exp(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*exp(8)-9996/125*exp(4)-2752032/625*exp(2)+1792/625*x^6+21504/625*x^5-2496/125*x^4-134656/125*x^3-3998
4/125*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)-6178
12/625)*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+(-2471248/15625*x-2688/15625*x*exp(10)-3584/15625*x^6*exp(2)-4992/312
5*x^3*exp(4)-201984/3125*x^2*exp(4)+67328/3125*x*exp(6)+269312/3125*x^3*exp(2)+79968/3125*x^2*exp(2)+4992/3125
*x^4*exp(2)-672/15625*x^2*exp(10)+10752/3125*x^4*exp(4)+5376/15625*x^5*exp(4)-39984/3125*x*exp(4)+2688/3125*x^
2*exp(8)+1024/15625*x^7+14336/15625*x^6-9984/15625*x^5-134656/3125*x^4-53312/3125*x^3+11008128/15625*x^2-43008
/15625*exp(2)*x^5-11008128/15625*exp(2)*x-7168/3125*x^3*exp(6)+2496/3125*x^2*exp(6)-624/3125*x*exp(8)+448/3125
*x^3*exp(8)-896/3125*exp(6)*x^4+112/15625*x*exp(12))*ln(-x+3)+224/78125*x^4*exp(8)+1792/78125*x^3*exp(8)+6664/
3125*ln(-3+x)*exp(6)+1235624/15625*ln(-3+x)*exp(2)+(250000*x-125000*exp(2)+500000)*ln(-x+3)^7-3584/78125*exp(6
)*x^4+141158161/390625-8/15625*ln(-3+x)*exp(14)+312/15625*ln(-3+x)*exp(10)+2752032/15625*exp(4)*ln(-3+x)-1024/
390625*exp(2)*x^7+448/390625*x*exp(12)-8416/3125*ln(-3+x)*exp(8)-1792/390625*exp(6)*x^5+(112/5*x*exp(8)-448/5*
x^2*exp(6)+896/5*x^3*exp(4)-896/5*x^4*exp(2)+1792/25*x^5-1792/5*x*exp(6)+5376/5*x^2*exp(4)-7168/5*x^3*exp(2)+3
584/5*x^4-1248/5*x*exp(4)+2496/5*x^2*exp(2)-1664/5*x^3+67328/5*exp(2)*x-67328/5*x^2-13328/5*x+917344/25-56/25*
exp(10)+224/5*exp(8)+208/5*exp(6)-16832/5*exp(4)+6664/5*exp(2))*ln(-x+3)^3+224/15625*ln(-3+x)*exp(12)+(17500*e
xp(4)-70000*exp(2)*x+70000*x^2-140000*exp(2)+280000*x-32500)*ln(-x+3)^6+(70*exp(8)-560*x*exp(6)+1680*x^2*exp(4
)-2240*x^3*exp(2)+1120*x^4-1120*exp(6)+6720*x*exp(4)-13440*x^2*exp(2)+8960*x^3-780*exp(4)+3120*exp(2)*x-3120*x
^2+42080*exp(2)-84160*x-8330)*ln(-x+3)^4
Fricas [B] (verification not implemented)
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
\[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx=\text {Too large to display}
\]
[In]
integrate(((97656250000*x+927734375000)*log(-x+3)^7+((-27343750000*x-259765625000)*exp(2)+54687500000*x^2+6289
06250000*x+1039062500000)*log(-x+3)^6+((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-24
9375000000)*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-57890625000)*log(-x+3)^5+((-218750000*x-207
8125000)*exp(2)^3+(1312500000*x^2+15093750000*x+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-9853125
0000*x+11578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-56031250000*x-312312500000)*log(-x+3
)^4+((8750000*x+83125000)*exp(2)^4+(-70000000*x^2-805000000*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+8965000000*x+49970000000)*e
xp(2)+140000000*x^5+2450000000*x^4+10250000000*x^3-14225000000*x^2-100981250000*x-9891875000)*log(-x+3)^3+((-2
10000*x-1995000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3-113400000*x^2-315300000*x+3
7050000)*exp(2)^3+(16800000*x^4+260400000*x^3+934200000*x^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-29
4000000*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-638400)*exp(2)^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000*x^4-6944000*x^3-2491200
0*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*e
xp(2)^2+(-537600*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-2614430400)*exp(2)+17920
0*x^7+3852800*x^6+19180800*x^5-79184000*x^4-659608000*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^5-156800*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^6-7
67232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-206683184*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-153
6256*x^5-13325440*x^4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x, algorithm="frica
s")
[Out]
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 - 269312/390625*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 - 1040*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 - 3
9*x - 526)*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 - 2104
0*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 + 112/390625*(x^2 + 4*x)*e^12 - 16/390625*(28*x^3 + 168*x^2 - 39*x)*e^10 + 16/78125*(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 + 1
344*x^5 - 780*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 + 8/15625*(128*x^7 + 1792*x^6 - 1248*x^5 - 84160*x^4 - 33320*x^3 + 13
76016*x^2 + 14*(x + 2)*e^12 - 3*(28*x^2 + 112*x - 13)*e^10 + 10*(28*x^3 + 168*x^2 - 39*x - 526)*e^8 - 5*(112*x
^4 + 896*x^3 - 312*x^2 - 8416*x - 833)*e^6 + 6*(112*x^5 + 1120*x^4 - 520*x^3 - 21040*x^2 - 4165*x + 57334)*e^4
- (448*x^6 + 5376*x^5 - 3120*x^4 - 168320*x^3 - 49980*x^2 + 1376016*x - 154453)*e^2 - 308906*x - e^14 - 51801
16)*log(-x + 3) - 82881856/390625*x
Sympy [B] (verification not implemented)
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
\[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx=\text {Too large to display}
\]
[In]
integrate(((97656250000*x+927734375000)*ln(-x+3)**7+((-27343750000*x-259765625000)*exp(2)+54687500000*x**2+628
906250000*x+1039062500000)*ln(-x+3)**6+((3281250000*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+24937500000)*exp(2)**2+(-2625000000*x**3-35437500000*x*
*2-98531250000*x+11578125000)*exp(2)+1750000000*x**4+27125000000*x**3+97312500000*x**2-56031250000*x-312312500
000)*ln(-x+3)**4+((8750000*x+83125000)*exp(2)**4+(-70000000*x**2-805000000*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+89650
00000*x+49970000000)*exp(2)+140000000*x**5+2450000000*x**4+10250000000*x**3-14225000000*x**2-100981250000*x-98
91875000)*ln(-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-299
8200000)*exp(2)**2+(-16800000*x**5-294000000*x**4-1230000000*x**3+1707000000*x**2+12117750000*x+1187025000)*ex
p(2)+6720000*x**6+131040000*x**5+607200000*x**4-1558800000*x**3-12242700000*x**2+1065990000*x+32680380000)*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+117600
00*x**4+49200000*x**3-68280000*x**2-484710000*x-47481000)*exp(2)**2+(-537600*x**6-10483200*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+(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)*e
xp(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+9
71520*x**4-2494080*x**3-19588320*x**2+1705584*x+52288608)*exp(2)**2+(-7168*x**7-154112*x**6-767232*x**5+316736
0*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)
[Out]
256*x**8/390625 + x**7*(4096/390625 - 1024*exp(2)/390625) + x**6*(-14336*exp(2)/390625 - 3328/390625 + 1792*ex
p(4)/390625) + x**5*(-1792*exp(6)/390625 - 269312/390625 + 9984*exp(2)/390625 + 21504*exp(4)/390625) + x**4*(-
3584*exp(6)/78125 - 2496*exp(4)/78125 - 26656/78125 + 224*exp(8)/78125 + 134656*exp(2)/78125) + x**3*(-134656*
exp(4)/78125 - 448*exp(10)/390625 + 53312*exp(2)/78125 + 1664*exp(6)/78125 + 7338752/390625 + 1792*exp(8)/7812
5) + x**2*(-11008128*exp(2)/390625 - 2688*exp(10)/390625 - 39984*exp(4)/78125 - 624*exp(8)/78125 - 2471248/390
625 + 112*exp(12)/390625 + 67328*exp(6)/78125) + 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
) - 32500 + 17500*exp(4))*log(3 - x)**6 + (11200*x**3 - 16800*x**2*exp(2) + 67200*x**2 - 67200*x*exp(2) - 1560
0*x + 8400*x*exp(4) - 1400*exp(6) - 210400 + 7800*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*exp(4)/5 - 1792*x*exp(6)/5 - 1248*x*exp(4)/5 - 13328*x/5 + 112
*x*exp(8)/5 + 67328*x*exp(2)/5 - 16832*exp(4)/5 - 56*exp(10)/25 + 6664*exp(2)/5 + 208*exp(6)/5 + 917344/25 + 2
24*exp(8)/5)*log(3 - x)**3 + (1792*x**6/625 - 5376*x**5*exp(2)/625 + 21504*x**5/625 - 10752*x**4*exp(2)/125 -
2496*x**4/125 + 1344*x**4*exp(4)/125 - 896*x**3*exp(6)/125 - 134656*x**3/125 + 4992*x**3*exp(2)/125 + 10752*x*
*3*exp(4)/125 - 5376*x**2*exp(6)/125 - 3744*x**2*exp(4)/125 - 39984*x**2/125 + 336*x**2*exp(8)/125 + 201984*x*
*2*exp(2)/125 - 100992*x*exp(4)/125 - 336*x*exp(10)/625 + 39984*x*exp(2)/125 + 1248*x*exp(6)/125 + 5504064*x/6
25 + 1344*x*exp(8)/125 - 2752032*exp(2)/625 - 672*exp(10)/625 - 9996*exp(4)/125 - 156*exp(8)/125 - 617812/625
+ 28*exp(12)/625 + 16832*exp(6)/125)*log(3 - x)**2 + (1024*x**7/15625 - 3584*x**6*exp(2)/15625 + 14336*x**6/15
625 - 43008*x**5*exp(2)/15625 - 9984*x**5/15625 + 5376*x**5*exp(4)/15625 - 896*x**4*exp(6)/3125 - 134656*x**4/
3125 + 4992*x**4*exp(2)/3125 + 10752*x**4*exp(4)/3125 - 7168*x**3*exp(6)/3125 - 4992*x**3*exp(4)/3125 - 53312*
x**3/3125 + 448*x**3*exp(8)/3125 + 269312*x**3*exp(2)/3125 - 201984*x**2*exp(4)/3125 - 672*x**2*exp(10)/15625
+ 79968*x**2*exp(2)/3125 + 2496*x**2*exp(6)/3125 + 11008128*x**2/15625 + 2688*x**2*exp(8)/3125 - 11008128*x*ex
p(2)/15625 - 2688*x*exp(10)/15625 - 39984*x*exp(4)/3125 - 624*x*exp(8)/3125 - 2471248*x/15625 + 112*x*exp(12)/
15625 + 67328*x*exp(6)/3125)*log(3 - x) + 390625*log(3 - x)**8 - 8*(-2 + E)*(2 + E)*(-109 - 8*exp(2) + exp(4))
**3*log(x - 3)/15625
Maxima [B] (verification not implemented)
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
\[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx=\text {Too large to display}
\]
[In]
integrate(((97656250000*x+927734375000)*log(-x+3)^7+((-27343750000*x-259765625000)*exp(2)+54687500000*x^2+6289
06250000*x+1039062500000)*log(-x+3)^6+((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-24
9375000000)*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-57890625000)*log(-x+3)^5+((-218750000*x-207
8125000)*exp(2)^3+(1312500000*x^2+15093750000*x+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-9853125
0000*x+11578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-56031250000*x-312312500000)*log(-x+3
)^4+((8750000*x+83125000)*exp(2)^4+(-70000000*x^2-805000000*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+8965000000*x+49970000000)*e
xp(2)+140000000*x^5+2450000000*x^4+10250000000*x^3-14225000000*x^2-100981250000*x-9891875000)*log(-x+3)^3+((-2
10000*x-1995000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3-113400000*x^2-315300000*x+3
7050000)*exp(2)^3+(16800000*x^4+260400000*x^3+934200000*x^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-29
4000000*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-638400)*exp(2)^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000*x^4-6944000*x^3-2491200
0*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*e
xp(2)^2+(-537600*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-2614430400)*exp(2)+17920
0*x^7+3852800*x^6+19180800*x^5-79184000*x^4-659608000*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^5-156800*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^6-7
67232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-206683184*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-153
6256*x^5-13325440*x^4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x, algorithm="maxim
a")
[Out]
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 + 13300*e^4*log(-x + 3)^6 - 106400*e^2*log(-x + 3)^6 + 1250000*log(-x + 3)^7 +
1792/3125*(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 - 589952/3515625*x^6 - 1064*e^6*log(-x + 3)^5 + 12768*e^4*log(-x + 3)^5 + 59
28*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*log(-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*l
og(-x + 3)^4 - 2964/5*e^4*log(-x + 3)^4 + 159904/5*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 + 123
200/81*(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*log(-x + 3)^3 + 4256/125*e^8*log(-x + 3)^3 + 3952/125*e^6*log(-x
+ 3)^3 - 319808/125*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 - 60*log(-x + 3)^3 + 90*log(-x + 3)^2 - 90*log(-x + 3) + 45)*(x -
3)^2 + 94500*(4*log(-x + 3)^5 - 10*log(-x + 3)^4 + 20*log(-x + 3)^3 - 30*log(-x + 3)^2 + 30*log(-x + 3) - 15)
*(x - 3)^2 + 279000*(2*log(-x + 3)^4 - 4*log(-x + 3)^3 + 6*log(-x + 3)^2 - 6*log(-x + 3) + 3)*(x - 3)^2 + 7940
0*(4*log(-x + 3)^3 - 6*log(-x + 3)^2 + 6*log(-x + 3) - 3)*(x - 3)^2 + 32040*(2*log(-x + 3)^2 - 2*log(-x + 3) +
1)*(x - 3)^2 + 248668768/3515625*x^3 + 112/15625*(x + 3*log(x - 3))*e^12*log(-x + 3) - 672/15625*(x^2 + 6*x +
18*log(x - 3))*e^10*log(-x + 3) - 15456/15625*(x + 3*log(x - 3))*e^10*log(-x + 3) + 224/3125*(2*x^3 + 9*x^2 +
54*x + 162*log(x - 3))*e^8*log(-x + 3) + 9072/3125*(x^2 + 6*x + 18*log(x - 3))*e^8*log(-x + 3) + 50448/3125*(
x + 3*log(x - 3))*e^8*log(-x + 3) - 896/3125*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^6*log(-x + 3) -
27776/9375*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^6*log(-x + 3) - 99648/3125*(x^2 + 6*x + 18*log(x - 3))*e
^6*log(-x + 3) + 114752/3125*(x + 3*log(x - 3))*e^6*log(-x + 3) + 1344/15625*(4*x^5 + 15*x^4 + 60*x^3 + 270*x^
2 + 1620*x + 4860*log(x - 3))*e^4*log(-x + 3) + 4704/625*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^4*l
og(-x + 3) + 2624/125*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^4*log(-x + 3) - 54624/625*(x^2 + 6*x + 18*log(
x - 3))*e^4*log(-x + 3) - 775536/625*(x + 3*log(x - 3))*e^4*log(-x + 3) - 1792/78125*(10*x^6 + 36*x^5 + 135*x^
4 + 540*x^3 + 2430*x^2 + 14580*x + 43740*log(x - 3))*e^2*log(-x + 3) - 104832/78125*(4*x^5 + 15*x^4 + 60*x^3 +
270*x^2 + 1620*x + 4860*log(x - 3))*e^2*log(-x + 3) - 97152/3125*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x -
3))*e^2*log(-x + 3) + 166272/3125*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^2*log(-x + 3) + 3917664/3125*(x^2
+ 6*x + 18*log(x - 3))*e^2*log(-x + 3) - 3411168/15625*(x + 3*log(x - 3))*e^2*log(-x + 3) + 1064/15625*e^12*lo
g(x - 3)*log(-x + 3) - 25536/15625*e^10*log(x - 3)*log(-x + 3) - 5928/3125*e^8*log(x - 3)*log(-x + 3) + 639616
/3125*e^6*log(x - 3)*log(-x + 3) - 379848/3125*e^4*log(x - 3)*log(-x + 3) - 104577216/15625*e^2*log(x - 3)*log
(-x + 3) - 26000*log(-x + 3)^3 + 250000*(log(-x + 3)^7 - 7*log(-x + 3)^6 + 42*log(-x + 3)^5 - 210*log(-x + 3)^
4 + 840*log(-x + 3)^3 - 2520*log(-x + 3)^2 + 5040*log(-x + 3) - 5040)*(x - 3) + 2450000*(log(-x + 3)^6 - 6*log
(-x + 3)^5 + 30*log(-x + 3)^4 - 120*log(-x + 3)^3 + 360*log(-x + 3)^2 - 720*log(-x + 3) + 720)*(x - 3) + 48900
00*(log(-x + 3)^5 - 5*log(-x + 3)^4 + 20*log(-x + 3)^3 - 60*log(-x + 3)^2 + 120*log(-x + 3) - 120)*(x - 3) + 3
710000*(log(-x + 3)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3) + 1054000*(log(-x +
3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3) + 35760*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3) + 5908
13752/390625*x^2 - 16/390625*(x + 3*log(x - 3))*e^14 + 112/390625*(x^2 + 6*x + 18*log(x - 3))*e^12 - 56/15625*
(3*log(x - 3)^2 + 2*x + 6*log(x - 3))*e^12 - 532/15625*(2*log(x - 3)*log(-x + 3) - log(-x + 3)^2)*e^12 + 2576/
390625*(x + 3*log(x - 3))*e^12 - 224/390625*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^10 - 336/625*(log(-x + 3
)^3 + (log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^10 + 336/15625*(x^2 + 18*log(x - 3)^2 + 18*x + 54*log(x -
3))*e^10 - 9072/390625*(x^2 + 6*x + 18*log(x - 3))*e^10 + 7728/15625*(3*log(x - 3)^2 + 2*x + 6*log(x - 3))*e^
10 + 12768/15625*(2*log(x - 3)*log(-x + 3) - log(-x + 3)^2)*e^10 - 50448/390625*(x + 3*log(x - 3))*e^10 + 224/
78125*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^8 + 28/5*(3*log(-x + 3)^4 + 4*(log(-x + 3)^3 - 3*log(-
x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^8 + 168/125*((2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 12*log
(-x + 3)^3 + 24*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^8 - 112/9375*(4*x^3 + 45*x^2 + 486*log(x - 3)^2
+ 594*x + 1782*log(x - 3))*e^8 + 6944/234375*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^8 + 7728/125*(log(-x +
3)^3 + (log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^8 - 4536/3125*(x^2 + 18*log(x - 3)^2 + 18*x + 54*log(x
- 3))*e^8 + 24912/78125*(x^2 + 6*x + 18*log(x - 3))*e^8 - 25224/3125*(3*log(x - 3)^2 + 2*x + 6*log(x - 3))*e^8
+ 2964/3125*(2*log(x - 3)*log(-x + 3) - log(-x + 3)^2)*e^8 - 28688/78125*(x + 3*log(x - 3))*e^8 - 448/390625*
(4*x^5 + 15*x^4 + 60*x^3 + 270*x^2 + 1620*x + 4860*log(x - 3))*e^6 - 112*(3*log(-x + 3)^5 + 5*(log(-x + 3)^4 -
4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3))*e^6 - 224/1125*(4*(9*log(-x + 3)^2 - 6*log
(-x + 3) + 2)*(x - 3)^3 + 243*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 972*log(-x + 3)^3 + 2916*(log(
-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^6 + 224/9375*(3*x^4 + 28*x^3 + 234*x^2 + 1944*log(x - 3)^2 + 2700*x
+ 8100*log(x - 3))*e^6 - 1568/15625*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*e^6 - 112/5*(18*log(-x + 3
)^4 + (4*log(-x + 3)^3 - 6*log(-x + 3)^2 + 6*log(-x + 3) - 3)*(x - 3)^2 + 48*(log(-x + 3)^3 - 3*log(-x + 3)^2
+ 6*log(-x + 3) - 6)*(x - 3))*e^6 - 2576/5*(3*log(-x + 3)^4 + 4*(log(-x + 3)^3 - 3*log(-x + 3)^2 + 6*log(-x +
3) - 6)*(x - 3))*e^6 - 9072/125*((2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 12*log(-x + 3)^3 + 24*(log(
-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^6 + 13888/28125*(4*x^3 + 45*x^2 + 486*log(x - 3)^2 + 594*x + 1782*lo
g(x - 3))*e^6 - 2624/9375*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^6 - 100896/125*(log(-x + 3)^3 + (log(-x +
3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^6 + 49824/3125*(x^2 + 18*log(x - 3)^2 + 18*x + 54*log(x - 3))*e^6 + 18208
/15625*(x^2 + 6*x + 18*log(x - 3))*e^6 - 57376/3125*(3*log(x - 3)^2 + 2*x + 6*log(x - 3))*e^6 - 319808/3125*(2
*log(x - 3)*log(-x + 3) - log(-x + 3)^2)*e^6 + 258512/15625*(x + 3*log(x - 3))*e^6 + 896/1953125*(10*x^6 + 36*
x^5 + 135*x^4 + 540*x^3 + 2430*x^2 + 14580*x + 43740*log(x - 3))*e^4 + 4200*(log(-x + 3)^6 + 2*(log(-x + 3)^5
- 5*log(-x + 3)^4 + 20*log(-x + 3)^3 - 60*log(-x + 3)^2 + 120*log(-x + 3) - 120)*(x - 3))*e^4 + 56/375*(9*(8*l
og(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4 + 128*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 + 3888*(2*lo
g(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 7776*log(-x + 3)^3 + 31104*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x
- 3))*e^4 - 336/78125*(16*x^5 + 135*x^4 + 940*x^3 + 6930*x^2 + 48600*log(x - 3)^2 + 73980*x + 221940*log(x -
3))*e^4 + 52416/1953125*(4*x^5 + 15*x^4 + 60*x^3 + 270*x^2 + 1620*x + 4860*log(x - 3))*e^4 + 168*(36*log(-x +
3)^5 + 5*(2*log(-x + 3)^4 - 4*log(-x + 3)^3 + 6*log(-x + 3)^2 - 6*log(-x + 3) + 3)*(x - 3)^2 + 120*(log(-x + 3
)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3))*e^4 + 7728*(3*log(-x + 3)^5 + 5*(log(
-x + 3)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3))*e^4 + 112/45*(8*(9*log(-x + 3)^
3 - 9*log(-x + 3)^2 + 6*log(-x + 3) - 2)*(x - 3)^3 + 1458*log(-x + 3)^4 + 243*(4*log(-x + 3)^3 - 6*log(-x + 3)
^2 + 6*log(-x + 3) - 3)*(x - 3)^2 + 5832*(log(-x + 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^4 +
6944/1125*(4*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 + 243*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x -
3)^2 + 972*log(-x + 3)^3 + 2916*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^4 - 392/625*(3*x^4 + 28*x^3 + 2
34*x^2 + 1944*log(x - 3)^2 + 2700*x + 8100*log(x - 3))*e^4 + 48576/78125*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*l
og(x - 3))*e^4 + 4536/5*(18*log(-x + 3)^4 + (4*log(-x + 3)^3 - 6*log(-x + 3)^2 + 6*log(-x + 3) - 3)*(x - 3)^2
+ 48*(log(-x + 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^4 + 25224/5*(3*log(-x + 3)^4 + 4*(log(-x
+ 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^4 + 74736/125*((2*log(-x + 3)^2 - 2*log(-x + 3) + 1)
*(x - 3)^2 + 12*log(-x + 3)^3 + 24*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^4 - 1312/375*(4*x^3 + 45*x^2
+ 486*log(x - 3)^2 + 594*x + 1782*log(x - 3))*e^4 - 83136/78125*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e^4 -
172128/125*(log(-x + 3)^3 + (log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^4 + 27312/625*(x^2 + 18*log(x - 3)
^2 + 18*x + 54*log(x - 3))*e^4 - 1958832/78125*(x^2 + 6*x + 18*log(x - 3))*e^4 + 387768/625*(3*log(x - 3)^2 +
2*x + 6*log(x - 3))*e^4 + 189924/3125*(2*log(x - 3)*log(-x + 3) - log(-x + 3)^2)*e^4 + 1705584/390625*(x + 3*l
og(x - 3))*e^4 - 256/1953125*(20*x^7 + 70*x^6 + 252*x^5 + 945*x^4 + 3780*x^3 + 17010*x^2 + 102060*x + 306180*l
og(x - 3))*e^2 - 10000*(3*log(-x + 3)^7 + 7*(log(-x + 3)^6 - 6*log(-x + 3)^5 + 30*log(-x + 3)^4 - 120*log(-x +
3)^3 + 360*log(-x + 3)^2 - 720*log(-x + 3) + 720)*(x - 3))*e^2 - 56/15625*(96*(25*log(-x + 3)^2 - 10*log(-x +
3) + 2)*(x - 3)^5 + 5625*(8*log(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4 + 40000*(9*log(-x + 3)^2 - 6*log(-x
+ 3) + 2)*(x - 3)^3 + 810000*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 972000*log(-x + 3)^3 + 4860000*
(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^2 + 448/1171875*(100*x^6 + 792*x^5 + 4995*x^4 + 30780*x^3 + 211
410*x^2 + 1312200*log(x - 3)^2 + 2143260*x + 6429780*log(x - 3))*e^2 - 38528/5859375*(10*x^6 + 36*x^5 + 135*x^
4 + 540*x^3 + 2430*x^2 + 14580*x + 43740*log(x - 3))*e^2 - 4200*(12*log(-x + 3)^6 + (4*log(-x + 3)^5 - 10*log(
-x + 3)^4 + 20*log(-x + 3)^3 - 30*log(-x + 3)^2 + 30*log(-x + 3) - 15)*(x - 3)^2 + 48*(log(-x + 3)^5 - 5*log(-
x + 3)^4 + 20*log(-x + 3)^3 - 60*log(-x + 3)^2 + 120*log(-x + 3) - 120)*(x - 3))*e^2 - 193200*(log(-x + 3)^6 +
2*(log(-x + 3)^5 - 5*log(-x + 3)^4 + 20*log(-x + 3)^3 - 60*log(-x + 3)^2 + 120*log(-x + 3) - 120)*(x - 3))*e^
2 - 28/45*(9*(32*log(-x + 3)^3 - 24*log(-x + 3)^2 + 12*log(-x + 3) - 3)*(x - 3)^4 + 512*(9*log(-x + 3)^3 - 9*l
og(-x + 3)^2 + 6*log(-x + 3) - 2)*(x - 3)^3 + 23328*log(-x + 3)^4 + 7776*(4*log(-x + 3)^3 - 6*log(-x + 3)^2 +
6*log(-x + 3) - 3)*(x - 3)^2 + 124416*(log(-x + 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^2 - 196
/75*(9*(8*log(-x + 3)^2 - 4*log(-x + 3) + 1)*(x - 3)^4 + 128*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 +
3888*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2 + 7776*log(-x + 3)^3 + 31104*(log(-x + 3)^2 - 2*log(-x +
3) + 2)*(x - 3))*e^2 + 26208/390625*(16*x^5 + 135*x^4 + 940*x^3 + 6930*x^2 + 48600*log(x - 3)^2 + 73980*x + 2
21940*log(x - 3))*e^2 - 191808/1953125*(4*x^5 + 15*x^4 + 60*x^3 + 270*x^2 + 1620*x + 4860*log(x - 3))*e^2 - 11
2/27*(8748*log(-x + 3)^5 + 20*(27*log(-x + 3)^4 - 36*log(-x + 3)^3 + 36*log(-x + 3)^2 - 24*log(-x + 3) + 8)*(x
- 3)^3 + 3645*(2*log(-x + 3)^4 - 4*log(-x + 3)^3 + 6*log(-x + 3)^2 - 6*log(-x + 3) + 3)*(x - 3)^2 + 43740*(lo
g(-x + 3)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3))*e^2 - 4536*(36*log(-x + 3)^5
+ 5*(2*log(-x + 3)^4 - 4*log(-x + 3)^3 + 6*log(-x + 3)^2 - 6*log(-x + 3) + 3)*(x - 3)^2 + 120*(log(-x + 3)^4 -
4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3))*e^2 - 50448*(3*log(-x + 3)^5 + 5*(log(-x +
3)^4 - 4*log(-x + 3)^3 + 12*log(-x + 3)^2 - 24*log(-x + 3) + 24)*(x - 3))*e^2 - 6944/135*(8*(9*log(-x + 3)^3
- 9*log(-x + 3)^2 + 6*log(-x + 3) - 2)*(x - 3)^3 + 1458*log(-x + 3)^4 + 243*(4*log(-x + 3)^3 - 6*log(-x + 3)^2
+ 6*log(-x + 3) - 3)*(x - 3)^2 + 5832*(log(-x + 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^2 - 13
12/45*(4*(9*log(-x + 3)^2 - 6*log(-x + 3) + 2)*(x - 3)^3 + 243*(2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*(x - 3)^2
+ 972*log(-x + 3)^3 + 2916*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^2 + 8096/3125*(3*x^4 + 28*x^3 + 234
*x^2 + 1944*log(x - 3)^2 + 2700*x + 8100*log(x - 3))*e^2 + 158368/78125*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*lo
g(x - 3))*e^2 - 24912/5*(18*log(-x + 3)^4 + (4*log(-x + 3)^3 - 6*log(-x + 3)^2 + 6*log(-x + 3) - 3)*(x - 3)^2
+ 48*(log(-x + 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^2 + 28688/5*(3*log(-x + 3)^4 + 4*(log(-x
+ 3)^3 - 3*log(-x + 3)^2 + 6*log(-x + 3) - 6)*(x - 3))*e^2 + 27312/25*((2*log(-x + 3)^2 - 2*log(-x + 3) + 1)*
(x - 3)^2 + 12*log(-x + 3)^3 + 24*(log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^2 - 27712/3125*(4*x^3 + 45*x^
2 + 486*log(x - 3)^2 + 594*x + 1782*log(x - 3))*e^2 + 2638432/234375*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*e
^2 + 775536/25*(log(-x + 3)^3 + (log(-x + 3)^2 - 2*log(-x + 3) + 2)*(x - 3))*e^2 - 1958832/3125*(x^2 + 18*log(
x - 3)^2 + 18*x + 54*log(x - 3))*e^2 - 7209648/390625*(x^2 + 6*x + 18*log(x - 3))*e^2 + 1705584/15625*(3*log(x
- 3)^2 + 2*x + 6*log(x - 3))*e^2 + 52288608/15625*(2*log(x - 3)*log(-x + 3) - log(-x + 3)^2)*e^2 - 206683184/
390625*(x + 3*log(x - 3))*e^2 - 152/390625*e^14*log(x - 3) + 4256/390625*e^12*log(x - 3) + 5928/390625*e^10*lo
g(x - 3) - 159904/78125*e^8*log(x - 3) + 126616/78125*e^6*log(x - 3) + 52288608/390625*e^4*log(x - 3) + 234768
56/390625*e^2*log(x - 3) - 47675928/15625*log(x - 3)^2 + 256/78125*(20*x^7 + 70*x^6 + 252*x^5 + 945*x^4 + 3780
*x^3 + 17010*x^2 + 102060*x + 306180*log(x - 3))*log(-x + 3) + 38528/234375*(10*x^6 + 36*x^5 + 135*x^4 + 540*x
^3 + 2430*x^2 + 14580*x + 43740*log(x - 3))*log(-x + 3) + 191808/78125*(4*x^5 + 15*x^4 + 60*x^3 + 270*x^2 + 16
20*x + 4860*log(x - 3))*log(-x + 3) - 158368/3125*(x^4 + 4*x^3 + 18*x^2 + 108*x + 324*log(x - 3))*log(-x + 3)
- 2638432/9375*(2*x^3 + 9*x^2 + 54*x + 162*log(x - 3))*log(-x + 3) + 7209648/15625*(x^2 + 6*x + 18*log(x - 3))
*log(-x + 3) + 206683184/15625*(x + 3*log(x - 3))*log(-x + 3) - 11738428/15625*log(-x + 3)^2 + 2620448144/3906
25*x + 282958672/15625*log(x - 3)
Giac [B] (verification not implemented)
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
\[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx=\text {Too large to display}
\]
[In]
integrate(((97656250000*x+927734375000)*log(-x+3)^7+((-27343750000*x-259765625000)*exp(2)+54687500000*x^2+6289
06250000*x+1039062500000)*log(-x+3)^6+((3281250000*x+31171875000)*exp(2)^2+(-13125000000*x^2-150937500000*x-24
9375000000)*exp(2)+13125000000*x^3+177187500000*x^2+492656250000*x-57890625000)*log(-x+3)^5+((-218750000*x-207
8125000)*exp(2)^3+(1312500000*x^2+15093750000*x+24937500000)*exp(2)^2+(-2625000000*x^3-35437500000*x^2-9853125
0000*x+11578125000)*exp(2)+1750000000*x^4+27125000000*x^3+97312500000*x^2-56031250000*x-312312500000)*log(-x+3
)^4+((8750000*x+83125000)*exp(2)^4+(-70000000*x^2-805000000*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+8965000000*x+49970000000)*e
xp(2)+140000000*x^5+2450000000*x^4+10250000000*x^3-14225000000*x^2-100981250000*x-9891875000)*log(-x+3)^3+((-2
10000*x-1995000)*exp(2)^5+(2100000*x^2+24150000*x+39900000)*exp(2)^4+(-8400000*x^3-113400000*x^2-315300000*x+3
7050000)*exp(2)^3+(16800000*x^4+260400000*x^3+934200000*x^2-537900000*x-2998200000)*exp(2)^2+(-16800000*x^5-29
4000000*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-638400)*exp(2)^5+(168000*x^3+2268000*x^2+6306000*x-741000)*exp(2)^4+(-448000*x^4-6944000*x^3-2491200
0*x^2+14344000*x+79952000)*exp(2)^3+(672000*x^5+11760000*x^4+49200000*x^3-68280000*x^2-484710000*x-47481000)*e
xp(2)^2+(-537600*x^6-10483200*x^5-48576000*x^4+124704000*x^3+979416000*x^2-85279200*x-2614430400)*exp(2)+17920
0*x^7+3852800*x^6+19180800*x^5-79184000*x^4-659608000*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^5-156800*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^6-7
67232*x^5+3167360*x^4+26384320*x^3-14419296*x^2-206683184*x+23476856)*exp(2)+2048*x^8+48128*x^7+252416*x^6-153
6256*x^5-13325440*x^4+16951616*x^3+204211936*x^2-129835568*x-787377632)/(390625*x-1171875),x, algorithm="giac"
)
[Out]
256/390625*(x - 3)^8 - 1024/390625*(x - 3)^7*e^2 + 1024/15625*(x - 3)^7*log(-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 - 16800*(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 + 168
0*(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*log(-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 + 10
752/78125*(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 + 3) - 8832/125*(x - 3)^4*e^2*log(-x + 3) + 4416/5*(x - 3)^4*log(
-x + 3)^2 - 896/125*(x - 3)^3*e^6*log(-x + 3)^2 + 5376/25*(x - 3)^3*e^4*log(-x + 3)^2 - 8832/5*(x - 3)^3*e^2*l
og(-x + 3)^2 + 14720*(x - 3)^3*log(-x + 3)^3 - 448/5*(x - 3)^2*e^6*log(-x + 3)^3 + 2688*(x - 3)^2*e^4*log(-x +
3)^3 - 22080*(x - 3)^2*e^2*log(-x + 3)^3 + 138000*(x - 3)^2*log(-x + 3)^4 - 560*(x - 3)*e^6*log(-x + 3)^4 + 1
6800*(x - 3)*e^4*log(-x + 3)^4 - 138000*(x - 3)*e^2*log(-x + 3)^4 + 690000*(x - 3)*log(-x + 3)^5 - 1400*e^6*lo
g(-x + 3)^5 + 42000*e^4*log(-x + 3)^5 - 345000*e^2*log(-x + 3)^5 + 1437500*log(-x + 3)^6 + 6656/3125*(x - 3)^5
+ 224/78125*(x - 3)^4*e^8 - 1792/15625*(x - 3)^4*e^6 + 4416/3125*(x - 3)^4*e^4 - 3328/625*(x - 3)^4*e^2 + 332
8/25*(x - 3)^4*log(-x + 3) + 448/3125*(x - 3)^3*e^8*log(-x + 3) - 3584/625*(x - 3)^3*e^6*log(-x + 3) + 8832/12
5*(x - 3)^3*e^4*log(-x + 3) - 6656/25*(x - 3)^3*e^2*log(-x + 3) + 3328*(x - 3)^3*log(-x + 3)^2 + 336/125*(x -
3)^2*e^8*log(-x + 3)^2 - 2688/25*(x - 3)^2*e^6*log(-x + 3)^2 + 6624/5*(x - 3)^2*e^4*log(-x + 3)^2 - 4992*(x -
3)^2*e^2*log(-x + 3)^2 + 41600*(x - 3)^2*log(-x + 3)^3 + 112/5*(x - 3)*e^8*log(-x + 3)^3 - 896*(x - 3)*e^6*log
(-x + 3)^3 + 11040*(x - 3)*e^4*log(-x + 3)^3 - 41600*(x - 3)*e^2*log(-x + 3)^3 + 260000*(x - 3)*log(-x + 3)^4
+ 70*e^8*log(-x + 3)^4 - 2800*e^6*log(-x + 3)^4 + 34500*e^4*log(-x + 3)^4 - 130000*e^2*log(-x + 3)^4 + 650000*
log(-x + 3)^5 + 224/125*(x - 3)^4 - 448/390625*(x - 3)^3*e^10 + 896/15625*(x - 3)^3*e^8 - 2944/3125*(x - 3)^3*
e^6 + 3328/625*(x - 3)^3*e^4 - 448/125*(x - 3)^3*e^2 + 448/5*(x - 3)^3*log(-x + 3) - 672/15625*(x - 3)^2*e^10*
log(-x + 3) + 1344/625*(x - 3)^2*e^8*log(-x + 3) - 4416/125*(x - 3)^2*e^6*log(-x + 3) + 4992/25*(x - 3)^2*e^4*
log(-x + 3) - 672/5*(x - 3)^2*e^2*log(-x + 3) + 1680*(x - 3)^2*log(-x + 3)^2 - 336/625*(x - 3)*e^10*log(-x + 3
)^2 + 672/25*(x - 3)*e^8*log(-x + 3)^2 - 2208/5*(x - 3)*e^6*log(-x + 3)^2 + 2496*(x - 3)*e^4*log(-x + 3)^2 - 1
680*(x - 3)*e^2*log(-x + 3)^2 + 14000*(x - 3)*log(-x + 3)^3 - 56/25*e^10*log(-x + 3)^3 + 112*e^8*log(-x + 3)^3
- 1840*e^6*log(-x + 3)^3 + 10400*e^4*log(-x + 3)^3 - 7000*e^2*log(-x + 3)^3 + 43750*log(-x + 3)^4 - 1664/125*
(x - 3)^3 + 112/390625*(x - 3)^2*e^12 - 1344/78125*(x - 3)^2*e^10 + 1104/3125*(x - 3)^2*e^8 - 1664/625*(x - 3)
^2*e^6 + 336/125*(x - 3)^2*e^4 + 2496/125*(x - 3)^2*e^2 - 2496/5*(x - 3)^2*log(-x + 3) + 112/15625*(x - 3)*e^1
2*log(-x + 3) - 1344/3125*(x - 3)*e^10*log(-x + 3) + 1104/125*(x - 3)*e^8*log(-x + 3) - 1664/25*(x - 3)*e^6*lo
g(-x + 3) + 336/5*(x - 3)*e^4*log(-x + 3) + 2496/5*(x - 3)*e^2*log(-x + 3) - 6240*(x - 3)*log(-x + 3)^2 + 28/6
25*e^12*log(-x + 3)^2 - 336/125*e^10*log(-x + 3)^2 + 276/5*e^8*log(-x + 3)^2 - 416*e^6*log(-x + 3)^2 + 420*e^4
*log(-x + 3)^2 + 3120*e^2*log(-x + 3)^2 - 26000*log(-x + 3)^3 + 368/25*(x - 3)^2 - 16/390625*(x - 3)*e^14 + 22
4/78125*(x - 3)*e^12 - 1104/15625*(x - 3)*e^10 + 416/625*(x - 3)*e^8 - 112/125*(x - 3)*e^6 - 1248/125*(x - 3)*
e^4 - 368/25*(x - 3)*e^2 + 368*(x - 3)*log(-x + 3) - 8/15625*e^14*log(-x + 3) + 112/3125*e^12*log(-x + 3) - 55
2/625*e^10*log(-x + 3) + 208/25*e^8*log(-x + 3) - 56/5*e^6*log(-x + 3) - 624/5*e^4*log(-x + 3) - 184*e^2*log(-
x + 3) + 2300*log(-x + 3)^2 - 32/5*x - 80*log(-x + 3) + 96/5
Mupad [B] (verification not implemented)
Time = 18.69 (sec) , antiderivative size = 772, normalized size of antiderivative = 24.90
\[
\int \frac {-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} \left (4256+2576 x+224 x^2\right )+e^{10} \left (5928-50448 x-18144 x^2-1344 x^3\right )+e^8 \left (-799520-143440 x+249120 x^2+69440 x^3+4480 x^4\right )+e^6 \left (633080+6462800 x+910400 x^2-656000 x^3-156800 x^4-8960 x^5\right )+e^4 \left (52288608+1705584 x-19588320 x^2-2494080 x^3+971520 x^4+209664 x^5+10752 x^6\right )+e^2 \left (23476856-206683184 x-14419296 x^2+26384320 x^3+3167360 x^4-767232 x^5-154112 x^6-7168 x^7\right )+\left (-586921400+5167079600 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} \left (-638400-386400 x-33600 x^2\right )+e^8 \left (-741000+6306000 x+2268000 x^2+168000 x^3\right )+e^6 \left (79952000+14344000 x-24912000 x^2-6944000 x^3-448000 x^4\right )+e^4 \left (-47481000-484710000 x-68280000 x^2+49200000 x^3+11760000 x^4+672000 x^5\right )+e^2 \left (-2614430400-85279200 x+979416000 x^2+124704000 x^3-48576000 x^4-10483200 x^5-537600 x^6\right )\right ) \log (3-x)+\left (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 \left (39900000+24150000 x+2100000 x^2\right )+e^6 \left (37050000-315300000 x-113400000 x^2-8400000 x^3\right )+e^4 \left (-2998200000-537900000 x+934200000 x^2+260400000 x^3+16800000 x^4\right )+e^2 \left (1187025000+12117750000 x+1707000000 x^2-1230000000 x^3-294000000 x^4-16800000 x^5\right )\right ) \log ^2(3-x)+\left (-9891875000-100981250000 x-14225000000 x^2+10250000000 x^3+2450000000 x^4+140000000 x^5+e^8 (83125000+8750000 x)+e^6 \left (-1330000000-805000000 x-70000000 x^2\right )+e^4 \left (-926250000+7882500000 x+2835000000 x^2+210000000 x^3\right )+e^2 \left (49970000000+8965000000 x-15570000000 x^2-4340000000 x^3-280000000 x^4\right )\right ) \log ^3(3-x)+\left (-312312500000+e^6 (-2078125000-218750000 x)-56031250000 x+97312500000 x^2+27125000000 x^3+1750000000 x^4+e^4 \left (24937500000+15093750000 x+1312500000 x^2\right )+e^2 \left (11578125000-98531250000 x-35437500000 x^2-2625000000 x^3\right )\right ) \log ^4(3-x)+\left (-57890625000+492656250000 x+177187500000 x^2+13125000000 x^3+e^4 (31171875000+3281250000 x)+e^2 \left (-249375000000-150937500000 x-13125000000 x^2\right )\right ) \log ^5(3-x)+\left (1039062500000+e^2 (-259765625000-27343750000 x)+628906250000 x+54687500000 x^2\right ) \log ^6(3-x)+(927734375000+97656250000 x) \log ^7(3-x)}{-1171875+390625 x} \, dx=\text {Too large to display}
\]
[In]
int((log(3 - x)^2*(1065990000*x + exp(8)*(24150000*x + 2100000*x^2 + 39900000) - exp(6)*(315300000*x + 1134000
00*x^2 + 8400000*x^3 - 37050000) + exp(2)*(12117750000*x + 1707000000*x^2 - 1230000000*x^3 - 294000000*x^4 - 1
6800000*x^5 + 1187025000) + exp(4)*(934200000*x^2 - 537900000*x + 260400000*x^3 + 16800000*x^4 - 2998200000) -
12242700000*x^2 - 1558800000*x^3 + 607200000*x^4 + 131040000*x^5 + 6720000*x^6 - exp(10)*(210000*x + 1995000)
+ 32680380000) - 129835568*x + exp(4)*(1705584*x - 19588320*x^2 - 2494080*x^3 + 971520*x^4 + 209664*x^5 + 107
52*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 + 6
944000*x^3 + 448000*x^4 - 79952000) + 360482400*x^2 - 659608000*x^3 - 79184000*x^4 + 19180800*x^5 + 3852800*x^
6 + 179200*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) - exp(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 + 76723
2*x^5 + 154112*x^6 + 7168*x^7 - 23476856) + log(3 - x)^7*(97656250000*x + 927734375000) - exp(10)*(50448*x + 1
8144*x^2 + 1344*x^3 - 5928) - log(3 - x)^3*(100981250000*x - exp(8)*(8750000*x + 83125000) + exp(2)*(155700000
00*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) + 14225000000*x^2 - 1025000000
0*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)*(15093750000*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) + 204211936*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 + 633
080) - exp(14)*(16*x + 152) + log(3 - x)^5*(492656250000*x + exp(4)*(3281250000*x + 31171875000) - exp(2)*(150
937500000*x + 13125000000*x^2 + 249375000000) + 177187500000*x^2 + 13125000000*x^3 - 57890625000) - 787377632)
/(390625*x - 1171875),x)
[Out]
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))/78125 + (624*exp(8))/78125 + (2688*exp(10))/390625 - (112*exp(12))/39062
5 + 2471248/390625) - x^7*((1024*exp(2))/390625 - 4096/390625) + log(3 - x)^7*(250000*x - 125000*exp(2) + 5000
00) - log(3 - x)^5*(1400*exp(6) - 16800*exp(4) - 7800*exp(2) + x^2*(16800*exp(2) - 67200) + x*(67200*exp(2) -
8400*exp(4) + 15600) - 11200*x^3 + 210400) + log(x - 3)*((1235624*exp(2))/15625 + (2752032*exp(4))/15625 + (66
64*exp(6))/3125 - (8416*exp(8))/3125 + (312*exp(10))/15625 + (224*exp(12))/15625 - (8*exp(14))/15625 - 4144092
8/15625) + x^3*((53312*exp(2))/78125 - (134656*exp(4))/78125 + (1664*exp(6))/78125 + (1792*exp(8))/78125 - (44
8*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*e
xp(2))/5 + (1792*exp(6))/5 - (112*exp(8))/5 + 13328/5) - 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) - 175
00*exp(4) - 70000*x^2 + x*(70000*exp(2) - 280000) + 32500) - x^4*((2496*exp(4))/78125 - (134656*exp(2))/78125
+ (3584*exp(6))/78125 - (224*exp(8))/78125 + 26656/78125) - log(3 - x)^2*((2752032*exp(2))/625 + (9996*exp(4))
/125 - (16832*exp(6))/125 + (156*exp(8))/125 + (672*exp(10))/625 - (28*exp(12))/625 - x*((39984*exp(2))/125 -
(100992*exp(4))/125 + (1248*exp(6))/125 + (1344*exp(8))/125 - (336*exp(10))/625 + 5504064/625) + x^4*((10752*e
xp(2))/125 - (1344*exp(4))/125 + 2496/125) + x^5*((5376*exp(2))/625 - 21504/625) + x^2*((3744*exp(4))/125 - (2
01984*exp(2))/125 + (5376*exp(6))/125 - (336*exp(8))/125 + 39984/125) - (1792*x^6)/625 - x^3*((4992*exp(2))/12
5 + (10752*exp(4))/125 - (896*exp(6))/125 - 134656/125) + 617812/625) - x*((66048768*exp(2))/390625 + (239904*
exp(4))/78125 - (403968*exp(6))/78125 + (3744*exp(8))/78125 + (16128*exp(10))/390625 - (672*exp(12))/390625 +
(16*(8*exp(2) - exp(4) + 109)^2*(30*exp(4) - 413*exp(2) + exp(6) + 358))/390625 + 14827488/390625) + (256*x^8)
/390625 + x^5*((9984*exp(2))/390625 + (21504*exp(4))/390625 - (1792*exp(6))/390625 - 269312/390625) - log(3 -
x)*(x^5*((43008*exp(2))/15625 - (5376*exp(4))/15625 + 9984/15625) + x^6*((3584*exp(2))/15625 - 14336/15625) -
x^2*((79968*exp(2))/3125 - (201984*exp(4))/3125 + (2496*exp(6))/3125 + (2688*exp(8))/3125 - (672*exp(10))/1562
5 + 11008128/15625) + x^3*((4992*exp(4))/3125 - (269312*exp(2))/3125 + (7168*exp(6))/3125 - (448*exp(8))/3125
+ 53312/3125) + x*((11008128*exp(2))/15625 + (39984*exp(4))/3125 - (67328*exp(6))/3125 + (624*exp(8))/3125 + (
2688*exp(10))/15625 - (112*exp(12))/15625 + 2471248/15625) - (1024*x^7)/15625 - x^4*((4992*exp(2))/3125 + (107
52*exp(4))/3125 - (896*exp(6))/3125 - 134656/3125))