Integrand size = 633, antiderivative size = 28 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx=\left (7-e^{e^x x}-x\right )^4 \left (\frac {2}{5}+x\right )^4 (x+\log (2)) \]
Leaf count is larger than twice the leaf count of optimal. \(510\) vs. \(2(28)=56\).
Time = 3.56 (sec) , antiderivative size = 510, normalized size of antiderivative = 18.21 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx=\frac {1}{625} \left (625 x^9+16 e^{e^x x} \left (-1372+294 e^{e^x x}-28 e^{2 e^x x}+e^{3 e^x x}\right ) \log (2)+\frac {1}{2} x^4 \left (-200 e^{3 e^x x} (256+135 \log (2))+60 e^{2 e^x x} (8152+3445 \log (2))-24 e^{e^x x} (86048+26605 \log (2))+250 e^{4 e^x x} (8+\log (32))+3 (1082928+485694 \log (2)-35665 \log (256))\right )+4 x^3 \left (-40 e^{3 e^x x} (101+160 \log (2))+12 e^{2 e^x x} (3397+5095 \log (2))-24 e^{e^x x} (7609+10756 \log (2))+50 e^{4 e^x x} (3+\log (32))+7 (43778+67254 \log (2)-1155 \log (256))\right )+4 x^2 \left (10 e^{4 e^x x} (4+15 \log (2))-8 e^{3 e^x x} (138+505 \log (2))-56 e^{e^x x} (938+3261 \log (2))+12 e^{2 e^x x} (952+3397 \log (2))+49 (1848+6534 \log (2)-35 \log (256))\right )+x^5 \left (300561+625 e^{4 e^x x}-403524 \log (2)-150 e^{2 e^x x} (-689+310 \log (2))+60 e^{e^x x} (-5321+4765 \log (2))+500 e^{3 e^x x} (-27+\log (32))-22077 \log (256)\right )+\frac {25}{7} x^7 \left (43778+1050 e^{2 e^x x}-660 \log (2)+140 e^{e^x x} (-97+\log (32))-495 \log (256)\right )+\frac {125}{8} x^8 \left (-1056+160 e^{e^x x}+5 \log (256)\right )+\frac {5}{2} x^6 \left (-232056+1000 e^{3 e^x x}+21780 \log (2)-40 e^{e^x x} (-2859+485 \log (2))+300 e^{2 e^x x} (-62+\log (32))+5095 \log (256)\right )+16 \left (-7+e^{e^x x}\right )^3 x \left (-7-66 \log (2)+e^{e^x x} (1+\log (1024))\right )\right ) \]
Integrate[(38416 + 724416*x + 3677352*x^2 + 6497568*x^3 + 1502805*x^4 - 34 80840*x^5 + 1094450*x^6 - 132000*x^7 + 5625*x^8 + (362208 + 2451568*x + 48 73176*x^2 + 1202244*x^3 - 2900700*x^4 + 938100*x^5 - 115500*x^6 + 5000*x^7 )*Log[2] + E^(4*E^x*x)*(16 + 320*x + 1800*x^2 + 4000*x^3 + 3125*x^4 + (160 + 1200*x + 3000*x^2 + 2500*x^3)*Log[2] + E^x*(64*x + 704*x^2 + 3040*x^3 + 6400*x^4 + 6500*x^5 + 2500*x^6 + (64 + 704*x + 3040*x^2 + 6400*x^3 + 6500 *x^4 + 2500*x^5)*Log[2])) + E^(3*E^x*x)*(-448 - 8832*x - 48480*x^2 - 10240 0*x^3 - 67500*x^4 + 15000*x^5 + (-4416 - 32320*x - 76800*x^2 - 54000*x^3 + 12500*x^4)*Log[2] + E^x*(-1344*x - 14592*x^2 - 61728*x^3 - 125280*x^4 - 1 17300*x^5 - 33000*x^6 + 7500*x^7 + (-1344 - 14592*x - 61728*x^2 - 125280*x ^3 - 117300*x^4 - 33000*x^5 + 7500*x^6)*Log[2])) + E^(2*E^x*x)*(4704 + 913 92*x + 489168*x^2 + 978240*x^3 + 516750*x^4 - 279000*x^5 + 26250*x^6 + (45 696 + 326112*x + 733680*x^2 + 413400*x^3 - 232500*x^4 + 22500*x^5)*Log[2] + E^x*(9408*x + 100800*x^2 + 417504*x^3 + 815232*x^4 + 695820*x^5 + 113700 *x^6 - 85500*x^7 + 7500*x^8 + (9408 + 100800*x + 417504*x^2 + 815232*x^3 + 695820*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7)*Log[2])) + E^(E^x*x)*(-21 952 - 420224*x - 2191392*x^2 - 4130304*x^3 - 1596300*x^4 + 1715400*x^5 - 3 39500*x^6 + 20000*x^7 + (-210112 - 1460928*x - 3097728*x^2 - 1277040*x^3 + 1429500*x^4 - 291000*x^5 + 17500*x^6)*Log[2] + E^x*(-21952*x - 232064*x^2 - 940576*x^3 - 1763040*x^4 - 1351836*x^5 - 33360*x^6 + 237400*x^7 - 46000 *x^8 + 2500*x^9 + (-21952 - 232064*x - 940576*x^2 - 1763040*x^3 - 1351836* x^4 - 33360*x^5 + 237400*x^6 - 46000*x^7 + 2500*x^8)*Log[2])))/625,x]
(625*x^9 + 16*E^(E^x*x)*(-1372 + 294*E^(E^x*x) - 28*E^(2*E^x*x) + E^(3*E^x *x))*Log[2] + (x^4*(-200*E^(3*E^x*x)*(256 + 135*Log[2]) + 60*E^(2*E^x*x)*( 8152 + 3445*Log[2]) - 24*E^(E^x*x)*(86048 + 26605*Log[2]) + 250*E^(4*E^x*x )*(8 + Log[32]) + 3*(1082928 + 485694*Log[2] - 35665*Log[256])))/2 + 4*x^3 *(-40*E^(3*E^x*x)*(101 + 160*Log[2]) + 12*E^(2*E^x*x)*(3397 + 5095*Log[2]) - 24*E^(E^x*x)*(7609 + 10756*Log[2]) + 50*E^(4*E^x*x)*(3 + Log[32]) + 7*( 43778 + 67254*Log[2] - 1155*Log[256])) + 4*x^2*(10*E^(4*E^x*x)*(4 + 15*Log [2]) - 8*E^(3*E^x*x)*(138 + 505*Log[2]) - 56*E^(E^x*x)*(938 + 3261*Log[2]) + 12*E^(2*E^x*x)*(952 + 3397*Log[2]) + 49*(1848 + 6534*Log[2] - 35*Log[25 6])) + x^5*(300561 + 625*E^(4*E^x*x) - 403524*Log[2] - 150*E^(2*E^x*x)*(-6 89 + 310*Log[2]) + 60*E^(E^x*x)*(-5321 + 4765*Log[2]) + 500*E^(3*E^x*x)*(- 27 + Log[32]) - 22077*Log[256]) + (25*x^7*(43778 + 1050*E^(2*E^x*x) - 660* Log[2] + 140*E^(E^x*x)*(-97 + Log[32]) - 495*Log[256]))/7 + (125*x^8*(-105 6 + 160*E^(E^x*x) + 5*Log[256]))/8 + (5*x^6*(-232056 + 1000*E^(3*E^x*x) + 21780*Log[2] - 40*E^(E^x*x)*(-2859 + 485*Log[2]) + 300*E^(2*E^x*x)*(-62 + Log[32]) + 5095*Log[256]))/2 + 16*(-7 + E^(E^x*x))^3*x*(-7 - 66*Log[2] + E ^(E^x*x)*(1 + Log[1024])))/625
Leaf count is larger than twice the leaf count of optimal. \(480\) vs. \(2(28)=56\).
Time = 1.13 (sec) , antiderivative size = 480, normalized size of antiderivative = 17.14, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.003, Rules used = {27, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {1}{625} \left (5625 x^8-132000 x^7+1094450 x^6-3480840 x^5+1502805 x^4+6497568 x^3+3677352 x^2+e^{4 e^x x} \left (3125 x^4+4000 x^3+1800 x^2+\left (2500 x^3+3000 x^2+1200 x+160\right ) \log (2)+e^x \left (2500 x^6+6500 x^5+6400 x^4+3040 x^3+704 x^2+\left (2500 x^5+6500 x^4+6400 x^3+3040 x^2+704 x+64\right ) \log (2)+64 x\right )+320 x+16\right )+e^{3 e^x x} \left (15000 x^5-67500 x^4-102400 x^3-48480 x^2+\left (12500 x^4-54000 x^3-76800 x^2-32320 x-4416\right ) \log (2)+e^x \left (7500 x^7-33000 x^6-117300 x^5-125280 x^4-61728 x^3-14592 x^2+\left (7500 x^6-33000 x^5-117300 x^4-125280 x^3-61728 x^2-14592 x-1344\right ) \log (2)-1344 x\right )-8832 x-448\right )+\left (5000 x^7-115500 x^6+938100 x^5-2900700 x^4+1202244 x^3+4873176 x^2+2451568 x+362208\right ) \log (2)+e^{2 e^x x} \left (26250 x^6-279000 x^5+516750 x^4+978240 x^3+489168 x^2+\left (22500 x^5-232500 x^4+413400 x^3+733680 x^2+326112 x+45696\right ) \log (2)+e^x \left (7500 x^8-85500 x^7+113700 x^6+695820 x^5+815232 x^4+417504 x^3+100800 x^2+\left (7500 x^7-85500 x^6+113700 x^5+695820 x^4+815232 x^3+417504 x^2+100800 x+9408\right ) \log (2)+9408 x\right )+91392 x+4704\right )+e^{e^x x} \left (20000 x^7-339500 x^6+1715400 x^5-1596300 x^4-4130304 x^3-2191392 x^2+\left (17500 x^6-291000 x^5+1429500 x^4-1277040 x^3-3097728 x^2-1460928 x-210112\right ) \log (2)+e^x \left (2500 x^9-46000 x^8+237400 x^7-33360 x^6-1351836 x^5-1763040 x^4-940576 x^3-232064 x^2+\left (2500 x^8-46000 x^7+237400 x^6-33360 x^5-1351836 x^4-1763040 x^3-940576 x^2-232064 x-21952\right ) \log (2)-21952 x\right )-420224 x-21952\right )+724416 x+38416\right ) \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{625} \int \left (5625 x^8-132000 x^7+1094450 x^6-3480840 x^5+1502805 x^4+6497568 x^3+3677352 x^2+724416 x+e^{4 e^x x} \left (3125 x^4+4000 x^3+1800 x^2+320 x+4 e^x \left (625 x^6+1625 x^5+1600 x^4+760 x^3+176 x^2+16 x+\left (625 x^5+1625 x^4+1600 x^3+760 x^2+176 x+16\right ) \log (2)\right )+20 \left (125 x^3+150 x^2+60 x+8\right ) \log (2)+16\right )-4 e^{3 e^x x} \left (-3750 x^5+16875 x^4+25600 x^3+12120 x^2+2208 x+3 e^x \left (-625 x^7+2750 x^6+9775 x^5+10440 x^4+5144 x^3+1216 x^2+112 x+\left (-625 x^6+2750 x^5+9775 x^4+10440 x^3+5144 x^2+1216 x+112\right ) \log (2)\right )+\left (-3125 x^4+13500 x^3+19200 x^2+8080 x+1104\right ) \log (2)+112\right )+6 e^{2 e^x x} \left (4375 x^6-46500 x^5+86125 x^4+163040 x^3+81528 x^2+15232 x+2 e^x \left (625 x^8-7125 x^7+9475 x^6+57985 x^5+67936 x^4+34792 x^3+8400 x^2+784 x+\left (625 x^7-7125 x^6+9475 x^5+57985 x^4+67936 x^3+34792 x^2+8400 x+784\right ) \log (2)\right )+2 \left (1875 x^5-19375 x^4+34450 x^3+61140 x^2+27176 x+3808\right ) \log (2)+784\right )-4 e^{e^x x} \left (-5000 x^7+84875 x^6-428850 x^5+399075 x^4+1032576 x^3+547848 x^2+105056 x+e^x \left (-625 x^9+11500 x^8-59350 x^7+8340 x^6+337959 x^5+440760 x^4+235144 x^3+58016 x^2+5488 x+\left (-625 x^8+11500 x^7-59350 x^6+8340 x^5+337959 x^4+440760 x^3+235144 x^2+58016 x+5488\right ) \log (2)\right )+\left (-4375 x^6+72750 x^5-357375 x^4+319260 x^3+774432 x^2+365232 x+52528\right ) \log (2)+5488\right )+4 \left (1250 x^7-28875 x^6+234525 x^5-725175 x^4+300561 x^3+1218294 x^2+612892 x+90552\right ) \log (2)+38416\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{625} \left (625 x^9-16500 x^8+625 x^8 \log (2)+156350 x^7-16500 x^7 \log (2)-580140 x^6+156350 x^6 \log (2)+300561 x^5-580140 x^5 \log (2)+1624392 x^4+300561 x^4 \log (2)+1225784 x^3+1624392 x^3 \log (2)+362208 x^2+1225784 x^2 \log (2)+\frac {e^{4 e^x x+x} \left (625 x^6+1625 x^5+1600 x^4+760 x^3+176 x^2+\left (625 x^5+1625 x^4+1600 x^3+760 x^2+176 x+16\right ) \log (2)+16 x\right )}{e^x x+e^x}-\frac {4 e^{3 e^x x+x} \left (-625 x^7+2750 x^6+9775 x^5+10440 x^4+5144 x^3+1216 x^2+\left (-625 x^6+2750 x^5+9775 x^4+10440 x^3+5144 x^2+1216 x+112\right ) \log (2)+112 x\right )}{e^x x+e^x}+\frac {6 e^{2 e^x x+x} \left (625 x^8-7125 x^7+9475 x^6+57985 x^5+67936 x^4+34792 x^3+8400 x^2+\left (625 x^7-7125 x^6+9475 x^5+57985 x^4+67936 x^3+34792 x^2+8400 x+784\right ) \log (2)+784 x\right )}{e^x x+e^x}-\frac {4 e^{e^x x+x} \left (-625 x^9+11500 x^8-59350 x^7+8340 x^6+337959 x^5+440760 x^4+235144 x^3+58016 x^2+\left (-625 x^8+11500 x^7-59350 x^6+8340 x^5+337959 x^4+440760 x^3+235144 x^2+58016 x+5488\right ) \log (2)+5488 x\right )}{e^x x+e^x}+38416 x+362208 x \log (2)\right )\) |
Int[(38416 + 724416*x + 3677352*x^2 + 6497568*x^3 + 1502805*x^4 - 3480840* x^5 + 1094450*x^6 - 132000*x^7 + 5625*x^8 + (362208 + 2451568*x + 4873176* x^2 + 1202244*x^3 - 2900700*x^4 + 938100*x^5 - 115500*x^6 + 5000*x^7)*Log[ 2] + E^(4*E^x*x)*(16 + 320*x + 1800*x^2 + 4000*x^3 + 3125*x^4 + (160 + 120 0*x + 3000*x^2 + 2500*x^3)*Log[2] + E^x*(64*x + 704*x^2 + 3040*x^3 + 6400* x^4 + 6500*x^5 + 2500*x^6 + (64 + 704*x + 3040*x^2 + 6400*x^3 + 6500*x^4 + 2500*x^5)*Log[2])) + E^(3*E^x*x)*(-448 - 8832*x - 48480*x^2 - 102400*x^3 - 67500*x^4 + 15000*x^5 + (-4416 - 32320*x - 76800*x^2 - 54000*x^3 + 12500 *x^4)*Log[2] + E^x*(-1344*x - 14592*x^2 - 61728*x^3 - 125280*x^4 - 117300* x^5 - 33000*x^6 + 7500*x^7 + (-1344 - 14592*x - 61728*x^2 - 125280*x^3 - 1 17300*x^4 - 33000*x^5 + 7500*x^6)*Log[2])) + E^(2*E^x*x)*(4704 + 91392*x + 489168*x^2 + 978240*x^3 + 516750*x^4 - 279000*x^5 + 26250*x^6 + (45696 + 326112*x + 733680*x^2 + 413400*x^3 - 232500*x^4 + 22500*x^5)*Log[2] + E^x* (9408*x + 100800*x^2 + 417504*x^3 + 815232*x^4 + 695820*x^5 + 113700*x^6 - 85500*x^7 + 7500*x^8 + (9408 + 100800*x + 417504*x^2 + 815232*x^3 + 69582 0*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7)*Log[2])) + E^(E^x*x)*(-21952 - 420224*x - 2191392*x^2 - 4130304*x^3 - 1596300*x^4 + 1715400*x^5 - 339500* x^6 + 20000*x^7 + (-210112 - 1460928*x - 3097728*x^2 - 1277040*x^3 + 14295 00*x^4 - 291000*x^5 + 17500*x^6)*Log[2] + E^x*(-21952*x - 232064*x^2 - 940 576*x^3 - 1763040*x^4 - 1351836*x^5 - 33360*x^6 + 237400*x^7 - 46000*x^8 + 2500*x^9 + (-21952 - 232064*x - 940576*x^2 - 1763040*x^3 - 1351836*x^4 - 33360*x^5 + 237400*x^6 - 46000*x^7 + 2500*x^8)*Log[2])))/625,x]
(38416*x + 362208*x^2 + 1225784*x^3 + 1624392*x^4 + 300561*x^5 - 580140*x^ 6 + 156350*x^7 - 16500*x^8 + 625*x^9 + 362208*x*Log[2] + 1225784*x^2*Log[2 ] + 1624392*x^3*Log[2] + 300561*x^4*Log[2] - 580140*x^5*Log[2] + 156350*x^ 6*Log[2] - 16500*x^7*Log[2] + 625*x^8*Log[2] + (E^(x + 4*E^x*x)*(16*x + 17 6*x^2 + 760*x^3 + 1600*x^4 + 1625*x^5 + 625*x^6 + (16 + 176*x + 760*x^2 + 1600*x^3 + 1625*x^4 + 625*x^5)*Log[2]))/(E^x + E^x*x) - (4*E^(x + 3*E^x*x) *(112*x + 1216*x^2 + 5144*x^3 + 10440*x^4 + 9775*x^5 + 2750*x^6 - 625*x^7 + (112 + 1216*x + 5144*x^2 + 10440*x^3 + 9775*x^4 + 2750*x^5 - 625*x^6)*Lo g[2]))/(E^x + E^x*x) + (6*E^(x + 2*E^x*x)*(784*x + 8400*x^2 + 34792*x^3 + 67936*x^4 + 57985*x^5 + 9475*x^6 - 7125*x^7 + 625*x^8 + (784 + 8400*x + 34 792*x^2 + 67936*x^3 + 57985*x^4 + 9475*x^5 - 7125*x^6 + 625*x^7)*Log[2]))/ (E^x + E^x*x) - (4*E^(x + E^x*x)*(5488*x + 58016*x^2 + 235144*x^3 + 440760 *x^4 + 337959*x^5 + 8340*x^6 - 59350*x^7 + 11500*x^8 - 625*x^9 + (5488 + 5 8016*x + 235144*x^2 + 440760*x^3 + 337959*x^4 + 8340*x^5 - 59350*x^6 + 115 00*x^7 - 625*x^8)*Log[2]))/(E^x + E^x*x))/625
3.20.17.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(417\) vs. \(2(24)=48\).
Time = 2.12 (sec) , antiderivative size = 418, normalized size of antiderivative = 14.93
| method | result | size |
| risch | \(\frac {\left (625 x^{4} \ln \left (2\right )+625 x^{5}+1000 x^{3} \ln \left (2\right )+1000 x^{4}+600 x^{2} \ln \left (2\right )+600 x^{3}+160 x \ln \left (2\right )+160 x^{2}+16 \ln \left (2\right )+16 x \right ) {\mathrm e}^{4 \,{\mathrm e}^{x} x}}{625}+\frac {\left (2500 x^{5} \ln \left (2\right )+2500 x^{6}-13500 x^{4} \ln \left (2\right )-13500 x^{5}-25600 x^{3} \ln \left (2\right )-25600 x^{4}-16160 x^{2} \ln \left (2\right )-16160 x^{3}-4416 x \ln \left (2\right )-4416 x^{2}-448 \ln \left (2\right )-448 x \right ) {\mathrm e}^{3 \,{\mathrm e}^{x} x}}{625}+\frac {\left (3750 x^{6} \ln \left (2\right )+3750 x^{7}-46500 x^{5} \ln \left (2\right )-46500 x^{6}+103350 x^{4} \ln \left (2\right )+103350 x^{5}+244560 x^{3} \ln \left (2\right )+244560 x^{4}+163056 x^{2} \ln \left (2\right )+163056 x^{3}+45696 x \ln \left (2\right )+45696 x^{2}+4704 \ln \left (2\right )+4704 x \right ) {\mathrm e}^{2 \,{\mathrm e}^{x} x}}{625}+\frac {\left (2500 x^{7} \ln \left (2\right )+2500 x^{8}-48500 x^{6} \ln \left (2\right )-48500 x^{7}+285900 x^{5} \ln \left (2\right )+285900 x^{6}-319260 x^{4} \ln \left (2\right )-319260 x^{5}-1032576 x^{3} \ln \left (2\right )-1032576 x^{4}-730464 x^{2} \ln \left (2\right )-730464 x^{3}-210112 x \ln \left (2\right )-210112 x^{2}-21952 \ln \left (2\right )-21952 x \right ) {\mathrm e}^{{\mathrm e}^{x} x}}{625}+x^{8} \ln \left (2\right )-\frac {132 x^{7} \ln \left (2\right )}{5}+\frac {6254 x^{6} \ln \left (2\right )}{25}-\frac {116028 x^{5} \ln \left (2\right )}{125}+\frac {300561 x^{4} \ln \left (2\right )}{625}+\frac {1624392 x^{3} \ln \left (2\right )}{625}+\frac {1225784 x^{2} \ln \left (2\right )}{625}+\frac {362208 x \ln \left (2\right )}{625}+x^{9}-\frac {132 x^{8}}{5}+\frac {6254 x^{7}}{25}-\frac {116028 x^{6}}{125}+\frac {300561 x^{5}}{625}+\frac {1624392 x^{4}}{625}+\frac {1225784 x^{3}}{625}+\frac {362208 x^{2}}{625}+\frac {38416 x}{625}\) | \(418\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(710\) |
int(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*ln(2)+2500*x^6+ 6500*x^5+6400*x^4+3040*x^3+704*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+1200*x+ 160)*ln(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+1/625*(((7 500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*ln(2)+7500 *x^7-33000*x^6-117300*x^5-125280*x^4-61728*x^3-14592*x^2-1344*x)*exp(x)+(1 2500*x^4-54000*x^3-76800*x^2-32320*x-4416)*ln(2)+15000*x^5-67500*x^4-10240 0*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85500*x^6+11 3700*x^5+695820*x^4+815232*x^3+417504*x^2+100800*x+9408)*ln(2)+7500*x^8-85 500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+100800*x^2+9408*x)*exp (x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696)*ln(2)+2625 0*x^6-279000*x^5+516750*x^4+978240*x^3+489168*x^2+91392*x+4704)*exp(exp(x) *x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5-1351836*x^4-1763040 *x^3-940576*x^2-232064*x-21952)*ln(2)+2500*x^9-46000*x^8+237400*x^7-33360* x^6-1351836*x^5-1763040*x^4-940576*x^3-232064*x^2-21952*x)*exp(x)+(17500*x ^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1460928*x-210112)*ln(2)+ 20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-2191392*x^2-42022 4*x-21952)*exp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x^5-2900700*x^4 +1202244*x^3+4873176*x^2+2451568*x+362208)*ln(2)+9*x^8-1056/5*x^7+43778/25 *x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/625*x^2+724416/ 625*x+38416/625,x,method=_RETURNVERBOSE)
1/625*(625*x^4*ln(2)+625*x^5+1000*x^3*ln(2)+1000*x^4+600*x^2*ln(2)+600*x^3 +160*x*ln(2)+160*x^2+16*ln(2)+16*x)*exp(exp(x)*x)^4+1/625*(2500*x^5*ln(2)+ 2500*x^6-13500*x^4*ln(2)-13500*x^5-25600*x^3*ln(2)-25600*x^4-16160*x^2*ln( 2)-16160*x^3-4416*x*ln(2)-4416*x^2-448*ln(2)-448*x)*exp(exp(x)*x)^3+1/625* (3750*x^6*ln(2)+3750*x^7-46500*x^5*ln(2)-46500*x^6+103350*x^4*ln(2)+103350 *x^5+244560*x^3*ln(2)+244560*x^4+163056*x^2*ln(2)+163056*x^3+45696*x*ln(2) +45696*x^2+4704*ln(2)+4704*x)*exp(exp(x)*x)^2+1/625*(2500*x^7*ln(2)+2500*x ^8-48500*x^6*ln(2)-48500*x^7+285900*x^5*ln(2)+285900*x^6-319260*x^4*ln(2)- 319260*x^5-1032576*x^3*ln(2)-1032576*x^4-730464*x^2*ln(2)-730464*x^3-21011 2*x*ln(2)-210112*x^2-21952*ln(2)-21952*x)*exp(exp(x)*x)+x^8*ln(2)-132/5*x^ 7*ln(2)+6254/25*x^6*ln(2)-116028/125*x^5*ln(2)+300561/625*x^4*ln(2)+162439 2/625*x^3*ln(2)+1225784/625*x^2*ln(2)+362208/625*x*ln(2)+x^9-132/5*x^8+625 4/25*x^7-116028/125*x^6+300561/625*x^5+1624392/625*x^4+1225784/625*x^3+362 208/625*x^2+38416/625*x
Leaf count of result is larger than twice the leaf count of optimal. 364 vs. \(2 (23) = 46\).
Time = 0.28 (sec) , antiderivative size = 364, normalized size of antiderivative = 13.00 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx=x^{9} - \frac {132}{5} \, x^{8} + \frac {6254}{25} \, x^{7} - \frac {116028}{125} \, x^{6} + \frac {300561}{625} \, x^{5} + \frac {1624392}{625} \, x^{4} + \frac {1225784}{625} \, x^{3} + \frac {362208}{625} \, x^{2} + \frac {1}{625} \, {\left (625 \, x^{5} + 1000 \, x^{4} + 600 \, x^{3} + 160 \, x^{2} + {\left (625 \, x^{4} + 1000 \, x^{3} + 600 \, x^{2} + 160 \, x + 16\right )} \log \left (2\right ) + 16 \, x\right )} e^{\left (4 \, x e^{x}\right )} + \frac {4}{625} \, {\left (625 \, x^{6} - 3375 \, x^{5} - 6400 \, x^{4} - 4040 \, x^{3} - 1104 \, x^{2} + {\left (625 \, x^{5} - 3375 \, x^{4} - 6400 \, x^{3} - 4040 \, x^{2} - 1104 \, x - 112\right )} \log \left (2\right ) - 112 \, x\right )} e^{\left (3 \, x e^{x}\right )} + \frac {6}{625} \, {\left (625 \, x^{7} - 7750 \, x^{6} + 17225 \, x^{5} + 40760 \, x^{4} + 27176 \, x^{3} + 7616 \, x^{2} + {\left (625 \, x^{6} - 7750 \, x^{5} + 17225 \, x^{4} + 40760 \, x^{3} + 27176 \, x^{2} + 7616 \, x + 784\right )} \log \left (2\right ) + 784 \, x\right )} e^{\left (2 \, x e^{x}\right )} + \frac {4}{625} \, {\left (625 \, x^{8} - 12125 \, x^{7} + 71475 \, x^{6} - 79815 \, x^{5} - 258144 \, x^{4} - 182616 \, x^{3} - 52528 \, x^{2} + {\left (625 \, x^{7} - 12125 \, x^{6} + 71475 \, x^{5} - 79815 \, x^{4} - 258144 \, x^{3} - 182616 \, x^{2} - 52528 \, x - 5488\right )} \log \left (2\right ) - 5488 \, x\right )} e^{\left (x e^{x}\right )} + \frac {1}{625} \, {\left (625 \, x^{8} - 16500 \, x^{7} + 156350 \, x^{6} - 580140 \, x^{5} + 300561 \, x^{4} + 1624392 \, x^{3} + 1225784 \, x^{2} + 362208 \, x\right )} \log \left (2\right ) + \frac {38416}{625} \, x \]
integrate(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*log(2)+25 00*x^6+6500*x^5+6400*x^4+3040*x^3+704*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+ 1200*x+160)*log(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+1/ 625*(((7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*lo g(2)+7500*x^7-33000*x^6-117300*x^5-125280*x^4-61728*x^3-14592*x^2-1344*x)* exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*log(2)+15000*x^5-67500 *x^4-102400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85 500*x^6+113700*x^5+695820*x^4+815232*x^3+417504*x^2+100800*x+9408)*log(2)+ 7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+100800*x^2+ 9408*x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696) *log(2)+26250*x^6-279000*x^5+516750*x^4+978240*x^3+489168*x^2+91392*x+4704 )*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5-1351836 *x^4-1763040*x^3-940576*x^2-232064*x-21952)*log(2)+2500*x^9-46000*x^8+2374 00*x^7-33360*x^6-1351836*x^5-1763040*x^4-940576*x^3-232064*x^2-21952*x)*ex p(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1460928*x-2 10112)*log(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-219 1392*x^2-420224*x-21952)*exp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x ^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*log(2)+9*x^8-1056 /5*x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/ 625*x^2+724416/625*x+38416/625,x, algorithm=\
x^9 - 132/5*x^8 + 6254/25*x^7 - 116028/125*x^6 + 300561/625*x^5 + 1624392/ 625*x^4 + 1225784/625*x^3 + 362208/625*x^2 + 1/625*(625*x^5 + 1000*x^4 + 6 00*x^3 + 160*x^2 + (625*x^4 + 1000*x^3 + 600*x^2 + 160*x + 16)*log(2) + 16 *x)*e^(4*x*e^x) + 4/625*(625*x^6 - 3375*x^5 - 6400*x^4 - 4040*x^3 - 1104*x ^2 + (625*x^5 - 3375*x^4 - 6400*x^3 - 4040*x^2 - 1104*x - 112)*log(2) - 11 2*x)*e^(3*x*e^x) + 6/625*(625*x^7 - 7750*x^6 + 17225*x^5 + 40760*x^4 + 271 76*x^3 + 7616*x^2 + (625*x^6 - 7750*x^5 + 17225*x^4 + 40760*x^3 + 27176*x^ 2 + 7616*x + 784)*log(2) + 784*x)*e^(2*x*e^x) + 4/625*(625*x^8 - 12125*x^7 + 71475*x^6 - 79815*x^5 - 258144*x^4 - 182616*x^3 - 52528*x^2 + (625*x^7 - 12125*x^6 + 71475*x^5 - 79815*x^4 - 258144*x^3 - 182616*x^2 - 52528*x - 5488)*log(2) - 5488*x)*e^(x*e^x) + 1/625*(625*x^8 - 16500*x^7 + 156350*x^6 - 580140*x^5 + 300561*x^4 + 1624392*x^3 + 1225784*x^2 + 362208*x)*log(2) + 38416/625*x
Leaf count of result is larger than twice the leaf count of optimal. 471 vs. \(2 (22) = 44\).
Time = 0.74 (sec) , antiderivative size = 471, normalized size of antiderivative = 16.82 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx =\text {Too large to display} \]
integrate(1/625*(((2500*x**5+6500*x**4+6400*x**3+3040*x**2+704*x+64)*ln(2) +2500*x**6+6500*x**5+6400*x**4+3040*x**3+704*x**2+64*x)*exp(x)+(2500*x**3+ 3000*x**2+1200*x+160)*ln(2)+3125*x**4+4000*x**3+1800*x**2+320*x+16)*exp(ex p(x)*x)**4+1/625*(((7500*x**6-33000*x**5-117300*x**4-125280*x**3-61728*x** 2-14592*x-1344)*ln(2)+7500*x**7-33000*x**6-117300*x**5-125280*x**4-61728*x **3-14592*x**2-1344*x)*exp(x)+(12500*x**4-54000*x**3-76800*x**2-32320*x-44 16)*ln(2)+15000*x**5-67500*x**4-102400*x**3-48480*x**2-8832*x-448)*exp(exp (x)*x)**3+1/625*(((7500*x**7-85500*x**6+113700*x**5+695820*x**4+815232*x** 3+417504*x**2+100800*x+9408)*ln(2)+7500*x**8-85500*x**7+113700*x**6+695820 *x**5+815232*x**4+417504*x**3+100800*x**2+9408*x)*exp(x)+(22500*x**5-23250 0*x**4+413400*x**3+733680*x**2+326112*x+45696)*ln(2)+26250*x**6-279000*x** 5+516750*x**4+978240*x**3+489168*x**2+91392*x+4704)*exp(exp(x)*x)**2+1/625 *(((2500*x**8-46000*x**7+237400*x**6-33360*x**5-1351836*x**4-1763040*x**3- 940576*x**2-232064*x-21952)*ln(2)+2500*x**9-46000*x**8+237400*x**7-33360*x **6-1351836*x**5-1763040*x**4-940576*x**3-232064*x**2-21952*x)*exp(x)+(175 00*x**6-291000*x**5+1429500*x**4-1277040*x**3-3097728*x**2-1460928*x-21011 2)*ln(2)+20000*x**7-339500*x**6+1715400*x**5-1596300*x**4-4130304*x**3-219 1392*x**2-420224*x-21952)*exp(exp(x)*x)+1/625*(5000*x**7-115500*x**6+93810 0*x**5-2900700*x**4+1202244*x**3+4873176*x**2+2451568*x+362208)*ln(2)+9*x* *8-1056/5*x**7+43778/25*x**6-696168/125*x**5+300561/125*x**4+6497568/625*x **3+3677352/625*x**2+724416/625*x+38416/625,x)
x**9 + x**8*(-132/5 + log(2)) + x**7*(6254/25 - 132*log(2)/5) + x**6*(-116 028/125 + 6254*log(2)/25) + x**5*(300561/625 - 116028*log(2)/125) + x**4*( 300561*log(2)/625 + 1624392/625) + x**3*(1624392*log(2)/625 + 1225784/625) + x**2*(362208/625 + 1225784*log(2)/625) + x*(38416/625 + 362208*log(2)/6 25) + (152587890625*x**5 + 152587890625*x**4*log(2) + 244140625000*x**4 + 146484375000*x**3 + 244140625000*x**3*log(2) + 39062500000*x**2 + 14648437 5000*x**2*log(2) + 3906250000*x + 39062500000*x*log(2) + 3906250000*log(2) )*exp(4*x*exp(x))/152587890625 + (610351562500*x**6 - 3295898437500*x**5 + 610351562500*x**5*log(2) - 6250000000000*x**4 - 3295898437500*x**4*log(2) - 6250000000000*x**3*log(2) - 3945312500000*x**3 - 3945312500000*x**2*log (2) - 1078125000000*x**2 - 1078125000000*x*log(2) - 109375000000*x - 10937 5000000*log(2))*exp(3*x*exp(x))/152587890625 + (915527343750*x**7 - 113525 39062500*x**6 + 915527343750*x**6*log(2) - 11352539062500*x**5*log(2) + 25 231933593750*x**5 + 25231933593750*x**4*log(2) + 59707031250000*x**4 + 398 08593750000*x**3 + 59707031250000*x**3*log(2) + 11156250000000*x**2 + 3980 8593750000*x**2*log(2) + 1148437500000*x + 11156250000000*x*log(2) + 11484 37500000*log(2))*exp(2*x*exp(x))/152587890625 + (610351562500*x**8 - 11840 820312500*x**7 + 610351562500*x**7*log(2) - 11840820312500*x**6*log(2) + 6 9799804687500*x**6 - 77944335937500*x**5 + 69799804687500*x**5*log(2) - 25 2093750000000*x**4 - 77944335937500*x**4*log(2) - 178335937500000*x**3 ...
Leaf count of result is larger than twice the leaf count of optimal. 390 vs. \(2 (23) = 46\).
Time = 0.30 (sec) , antiderivative size = 390, normalized size of antiderivative = 13.93 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx =\text {Too large to display} \]
integrate(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*log(2)+25 00*x^6+6500*x^5+6400*x^4+3040*x^3+704*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+ 1200*x+160)*log(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+1/ 625*(((7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*lo g(2)+7500*x^7-33000*x^6-117300*x^5-125280*x^4-61728*x^3-14592*x^2-1344*x)* exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*log(2)+15000*x^5-67500 *x^4-102400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85 500*x^6+113700*x^5+695820*x^4+815232*x^3+417504*x^2+100800*x+9408)*log(2)+ 7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+100800*x^2+ 9408*x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696) *log(2)+26250*x^6-279000*x^5+516750*x^4+978240*x^3+489168*x^2+91392*x+4704 )*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5-1351836 *x^4-1763040*x^3-940576*x^2-232064*x-21952)*log(2)+2500*x^9-46000*x^8+2374 00*x^7-33360*x^6-1351836*x^5-1763040*x^4-940576*x^3-232064*x^2-21952*x)*ex p(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1460928*x-2 10112)*log(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-219 1392*x^2-420224*x-21952)*exp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x ^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*log(2)+9*x^8-1056 /5*x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/ 625*x^2+724416/625*x+38416/625,x, algorithm=\
x^9 - 132/5*x^8 + 6254/25*x^7 - 116028/125*x^6 + 300561/625*x^5 + 1624392/ 625*x^4 + 1225784/625*x^3 + 362208/625*x^2 + 1/625*(625*x^5 + 125*x^4*(5*l og(2) + 8) + 200*x^3*(5*log(2) + 3) + 40*x^2*(15*log(2) + 4) + 16*x*(10*lo g(2) + 1) + 16*log(2))*e^(4*x*e^x) + 4/625*(625*x^6 + 125*x^5*(5*log(2) - 27) - 25*x^4*(135*log(2) + 256) - 40*x^3*(160*log(2) + 101) - 8*x^2*(505*l og(2) + 138) - 16*x*(69*log(2) + 7) - 112*log(2))*e^(3*x*e^x) + 6/625*(625 *x^7 + 125*x^6*(5*log(2) - 62) - 25*x^5*(310*log(2) - 689) + 5*x^4*(3445*l og(2) + 8152) + 8*x^3*(5095*log(2) + 3397) + 8*x^2*(3397*log(2) + 952) + 1 12*x*(68*log(2) + 7) + 784*log(2))*e^(2*x*e^x) + 4/625*(625*x^8 + 125*x^7* (5*log(2) - 97) - 25*x^6*(485*log(2) - 2859) + 15*x^5*(4765*log(2) - 5321) - 3*x^4*(26605*log(2) + 86048) - 24*x^3*(10756*log(2) + 7609) - 56*x^2*(3 261*log(2) + 938) - 784*x*(67*log(2) + 7) - 5488*log(2))*e^(x*e^x) + 1/625 *(625*x^8 - 16500*x^7 + 156350*x^6 - 580140*x^5 + 300561*x^4 + 1624392*x^3 + 1225784*x^2 + 362208*x)*log(2) + 38416/625*x
Leaf count of result is larger than twice the leaf count of optimal. 663 vs. \(2 (23) = 46\).
Time = 0.33 (sec) , antiderivative size = 663, normalized size of antiderivative = 23.68 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx=\text {Too large to display} \]
integrate(1/625*(((2500*x^5+6500*x^4+6400*x^3+3040*x^2+704*x+64)*log(2)+25 00*x^6+6500*x^5+6400*x^4+3040*x^3+704*x^2+64*x)*exp(x)+(2500*x^3+3000*x^2+ 1200*x+160)*log(2)+3125*x^4+4000*x^3+1800*x^2+320*x+16)*exp(exp(x)*x)^4+1/ 625*(((7500*x^6-33000*x^5-117300*x^4-125280*x^3-61728*x^2-14592*x-1344)*lo g(2)+7500*x^7-33000*x^6-117300*x^5-125280*x^4-61728*x^3-14592*x^2-1344*x)* exp(x)+(12500*x^4-54000*x^3-76800*x^2-32320*x-4416)*log(2)+15000*x^5-67500 *x^4-102400*x^3-48480*x^2-8832*x-448)*exp(exp(x)*x)^3+1/625*(((7500*x^7-85 500*x^6+113700*x^5+695820*x^4+815232*x^3+417504*x^2+100800*x+9408)*log(2)+ 7500*x^8-85500*x^7+113700*x^6+695820*x^5+815232*x^4+417504*x^3+100800*x^2+ 9408*x)*exp(x)+(22500*x^5-232500*x^4+413400*x^3+733680*x^2+326112*x+45696) *log(2)+26250*x^6-279000*x^5+516750*x^4+978240*x^3+489168*x^2+91392*x+4704 )*exp(exp(x)*x)^2+1/625*(((2500*x^8-46000*x^7+237400*x^6-33360*x^5-1351836 *x^4-1763040*x^3-940576*x^2-232064*x-21952)*log(2)+2500*x^9-46000*x^8+2374 00*x^7-33360*x^6-1351836*x^5-1763040*x^4-940576*x^3-232064*x^2-21952*x)*ex p(x)+(17500*x^6-291000*x^5+1429500*x^4-1277040*x^3-3097728*x^2-1460928*x-2 10112)*log(2)+20000*x^7-339500*x^6+1715400*x^5-1596300*x^4-4130304*x^3-219 1392*x^2-420224*x-21952)*exp(exp(x)*x)+1/625*(5000*x^7-115500*x^6+938100*x ^5-2900700*x^4+1202244*x^3+4873176*x^2+2451568*x+362208)*log(2)+9*x^8-1056 /5*x^7+43778/25*x^6-696168/125*x^5+300561/125*x^4+6497568/625*x^3+3677352/ 625*x^2+724416/625*x+38416/625,x, algorithm=\
x^9 + 4*x^8*e^(x*e^x) + 4*x^7*e^(x*e^x)*log(2) - 132/5*x^8 + 6*x^7*e^(2*x* e^x) - 388/5*x^7*e^(x*e^x) + 6*x^6*e^(2*x*e^x)*log(2) - 388/5*x^6*e^(x*e^x )*log(2) + 6254/25*x^7 + 4*x^6*e^(3*x*e^x) - 372/5*x^6*e^(2*x*e^x) + 11436 /25*x^6*e^(x*e^x) + 4*x^5*e^(3*x*e^x)*log(2) - 372/5*x^5*e^(2*x*e^x)*log(2 ) + 11436/25*x^5*e^(x*e^x)*log(2) - 116028/125*x^6 + x^5*e^(4*x*e^x) - 108 /5*x^5*e^(3*x*e^x) + 4134/25*x^5*e^(2*x*e^x) - 63852/125*x^5*e^(x*e^x) + x ^4*e^(4*x*e^x)*log(2) - 108/5*x^4*e^(3*x*e^x)*log(2) + 4134/25*x^4*e^(2*x* e^x)*log(2) - 63852/125*x^4*e^(x*e^x)*log(2) + 300561/625*x^5 + 8/5*x^4*e^ (4*x*e^x) - 1024/25*x^4*e^(3*x*e^x) + 48912/125*x^4*e^(2*x*e^x) - 1032576/ 625*x^4*e^(x*e^x) + 8/5*x^3*e^(4*x*e^x)*log(2) - 1024/25*x^3*e^(3*x*e^x)*l og(2) + 48912/125*x^3*e^(2*x*e^x)*log(2) - 1032576/625*x^3*e^(x*e^x)*log(2 ) + 1624392/625*x^4 + 24/25*x^3*e^(4*x*e^x) - 3232/125*x^3*e^(3*x*e^x) + 1 63056/625*x^3*e^(2*x*e^x) - 730464/625*x^3*e^(x*e^x) + 24/25*x^2*e^(4*x*e^ x)*log(2) - 3232/125*x^2*e^(3*x*e^x)*log(2) + 163056/625*x^2*e^(2*x*e^x)*l og(2) - 730464/625*x^2*e^(x*e^x)*log(2) + 1225784/625*x^3 + 32/125*x^2*e^( 4*x*e^x) - 4416/625*x^2*e^(3*x*e^x) + 45696/625*x^2*e^(2*x*e^x) - 210112/6 25*x^2*e^(x*e^x) + 32/125*x*e^(4*x*e^x)*log(2) - 4416/625*x*e^(3*x*e^x)*lo g(2) + 45696/625*x*e^(2*x*e^x)*log(2) - 210112/625*x*e^(x*e^x)*log(2) + 36 2208/625*x^2 + 16/625*x*e^(4*x*e^x) - 448/625*x*e^(3*x*e^x) + 4704/625*x*e ^(2*x*e^x) - 21952/625*x*e^(x*e^x) + 1/625*(625*x^8 - 16500*x^7 + 15635...
Time = 11.54 (sec) , antiderivative size = 365, normalized size of antiderivative = 13.04 \[ \int \frac {1}{625} \left (38416+724416 x+3677352 x^2+6497568 x^3+1502805 x^4-3480840 x^5+1094450 x^6-132000 x^7+5625 x^8+\left (362208+2451568 x+4873176 x^2+1202244 x^3-2900700 x^4+938100 x^5-115500 x^6+5000 x^7\right ) \log (2)+e^{4 e^x x} \left (16+320 x+1800 x^2+4000 x^3+3125 x^4+\left (160+1200 x+3000 x^2+2500 x^3\right ) \log (2)+e^x \left (64 x+704 x^2+3040 x^3+6400 x^4+6500 x^5+2500 x^6+\left (64+704 x+3040 x^2+6400 x^3+6500 x^4+2500 x^5\right ) \log (2)\right )\right )+e^{3 e^x x} \left (-448-8832 x-48480 x^2-102400 x^3-67500 x^4+15000 x^5+\left (-4416-32320 x-76800 x^2-54000 x^3+12500 x^4\right ) \log (2)+e^x \left (-1344 x-14592 x^2-61728 x^3-125280 x^4-117300 x^5-33000 x^6+7500 x^7+\left (-1344-14592 x-61728 x^2-125280 x^3-117300 x^4-33000 x^5+7500 x^6\right ) \log (2)\right )\right )+e^{2 e^x x} \left (4704+91392 x+489168 x^2+978240 x^3+516750 x^4-279000 x^5+26250 x^6+\left (45696+326112 x+733680 x^2+413400 x^3-232500 x^4+22500 x^5\right ) \log (2)+e^x \left (9408 x+100800 x^2+417504 x^3+815232 x^4+695820 x^5+113700 x^6-85500 x^7+7500 x^8+\left (9408+100800 x+417504 x^2+815232 x^3+695820 x^4+113700 x^5-85500 x^6+7500 x^7\right ) \log (2)\right )\right )+e^{e^x x} \left (-21952-420224 x-2191392 x^2-4130304 x^3-1596300 x^4+1715400 x^5-339500 x^6+20000 x^7+\left (-210112-1460928 x-3097728 x^2-1277040 x^3+1429500 x^4-291000 x^5+17500 x^6\right ) \log (2)+e^x \left (-21952 x-232064 x^2-940576 x^3-1763040 x^4-1351836 x^5-33360 x^6+237400 x^7-46000 x^8+2500 x^9+\left (-21952-232064 x-940576 x^2-1763040 x^3-1351836 x^4-33360 x^5+237400 x^6-46000 x^7+2500 x^8\right ) \log (2)\right )\right )\right ) \, dx =\text {Too large to display} \]
int((724416*x)/625 - (exp(3*x*exp(x))*(8832*x + log(2)*(32320*x + 76800*x^ 2 + 54000*x^3 - 12500*x^4 + 4416) + exp(x)*(1344*x + log(2)*(14592*x + 617 28*x^2 + 125280*x^3 + 117300*x^4 + 33000*x^5 - 7500*x^6 + 1344) + 14592*x^ 2 + 61728*x^3 + 125280*x^4 + 117300*x^5 + 33000*x^6 - 7500*x^7) + 48480*x^ 2 + 102400*x^3 + 67500*x^4 - 15000*x^5 + 448))/625 + (exp(4*x*exp(x))*(320 *x + exp(x)*(64*x + 704*x^2 + 3040*x^3 + 6400*x^4 + 6500*x^5 + 2500*x^6 + log(2)*(704*x + 3040*x^2 + 6400*x^3 + 6500*x^4 + 2500*x^5 + 64)) + log(2)* (1200*x + 3000*x^2 + 2500*x^3 + 160) + 1800*x^2 + 4000*x^3 + 3125*x^4 + 16 ))/625 + (log(2)*(2451568*x + 4873176*x^2 + 1202244*x^3 - 2900700*x^4 + 93 8100*x^5 - 115500*x^6 + 5000*x^7 + 362208))/625 - (exp(x*exp(x))*(420224*x + log(2)*(1460928*x + 3097728*x^2 + 1277040*x^3 - 1429500*x^4 + 291000*x^ 5 - 17500*x^6 + 210112) + exp(x)*(21952*x + log(2)*(232064*x + 940576*x^2 + 1763040*x^3 + 1351836*x^4 + 33360*x^5 - 237400*x^6 + 46000*x^7 - 2500*x^ 8 + 21952) + 232064*x^2 + 940576*x^3 + 1763040*x^4 + 1351836*x^5 + 33360*x ^6 - 237400*x^7 + 46000*x^8 - 2500*x^9) + 2191392*x^2 + 4130304*x^3 + 1596 300*x^4 - 1715400*x^5 + 339500*x^6 - 20000*x^7 + 21952))/625 + (3677352*x^ 2)/625 + (6497568*x^3)/625 + (300561*x^4)/125 - (696168*x^5)/125 + (43778* x^6)/25 - (1056*x^7)/5 + 9*x^8 + (exp(2*x*exp(x))*(91392*x + exp(x)*(9408* x + log(2)*(100800*x + 417504*x^2 + 815232*x^3 + 695820*x^4 + 113700*x^5 - 85500*x^6 + 7500*x^7 + 9408) + 100800*x^2 + 417504*x^3 + 815232*x^4 + 695 820*x^5 + 113700*x^6 - 85500*x^7 + 7500*x^8) + 489168*x^2 + 978240*x^3 + 5 16750*x^4 - 279000*x^5 + 26250*x^6 + log(2)*(326112*x + 733680*x^2 + 41340 0*x^3 - 232500*x^4 + 22500*x^5 + 45696) + 4704))/625 + 38416/625,x)
x*((362208*log(2))/625 + 38416/625) - exp(x*exp(x))*((21952*log(2))/625 + x*((210112*log(2))/625 + 21952/625) - x^7*(4*log(2) - 388/5) + x^6*((388*l og(2))/5 - 11436/25) - x^5*((11436*log(2))/25 - 63852/125) + x^2*((730464* log(2))/625 + 210112/625) + x^4*((63852*log(2))/125 + 1032576/625) + x^3*( (1032576*log(2))/625 + 730464/625) - 4*x^8) + exp(4*x*exp(x))*((16*log(2)) /625 + x*((32*log(2))/125 + 16/625) + x^4*(log(2) + 8/5) + x^3*((8*log(2)) /5 + 24/25) + x^2*((24*log(2))/25 + 32/125) + x^5) + x^8*(log(256)/8 - 132 /5) - x^7*((132*log(2))/5 - 6254/25) + x^6*((6254*log(2))/25 - 116028/125) - x^5*((116028*log(2))/125 - 300561/625) + x^2*((1225784*log(2))/625 + 36 2208/625) + x^4*((300561*log(2))/625 + 1624392/625) + x^3*((1624392*log(2) )/625 + 1225784/625) - exp(3*x*exp(x))*((448*log(2))/625 + x*((4416*log(2) )/625 + 448/625) - x^5*(4*log(2) - 108/5) + x^4*((108*log(2))/5 + 1024/25) + x^3*((1024*log(2))/25 + 3232/125) + x^2*((3232*log(2))/125 + 4416/625) - 4*x^6) + exp(2*x*exp(x))*((4704*log(2))/625 + x*((45696*log(2))/625 + 47 04/625) + x^6*(6*log(2) - 372/5) - x^5*((372*log(2))/5 - 4134/25) + x^4*(( 4134*log(2))/25 + 48912/125) + x^2*((163056*log(2))/625 + 45696/625) + x^3 *((48912*log(2))/125 + 163056/625) + 6*x^7) + x^9