Integrand size = 1676, antiderivative size = 21 \[ \text {the integral} =\left (-3+x+\frac {e^4}{-5+e^x+x}-\log (x)\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(308\) vs. \(2(21)=42\).
Time = 0.70 (sec) , antiderivative size = 308, normalized size of antiderivative = 14.67 \[ \text {the integral} =-108 x+54 x^2-12 x^3+x^4+\frac {e^{16}}{\left (-5+e^x+x\right )^4}+\frac {4 e^{12} (-3+x)}{\left (-5+e^x+x\right )^3}+\frac {6 e^8 (-3+x)^2}{\left (-5+e^x+x\right )^2}+\frac {4 e^4 (-3+x)^3}{-5+e^x+x}+108 \log (x)-\frac {4 \left (e^{12}+3 e^{8+x} (-3+x)+3 e^{4+2 x} (-3+x)^2+6 e^{4+x} (-5+x) (-3+x)^2+e^{3 x} x \left (27-9 x+x^2\right )+3 e^x (-5+x)^2 x \left (27-9 x+x^2\right )+(-5+x)^3 x \left (27-9 x+x^2\right )+3 e^8 \left (15-8 x+x^2\right )+3 e^4 \left (15-8 x+x^2\right )^2+3 e^{2 x} x \left (-135+72 x-14 x^2+x^3\right )\right ) \log (x)}{\left (-5+e^x+x\right )^3}+\frac {6 \left (15+e^4+e^x (-3+x)-8 x+x^2\right )^2 \log ^2(x)}{\left (-5+e^x+x\right )^2}-\frac {4 \left (15+e^4+e^x (-3+x)-8 x+x^2\right ) \log ^3(x)}{-5+e^x+x}+\log ^4(x) \]
Integrate[(-337500 + 1012500*x - 4*E^16*x - 1260000*x^2 + 872000*x^3 - 374 200*x^4 + 104008*x^5 - 18816*x^6 + 2144*x^7 - 140*x^8 + 4*x^9 + E^12*(-100 - 40*x + 52*x^2 - 8*x^3) + E^8*(-4500 + 6000*x - 2760*x^2 + 528*x^3 - 36* x^4) + E^(5*x)*(108 - 216*x + 144*x^2 - 40*x^3 + 4*x^4) + E^4*(-67500 + 15 3000*x - 137100*x^2 + 64440*x^3 - 17380*x^4 + 2712*x^5 - 228*x^6 + 8*x^7) + E^(4*x)*(-2700 + 5940*x - 4680*x^2 + 1720*x^3 - 300*x^4 + 20*x^5 + E^4*( -108 + 288*x - 192*x^2 + 48*x^3 - 4*x^4)) + E^(3*x)*(27000 - 64800*x + 586 80*x^2 - 26560*x^3 + 6440*x^4 - 800*x^5 + 40*x^6 + E^8*(36 - 156*x + 84*x^ 2 - 12*x^3) + E^4*(2160 - 5544*x + 4236*x^2 - 1404*x^3 + 212*x^4 - 12*x^5) ) + E^(2*x)*(-135000 + 351000*x - 358200*x^2 + 191480*x^3 - 58760*x^4 + 10 440*x^5 - 1000*x^6 + 40*x^7 + E^12*(-4 + 40*x - 12*x^2) + E^8*(-540 + 1800 *x - 1188*x^2 + 288*x^3 - 24*x^4) + E^4*(-16200 + 39960*x - 33444*x^2 + 13 320*x^3 - 2760*x^4 + 288*x^5 - 12*x^6)) + E^x*(337500 - 945000*x - 4*E^16* x + 1071000*x^2 - 657800*x^3 + 242640*x^4 - 55480*x^5 + 7720*x^6 - 600*x^7 + 20*x^8 + E^12*(40 - 192*x + 92*x^2 - 12*x^3) + E^8*(2700 - 6300*x + 439 2*x^2 - 1368*x^3 + 204*x^4 - 12*x^5) + E^4*(54000 - 127800*x + 112740*x^2 - 50388*x^3 + 12584*x^4 - 1776*x^5 + 132*x^6 - 4*x^7)) + (-337500 + 900000 *x - 960000*x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x^6 + 384*x^7 - 12*x^8 + E^12*(-60*x + 12*x^2) + E^(5*x)*(108 - 180*x + 84*x^2 - 12*x^3 ) + E^8*(-1500 + 600*x + 240*x^2 - 120*x^3 + 12*x^4) + E^4*(-45000 + 82500 *x - 56700*x^2 + 19320*x^3 - 3504*x^4 + 324*x^5 - 12*x^6) + E^(4*x)*(-2700 + 5040*x - 3000*x^2 + 720*x^3 - 60*x^4 + E^4*(-72 + 204*x - 96*x^2 + 12*x ^3)) + E^(3*x)*(27000 - 55800*x + 40080*x^2 - 13200*x^3 + 2040*x^4 - 120*x ^5 + E^8*(12 - 84*x + 24*x^2) + E^4*(1440 - 3720*x + 2196*x^2 - 480*x^3 + 36*x^4)) + E^(2*x)*(-135000 + 306000*x + 12*E^12*x - 256200*x^2 + 106080*x ^3 - 23400*x^4 + 2640*x^5 - 120*x^6 + E^8*(-180 + 864*x - 396*x^2 + 48*x^3 ) + E^4*(-10800 + 25200*x - 17028*x^2 + 5004*x^3 - 684*x^4 + 36*x^5)) + E^ x*(337500 - 832500*x + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x^6 - 60*x^7 + E^12*(-48*x + 12*x^2) + E^8*(900 - 2340*x + 1332*x^2 - 300*x^3 + 24*x^4) + E^4*(36000 - 75000*x + 53580*x^2 - 18384*x^3 + 3336*x ^4 - 312*x^5 + 12*x^6)))*Log[x] + (-112500 + 262500*x - 232500*x^2 + 10650 0*x^3 - 27900*x^4 + 4236*x^5 - 348*x^6 + 12*x^7 + E^(5*x)*(36 - 48*x + 12* x^2) + E^8*(-300*x + 120*x^2 - 12*x^3) + E^4*(-7500 + 9000*x - 3600*x^2 + 600*x^3 - 36*x^4) + E^(4*x)*(-900 + 1380*x - 540*x^2 + 60*x^3 + E^4*(-12 + 48*x - 12*x^2)) + E^(3*x)*(9000 - 15600*x - 12*E^8*x + 8160*x^2 - 1680*x^ 3 + 120*x^4 + E^4*(240 - 792*x + 324*x^2 - 36*x^3)) + E^(2*x)*(-45000 + 87 000*x - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 + E^8*(108*x - 24*x^2) + E^4*(-1800 + 4680*x - 2484*x^2 + 504*x^3 - 36*x^4)) + E^x*(112500 - 2400 00*x + 184500*x^2 - 69600*x^3 + 13980*x^4 - 1440*x^5 + 60*x^6 + E^8*(-180* x + 96*x^2 - 12*x^3) + E^4*(6000 - 11400*x + 6540*x^2 - 1740*x^3 + 228*x^4 - 12*x^5)))*Log[x]^2 + (-12500 + E^(5*x)*(4 - 4*x) + 25000*x - 17500*x^2 + 6000*x^3 - 1100*x^4 + 104*x^5 - 4*x^6 + E^(4*x)*(-100 + 120*x + 4*E^4*x - 20*x^2) + E^4*(-500*x + 300*x^2 - 60*x^3 + 4*x^4) + E^(3*x)*(1000 - 1400 *x + 440*x^2 - 40*x^3 + E^4*(-56*x + 12*x^2)) + E^(2*x)*(-5000 + 8000*x - 3600*x^2 + 640*x^3 - 40*x^4 + E^4*(240*x - 108*x^2 + 12*x^3)) + E^x*(12500 - 22500*x + 13000*x^2 - 3400*x^3 + 420*x^4 - 20*x^5 + E^4*(-200*x + 180*x ^2 - 48*x^3 + 4*x^4)))*Log[x]^3)/(-3125*x + E^(5*x)*x + 3125*x^2 - 1250*x^ 3 + 250*x^4 - 25*x^5 + x^6 + E^(4*x)*(-25*x + 5*x^2) + E^(3*x)*(250*x - 10 0*x^2 + 10*x^3) + E^(2*x)*(-1250*x + 750*x^2 - 150*x^3 + 10*x^4) + E^x*(31 25*x - 2500*x^2 + 750*x^3 - 100*x^4 + 5*x^5)),x]
-108*x + 54*x^2 - 12*x^3 + x^4 + E^16/(-5 + E^x + x)^4 + (4*E^12*(-3 + x)) /(-5 + E^x + x)^3 + (6*E^8*(-3 + x)^2)/(-5 + E^x + x)^2 + (4*E^4*(-3 + x)^ 3)/(-5 + E^x + x) + 108*Log[x] - (4*(E^12 + 3*E^(8 + x)*(-3 + x) + 3*E^(4 + 2*x)*(-3 + x)^2 + 6*E^(4 + x)*(-5 + x)*(-3 + x)^2 + E^(3*x)*x*(27 - 9*x + x^2) + 3*E^x*(-5 + x)^2*x*(27 - 9*x + x^2) + (-5 + x)^3*x*(27 - 9*x + x^ 2) + 3*E^8*(15 - 8*x + x^2) + 3*E^4*(15 - 8*x + x^2)^2 + 3*E^(2*x)*x*(-135 + 72*x - 14*x^2 + x^3))*Log[x])/(-5 + E^x + x)^3 + (6*(15 + E^4 + E^x*(-3 + x) - 8*x + x^2)^2*Log[x]^2)/(-5 + E^x + x)^2 - (4*(15 + E^4 + E^x*(-3 + x) - 8*x + x^2)*Log[x]^3)/(-5 + E^x + x) + Log[x]^4
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 {4 x^9-140 x^8+2144 x^7-18816 x^6+104008 x^5-374200 x^4+872000 x^3-1260000 x^2-4 e^{16} x+1012500 x+\left (-4 x^6+104 x^5-1100 x^4+6000 x^3-17500 x^2+25000 x+e^{5 x} (4-4 x)+e^{4 x} \left (-20 x^2+4 e^4 x+120 x-100\right )+e^4 \left (4 x^4-60 x^3+300 x^2-500 x\right )+e^{3 x} \left (-40 x^3+440 x^2-1400 x+e^4 \left (12 x^2-56 x\right )+1000\right )+e^{2 x} \left (-40 x^4+640 x^3-3600 x^2+8000 x+e^4 \left (12 x^3-108 x^2+240 x\right )-5000\right )+e^x \left (-20 x^5+420 x^4-3400 x^3+13000 x^2-22500 x+e^4 \left (4 x^4-48 x^3+180 x^2-200 x\right )+12500\right )-12500\right ) \log ^3(x)+\left (12 x^7-348 x^6+4236 x^5-27900 x^4+106500 x^3-232500 x^2+262500 x+e^{5 x} \left (12 x^2-48 x+36\right )+e^8 \left (-12 x^3+120 x^2-300 x\right )+e^4 \left (-36 x^4+600 x^3-3600 x^2+9000 x-7500\right )+e^{4 x} \left (60 x^3-540 x^2+1380 x+e^4 \left (-12 x^2+48 x-12\right )-900\right )+e^{3 x} \left (120 x^4-1680 x^3+8160 x^2-12 e^8 x-15600 x+e^4 \left (-36 x^3+324 x^2-792 x+240\right )+9000\right )+e^{2 x} \left (120 x^5-2280 x^4+16560 x^3-56400 x^2+87000 x+e^8 \left (108 x-24 x^2\right )+e^4 \left (-36 x^4+504 x^3-2484 x^2+4680 x-1800\right )-45000\right )+e^x \left (60 x^6-1440 x^5+13980 x^4-69600 x^3+184500 x^2-240000 x+e^8 \left (-12 x^3+96 x^2-180 x\right )+e^4 \left (-12 x^5+228 x^4-1740 x^3+6540 x^2-11400 x+6000\right )+112500\right )-112500\right ) \log ^2(x)+e^{12} \left (-8 x^3+52 x^2-40 x-100\right )+e^8 \left (-36 x^4+528 x^3-2760 x^2+6000 x-4500\right )+e^{5 x} \left (4 x^4-40 x^3+144 x^2-216 x+108\right )+e^4 \left (8 x^7-228 x^6+2712 x^5-17380 x^4+64440 x^3-137100 x^2+153000 x-67500\right )+e^{4 x} \left (20 x^5-300 x^4+1720 x^3-4680 x^2+5940 x+e^4 \left (-4 x^4+48 x^3-192 x^2+288 x-108\right )-2700\right )+e^{3 x} \left (40 x^6-800 x^5+6440 x^4-26560 x^3+58680 x^2-64800 x+e^8 \left (-12 x^3+84 x^2-156 x+36\right )+e^4 \left (-12 x^5+212 x^4-1404 x^3+4236 x^2-5544 x+2160\right )+27000\right )+e^{2 x} \left (40 x^7-1000 x^6+10440 x^5-58760 x^4+191480 x^3-358200 x^2+351000 x+e^{12} \left (-12 x^2+40 x-4\right )+e^8 \left (-24 x^4+288 x^3-1188 x^2+1800 x-540\right )+e^4 \left (-12 x^6+288 x^5-2760 x^4+13320 x^3-33444 x^2+39960 x-16200\right )-135000\right )+e^x \left (20 x^8-600 x^7+7720 x^6-55480 x^5+242640 x^4-657800 x^3+1071000 x^2-4 e^{16} x-945000 x+e^{12} \left (-12 x^3+92 x^2-192 x+40\right )+e^8 \left (-12 x^5+204 x^4-1368 x^3+4392 x^2-6300 x+2700\right )+e^4 \left (-4 x^7+132 x^6-1776 x^5+12584 x^4-50388 x^3+112740 x^2-127800 x+54000\right )+337500\right )+\left (-12 x^8+384 x^7-5280 x^6+40608 x^5-190200 x^4+552000 x^3-960000 x^2+900000 x+e^{12} \left (12 x^2-60 x\right )+e^{5 x} \left (-12 x^3+84 x^2-180 x+108\right )+e^8 \left (12 x^4-120 x^3+240 x^2+600 x-1500\right )+e^4 \left (-12 x^6+324 x^5-3504 x^4+19320 x^3-56700 x^2+82500 x-45000\right )+e^{4 x} \left (-60 x^4+720 x^3-3000 x^2+5040 x+e^4 \left (12 x^3-96 x^2+204 x-72\right )-2700\right )+e^{3 x} \left (-120 x^5+2040 x^4-13200 x^3+40080 x^2-55800 x+e^8 \left (24 x^2-84 x+12\right )+e^4 \left (36 x^4-480 x^3+2196 x^2-3720 x+1440\right )+27000\right )+e^{2 x} \left (-120 x^6+2640 x^5-23400 x^4+106080 x^3-256200 x^2+12 e^{12} x+306000 x+e^8 \left (48 x^3-396 x^2+864 x-180\right )+e^4 \left (36 x^5-684 x^4+5004 x^3-17028 x^2+25200 x-10800\right )-135000\right )+e^x \left (-60 x^7+1620 x^6-18300 x^5+111540 x^4-393300 x^3+793500 x^2-832500 x+e^{12} \left (12 x^2-48 x\right )+e^8 \left (24 x^4-300 x^3+1332 x^2-2340 x+900\right )+e^4 \left (12 x^6-312 x^5+3336 x^4-18384 x^3+53580 x^2-75000 x+36000\right )+337500\right )-337500\right ) \log (x)-337500}{x^6-25 x^5+250 x^4-1250 x^3+3125 x^2+e^{5 x} x-3125 x+e^{4 x} \left (5 x^2-25 x\right )+e^{3 x} \left (10 x^3-100 x^2+250 x\right )+e^{2 x} \left (10 x^4-150 x^3+750 x^2-1250 x\right )+e^x \left (5 x^5-100 x^4+750 x^3-2500 x^2+3125 x\right )} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {4 x^9-140 x^8+2144 x^7-18816 x^6+104008 x^5-374200 x^4+872000 x^3-1260000 x^2+\left (1012500-4 e^{16}\right ) x+\left (-4 x^6+104 x^5-1100 x^4+6000 x^3-17500 x^2+25000 x+e^{5 x} (4-4 x)+e^{4 x} \left (-20 x^2+4 e^4 x+120 x-100\right )+e^4 \left (4 x^4-60 x^3+300 x^2-500 x\right )+e^{3 x} \left (-40 x^3+440 x^2-1400 x+e^4 \left (12 x^2-56 x\right )+1000\right )+e^{2 x} \left (-40 x^4+640 x^3-3600 x^2+8000 x+e^4 \left (12 x^3-108 x^2+240 x\right )-5000\right )+e^x \left (-20 x^5+420 x^4-3400 x^3+13000 x^2-22500 x+e^4 \left (4 x^4-48 x^3+180 x^2-200 x\right )+12500\right )-12500\right ) \log ^3(x)+\left (12 x^7-348 x^6+4236 x^5-27900 x^4+106500 x^3-232500 x^2+262500 x+e^{5 x} \left (12 x^2-48 x+36\right )+e^8 \left (-12 x^3+120 x^2-300 x\right )+e^4 \left (-36 x^4+600 x^3-3600 x^2+9000 x-7500\right )+e^{4 x} \left (60 x^3-540 x^2+1380 x+e^4 \left (-12 x^2+48 x-12\right )-900\right )+e^{3 x} \left (120 x^4-1680 x^3+8160 x^2-12 e^8 x-15600 x+e^4 \left (-36 x^3+324 x^2-792 x+240\right )+9000\right )+e^{2 x} \left (120 x^5-2280 x^4+16560 x^3-56400 x^2+87000 x+e^8 \left (108 x-24 x^2\right )+e^4 \left (-36 x^4+504 x^3-2484 x^2+4680 x-1800\right )-45000\right )+e^x \left (60 x^6-1440 x^5+13980 x^4-69600 x^3+184500 x^2-240000 x+e^8 \left (-12 x^3+96 x^2-180 x\right )+e^4 \left (-12 x^5+228 x^4-1740 x^3+6540 x^2-11400 x+6000\right )+112500\right )-112500\right ) \log ^2(x)+e^{12} \left (-8 x^3+52 x^2-40 x-100\right )+e^8 \left (-36 x^4+528 x^3-2760 x^2+6000 x-4500\right )+e^{5 x} \left (4 x^4-40 x^3+144 x^2-216 x+108\right )+e^4 \left (8 x^7-228 x^6+2712 x^5-17380 x^4+64440 x^3-137100 x^2+153000 x-67500\right )+e^{4 x} \left (20 x^5-300 x^4+1720 x^3-4680 x^2+5940 x+e^4 \left (-4 x^4+48 x^3-192 x^2+288 x-108\right )-2700\right )+e^{3 x} \left (40 x^6-800 x^5+6440 x^4-26560 x^3+58680 x^2-64800 x+e^8 \left (-12 x^3+84 x^2-156 x+36\right )+e^4 \left (-12 x^5+212 x^4-1404 x^3+4236 x^2-5544 x+2160\right )+27000\right )+e^{2 x} \left (40 x^7-1000 x^6+10440 x^5-58760 x^4+191480 x^3-358200 x^2+351000 x+e^{12} \left (-12 x^2+40 x-4\right )+e^8 \left (-24 x^4+288 x^3-1188 x^2+1800 x-540\right )+e^4 \left (-12 x^6+288 x^5-2760 x^4+13320 x^3-33444 x^2+39960 x-16200\right )-135000\right )+e^x \left (20 x^8-600 x^7+7720 x^6-55480 x^5+242640 x^4-657800 x^3+1071000 x^2-4 e^{16} x-945000 x+e^{12} \left (-12 x^3+92 x^2-192 x+40\right )+e^8 \left (-12 x^5+204 x^4-1368 x^3+4392 x^2-6300 x+2700\right )+e^4 \left (-4 x^7+132 x^6-1776 x^5+12584 x^4-50388 x^3+112740 x^2-127800 x+54000\right )+337500\right )+\left (-12 x^8+384 x^7-5280 x^6+40608 x^5-190200 x^4+552000 x^3-960000 x^2+900000 x+e^{12} \left (12 x^2-60 x\right )+e^{5 x} \left (-12 x^3+84 x^2-180 x+108\right )+e^8 \left (12 x^4-120 x^3+240 x^2+600 x-1500\right )+e^4 \left (-12 x^6+324 x^5-3504 x^4+19320 x^3-56700 x^2+82500 x-45000\right )+e^{4 x} \left (-60 x^4+720 x^3-3000 x^2+5040 x+e^4 \left (12 x^3-96 x^2+204 x-72\right )-2700\right )+e^{3 x} \left (-120 x^5+2040 x^4-13200 x^3+40080 x^2-55800 x+e^8 \left (24 x^2-84 x+12\right )+e^4 \left (36 x^4-480 x^3+2196 x^2-3720 x+1440\right )+27000\right )+e^{2 x} \left (-120 x^6+2640 x^5-23400 x^4+106080 x^3-256200 x^2+12 e^{12} x+306000 x+e^8 \left (48 x^3-396 x^2+864 x-180\right )+e^4 \left (36 x^5-684 x^4+5004 x^3-17028 x^2+25200 x-10800\right )-135000\right )+e^x \left (-60 x^7+1620 x^6-18300 x^5+111540 x^4-393300 x^3+793500 x^2-832500 x+e^{12} \left (12 x^2-48 x\right )+e^8 \left (24 x^4-300 x^3+1332 x^2-2340 x+900\right )+e^4 \left (12 x^6-312 x^5+3336 x^4-18384 x^3+53580 x^2-75000 x+36000\right )+337500\right )-337500\right ) \log (x)-337500}{x^6-25 x^5+250 x^4-1250 x^3+3125 x^2+e^{5 x} x-3125 x+e^{4 x} \left (5 x^2-25 x\right )+e^{3 x} \left (10 x^3-100 x^2+250 x\right )+e^{2 x} \left (10 x^4-150 x^3+750 x^2-1250 x\right )+e^x \left (5 x^5-100 x^4+750 x^3-2500 x^2+3125 x\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (-2 e^x \left (x^2-6 x+5\right )-\left ((x-1) (x-5)^2\right )-e^{2 x} (x-1)+e^{x+4} x+e^4 x\right ) \left (x^2-8 x+e^x (x-3)-\left (x+e^x-5\right ) \log (x)+15 \left (1+\frac {e^4}{15}\right )\right )^3}{\left (-x-e^x+5\right )^5 x}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {\left ((1-x) (5-x)^2+e^{2 x} (1-x)+e^{x+4} x+e^4 x-2 e^x \left (x^2-6 x+5\right )\right ) \left (x^2-8 x-e^x (3-x)+\left (-x-e^x+5\right ) \log (x)+e^4+15\right )^3}{\left (-x-e^x+5\right )^5 x}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle 4 \int \frac {\left ((1-x) (5-x)^2+e^{2 x} (1-x)+e^{x+4} x+e^4 x-2 e^x \left (x^2-6 x+5\right )\right ) \left (x^2-8 x-e^x (3-x)+\left (-x-e^x+5\right ) \log (x)+15 \left (1+\frac {e^4}{15}\right )\right )^3}{\left (-x-e^x+5\right )^5 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {(x-1) (x-\log (x)-3)^3}{x}-\frac {e^4 \left (x^2-\log (x) x-6 x+3\right ) (x-\log (x)-3)^2}{x \left (x+e^x-5\right )}+\frac {e^{12} \left (3 x^2-3 \log (x) x-27 x+18 \log (x)+54 \left (1-\frac {e^4}{54}\right )\right )}{\left (-x-e^x+5\right )^4}+\frac {e^8 \left (-3 x^4+6 \log (x) x^3+36 x^3-3 \log ^2(x) x^2-54 \log (x) x^2-135 \left (1-\frac {e^4}{45}\right ) x^2+18 \log ^2(x) x+108 \left (1-\frac {e^4}{36}\right ) \log (x) x+162 \left (1-\frac {5 e^4}{81}\right ) x+e^4\right )}{\left (-x-e^x+5\right )^3 x}+\frac {e^4 (-x+\log (x)+3) \left (-x^4+2 \log (x) x^3+12 x^3-\log ^2(x) x^2-18 \log (x) x^2-45 \left (1-\frac {e^4}{15}\right ) x^2+6 \log ^2(x) x+36 \left (1-\frac {e^4}{12}\right ) \log (x) x+54 \left (1-\frac {2 e^4}{9}\right ) x+3 e^4\right )}{\left (-x-e^x+5\right )^2 x}+\frac {e^{16} (x-6)}{\left (x+e^x-5\right )^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \left (\frac {1}{4} (-x+\log (x)+3)^4-6 e^{16} \int \frac {1}{\left (x+e^x-5\right )^5}dx+e^{16} \int \frac {x}{\left (x+e^x-5\right )^5}dx+18 e^{12} \log (x) \int \frac {1}{\left (x+e^x-5\right )^4}dx+e^{12} \left (54-e^4\right ) \int \frac {1}{\left (x+e^x-5\right )^4}dx-3 e^{12} \log (x) \int \frac {x}{\left (x+e^x-5\right )^4}dx-27 e^{12} \int \frac {x}{\left (x+e^x-5\right )^4}dx+3 e^{12} \int \frac {x^2}{\left (x+e^x-5\right )^4}dx-3 e^8 \left (36-e^4\right ) \log (x) \int \frac {1}{\left (x+e^x-5\right )^3}dx-2 e^8 \left (81-5 e^4\right ) \int \frac {1}{\left (x+e^x-5\right )^3}dx-e^{12} \int \frac {1}{x \left (x+e^x-5\right )^3}dx+54 e^8 \log (x) \int \frac {x}{\left (x+e^x-5\right )^3}dx+3 e^8 \left (45-e^4\right ) \int \frac {x}{\left (x+e^x-5\right )^3}dx-6 e^8 \log (x) \int \frac {x^2}{\left (x+e^x-5\right )^3}dx-36 e^8 \int \frac {x^2}{\left (x+e^x-5\right )^3}dx+3 e^8 \int \frac {x^3}{\left (x+e^x-5\right )^3}dx+3 e^4 \left (54-7 e^4\right ) \log (x) \int \frac {1}{\left (x+e^x-5\right )^2}dx+3 e^4 \left (54-13 e^4\right ) \int \frac {1}{\left (x+e^x-5\right )^2}dx+3 e^8 \log (x) \int \frac {1}{x \left (x+e^x-5\right )^2}dx+9 e^8 \int \frac {1}{x \left (x+e^x-5\right )^2}dx-3 e^4 \left (45-2 e^4\right ) \log (x) \int \frac {x}{\left (x+e^x-5\right )^2}dx-21 e^4 \left (9-e^4\right ) \int \frac {x}{\left (x+e^x-5\right )^2}dx+36 e^4 \log (x) \int \frac {x^2}{\left (x+e^x-5\right )^2}dx+3 e^4 \left (27-e^4\right ) \int \frac {x^2}{\left (x+e^x-5\right )^2}dx-3 e^4 \log (x) \int \frac {x^3}{\left (x+e^x-5\right )^2}dx-15 e^4 \int \frac {x^3}{\left (x+e^x-5\right )^2}dx+e^4 \int \frac {x^4}{\left (x+e^x-5\right )^2}dx+51 e^4 \log (x) \int \frac {1}{x+e^x-5}dx+72 e^4 \int \frac {1}{x+e^x-5}dx-18 e^4 \log (x) \int \frac {1}{x \left (x+e^x-5\right )}dx-27 e^4 \int \frac {1}{x \left (x+e^x-5\right )}dx-24 e^4 \log (x) \int \frac {x}{x+e^x-5}dx-48 e^4 \int \frac {x}{x+e^x-5}dx+3 e^4 \log (x) \int \frac {x^2}{x+e^x-5}dx+12 e^4 \int \frac {x^2}{x+e^x-5}dx-e^4 \int \frac {x^3}{x+e^x-5}dx-18 e^8 \int \frac {\log ^2(x)}{\left (x+e^x-5\right )^3}dx+3 e^8 \int \frac {x \log ^2(x)}{\left (x+e^x-5\right )^3}dx+3 e^4 \left (18-e^4\right ) \int \frac {\log ^2(x)}{\left (x+e^x-5\right )^2}dx-27 e^4 \int \frac {x \log ^2(x)}{\left (x+e^x-5\right )^2}dx+3 e^4 \int \frac {x^2 \log ^2(x)}{\left (x+e^x-5\right )^2}dx+12 e^4 \int \frac {\log ^2(x)}{x+e^x-5}dx-3 e^4 \int \frac {\log ^2(x)}{x \left (x+e^x-5\right )}dx-3 e^4 \int \frac {x \log ^2(x)}{x+e^x-5}dx+6 e^4 \int \frac {\log ^3(x)}{\left (x+e^x-5\right )^2}dx-e^4 \int \frac {x \log ^3(x)}{\left (x+e^x-5\right )^2}dx+e^4 \int \frac {\log ^3(x)}{x+e^x-5}dx-18 e^{12} \int \frac {\int \frac {1}{\left (x+e^x-5\right )^4}dx}{x}dx+3 e^{12} \int \frac {\int \frac {x}{\left (x+e^x-5\right )^4}dx}{x}dx+3 e^8 \left (36-e^4\right ) \int \frac {\int \frac {1}{\left (x+e^x-5\right )^3}dx}{x}dx-54 e^8 \int \frac {\int \frac {x}{\left (x+e^x-5\right )^3}dx}{x}dx+6 e^8 \int \frac {\int \frac {x^2}{\left (x+e^x-5\right )^3}dx}{x}dx-3 e^4 \left (54-7 e^4\right ) \int \frac {\int \frac {1}{\left (x+e^x-5\right )^2}dx}{x}dx-3 e^8 \int \frac {\int \frac {1}{x \left (x+e^x-5\right )^2}dx}{x}dx+3 e^4 \left (45-2 e^4\right ) \int \frac {\int \frac {x}{\left (x+e^x-5\right )^2}dx}{x}dx-36 e^4 \int \frac {\int \frac {x^2}{\left (x+e^x-5\right )^2}dx}{x}dx+3 e^4 \int \frac {\int \frac {x^3}{\left (x+e^x-5\right )^2}dx}{x}dx-51 e^4 \int \frac {\int \frac {1}{x+e^x-5}dx}{x}dx+18 e^4 \int \frac {\int \frac {1}{x \left (x+e^x-5\right )}dx}{x}dx+24 e^4 \int \frac {\int \frac {x}{x+e^x-5}dx}{x}dx-3 e^4 \int \frac {\int \frac {x^2}{x+e^x-5}dx}{x}dx\right )\) |
Int[(-337500 + 1012500*x - 4*E^16*x - 1260000*x^2 + 872000*x^3 - 374200*x^ 4 + 104008*x^5 - 18816*x^6 + 2144*x^7 - 140*x^8 + 4*x^9 + E^12*(-100 - 40* x + 52*x^2 - 8*x^3) + E^8*(-4500 + 6000*x - 2760*x^2 + 528*x^3 - 36*x^4) + E^(5*x)*(108 - 216*x + 144*x^2 - 40*x^3 + 4*x^4) + E^4*(-67500 + 153000*x - 137100*x^2 + 64440*x^3 - 17380*x^4 + 2712*x^5 - 228*x^6 + 8*x^7) + E^(4 *x)*(-2700 + 5940*x - 4680*x^2 + 1720*x^3 - 300*x^4 + 20*x^5 + E^4*(-108 + 288*x - 192*x^2 + 48*x^3 - 4*x^4)) + E^(3*x)*(27000 - 64800*x + 58680*x^2 - 26560*x^3 + 6440*x^4 - 800*x^5 + 40*x^6 + E^8*(36 - 156*x + 84*x^2 - 12 *x^3) + E^4*(2160 - 5544*x + 4236*x^2 - 1404*x^3 + 212*x^4 - 12*x^5)) + E^ (2*x)*(-135000 + 351000*x - 358200*x^2 + 191480*x^3 - 58760*x^4 + 10440*x^ 5 - 1000*x^6 + 40*x^7 + E^12*(-4 + 40*x - 12*x^2) + E^8*(-540 + 1800*x - 1 188*x^2 + 288*x^3 - 24*x^4) + E^4*(-16200 + 39960*x - 33444*x^2 + 13320*x^ 3 - 2760*x^4 + 288*x^5 - 12*x^6)) + E^x*(337500 - 945000*x - 4*E^16*x + 10 71000*x^2 - 657800*x^3 + 242640*x^4 - 55480*x^5 + 7720*x^6 - 600*x^7 + 20* x^8 + E^12*(40 - 192*x + 92*x^2 - 12*x^3) + E^8*(2700 - 6300*x + 4392*x^2 - 1368*x^3 + 204*x^4 - 12*x^5) + E^4*(54000 - 127800*x + 112740*x^2 - 5038 8*x^3 + 12584*x^4 - 1776*x^5 + 132*x^6 - 4*x^7)) + (-337500 + 900000*x - 9 60000*x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x^6 + 384*x^7 - 12* x^8 + E^12*(-60*x + 12*x^2) + E^(5*x)*(108 - 180*x + 84*x^2 - 12*x^3) + E^ 8*(-1500 + 600*x + 240*x^2 - 120*x^3 + 12*x^4) + E^4*(-45000 + 82500*x - 5 6700*x^2 + 19320*x^3 - 3504*x^4 + 324*x^5 - 12*x^6) + E^(4*x)*(-2700 + 504 0*x - 3000*x^2 + 720*x^3 - 60*x^4 + E^4*(-72 + 204*x - 96*x^2 + 12*x^3)) + E^(3*x)*(27000 - 55800*x + 40080*x^2 - 13200*x^3 + 2040*x^4 - 120*x^5 + E ^8*(12 - 84*x + 24*x^2) + E^4*(1440 - 3720*x + 2196*x^2 - 480*x^3 + 36*x^4 )) + E^(2*x)*(-135000 + 306000*x + 12*E^12*x - 256200*x^2 + 106080*x^3 - 2 3400*x^4 + 2640*x^5 - 120*x^6 + E^8*(-180 + 864*x - 396*x^2 + 48*x^3) + E^ 4*(-10800 + 25200*x - 17028*x^2 + 5004*x^3 - 684*x^4 + 36*x^5)) + E^x*(337 500 - 832500*x + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x ^6 - 60*x^7 + E^12*(-48*x + 12*x^2) + E^8*(900 - 2340*x + 1332*x^2 - 300*x ^3 + 24*x^4) + E^4*(36000 - 75000*x + 53580*x^2 - 18384*x^3 + 3336*x^4 - 3 12*x^5 + 12*x^6)))*Log[x] + (-112500 + 262500*x - 232500*x^2 + 106500*x^3 - 27900*x^4 + 4236*x^5 - 348*x^6 + 12*x^7 + E^(5*x)*(36 - 48*x + 12*x^2) + E^8*(-300*x + 120*x^2 - 12*x^3) + E^4*(-7500 + 9000*x - 3600*x^2 + 600*x^ 3 - 36*x^4) + E^(4*x)*(-900 + 1380*x - 540*x^2 + 60*x^3 + E^4*(-12 + 48*x - 12*x^2)) + E^(3*x)*(9000 - 15600*x - 12*E^8*x + 8160*x^2 - 1680*x^3 + 12 0*x^4 + E^4*(240 - 792*x + 324*x^2 - 36*x^3)) + E^(2*x)*(-45000 + 87000*x - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 + E^8*(108*x - 24*x^2) + E^4* (-1800 + 4680*x - 2484*x^2 + 504*x^3 - 36*x^4)) + E^x*(112500 - 240000*x + 184500*x^2 - 69600*x^3 + 13980*x^4 - 1440*x^5 + 60*x^6 + E^8*(-180*x + 96 *x^2 - 12*x^3) + E^4*(6000 - 11400*x + 6540*x^2 - 1740*x^3 + 228*x^4 - 12* x^5)))*Log[x]^2 + (-12500 + E^(5*x)*(4 - 4*x) + 25000*x - 17500*x^2 + 6000 *x^3 - 1100*x^4 + 104*x^5 - 4*x^6 + E^(4*x)*(-100 + 120*x + 4*E^4*x - 20*x ^2) + E^4*(-500*x + 300*x^2 - 60*x^3 + 4*x^4) + E^(3*x)*(1000 - 1400*x + 4 40*x^2 - 40*x^3 + E^4*(-56*x + 12*x^2)) + E^(2*x)*(-5000 + 8000*x - 3600*x ^2 + 640*x^3 - 40*x^4 + E^4*(240*x - 108*x^2 + 12*x^3)) + E^x*(12500 - 225 00*x + 13000*x^2 - 3400*x^3 + 420*x^4 - 20*x^5 + E^4*(-200*x + 180*x^2 - 4 8*x^3 + 4*x^4)))*Log[x]^3)/(-3125*x + E^(5*x)*x + 3125*x^2 - 1250*x^3 + 25 0*x^4 - 25*x^5 + x^6 + E^(4*x)*(-25*x + 5*x^2) + E^(3*x)*(250*x - 100*x^2 + 10*x^3) + E^(2*x)*(-1250*x + 750*x^2 - 150*x^3 + 10*x^4) + E^x*(3125*x - 2500*x^2 + 750*x^3 - 100*x^4 + 5*x^5)),x]
3.25.49.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(953\) vs. \(2(19)=38\).
Time = 4.23 (sec) , antiderivative size = 954, normalized size of antiderivative = 45.43
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(954\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(2146\) |
int((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x^2-56* x)*exp(4)-40*x^3+440*x^2-1400*x+1000)*exp(x)^3+((12*x^3-108*x^2+240*x)*exp (4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+180*x^2-2 00*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x)+(4*x^ 4-60*x^3+300*x^2-500*x)*exp(4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500*x^2+2 5000*x-12500)*ln(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x-12)*exp(4) +60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x^2-792* x+240)*exp(4)+120*x^4-1680*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-24*x^2+1 08*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+120*x^5-2280* x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-180*x)*ex p(4)^2+(-12*x^5+228*x^4-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x^6-1440 *x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)+(-12*x^3+120*x ^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12*x^7-34 8*x^6+4236*x^5-27900*x^4+106500*x^3-232500*x^2+262500*x-112500)*ln(x)^2+(( -12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x-72)*exp(4)-60*x^4 +720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2+(36*x^4 -480*x^3+2196*x^2-3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+40080*x^2 -55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^2+864*x-180)*exp(4)^ 2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6+2640*x^ 5-23400*x^4+106080*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x^2-48*x) *exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4)^2+(12*x^6-312*x^5+33 36*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-18300*x^5 +111540*x^4-393300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2-60*x)*ex p(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^2+(-12*x^6+324*x^5-3504* x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280*x^6+4060 8*x^5-190200*x^4+552000*x^3-960000*x^2+900000*x-337500)*ln(x)+(4*x^4-40*x^ 3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-192*x^2+288*x-108)*exp(4)+20 *x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84*x^2-156* x+36)*exp(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*exp(4)+40*x ^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800*x+27000)*exp(x)^3+((-12*x^2+ 40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+(-12*x^6+2 88*x^5-2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7-1000*x^6+ 10440*x^5-58760*x^4+191480*x^3-358200*x^2+351000*x-135000)*exp(x)^2+(-4*x* exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368*x^3+4392 *x^2-6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-50388*x^3+11 2740*x^2-127800*x+54000)*exp(4)+20*x^8-600*x^7+7720*x^6-55480*x^5+242640*x ^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(-8*x^3+52* x^2-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp(4)^2+(8* x^7-228*x^6+2712*x^5-17380*x^4+64440*x^3-137100*x^2+153000*x-67500)*exp(4) +4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^3-1260000 *x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3-100*x^2+2 50*x)*exp(x)^3+(10*x^4-150*x^3+750*x^2-1250*x)*exp(x)^2+(5*x^5-100*x^4+750 *x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2-3125*x), x,method=_RETURNVERBOSE)
ln(x)^4-4*(x^2+exp(x)*x+exp(4)-8*x-3*exp(x)+15)/(exp(x)+x-5)*ln(x)^3+6*(x^ 4+2*exp(x)*x^3+exp(2*x)*x^2+2*x^2*exp(4)+2*x*exp(4+x)-16*x^3-22*exp(x)*x^2 -6*x*exp(2*x)+exp(8)-16*x*exp(4)-6*exp(4+x)+94*x^2+78*exp(x)*x+9*exp(2*x)+ 30*exp(4)-240*x-90*exp(x)+225)/(exp(x)+x-5)^2*ln(x)^2-4*(3375+3*x*exp(x+8) -5400*x+3*exp(2*x)*x^4-66*x^2*exp(4+x)-24*x*exp(8)-9*x^2*exp(3*x)-42*exp(2 *x)*x^3-48*x^3*exp(4)+27*x*exp(3*x)+216*exp(2*x)*x^2-486*x*exp(2*x)+282*x^ 2*exp(4)-57*exp(x)*x^4-1566*exp(x)*x^2+426*exp(x)*x^3+2835*exp(x)*x-9*exp( x+8)+exp(12)+27*exp(4+2*x)+234*x*exp(4+x)-270*exp(4+x)+3*x^4*exp(4)+45*exp (8)+3*x^5*exp(x)+x^3*exp(3*x)-720*x*exp(4)+6*x^3*exp(4+x)-27*exp(3*x)+405* exp(2*x)+675*exp(4)+x^6-24*x^5+237*x^4-1232*x^3+3555*x^2-2025*exp(x)+3*x^2 *exp(8)-18*x*exp(4+2*x)+3*x^2*exp(4+2*x))/(exp(x)+x-5)^3*ln(x)+(50625-96*x ^3*exp(8)+468*x*exp(x+8)-12*exp(x+12)+6*x^2*exp(2*x+8)+x^4*exp(4*x)-108000 *x+1194*exp(2*x)*x^4-6264*x^2*exp(4+x)-1440*x*exp(8)+4*x^7*exp(x)+108*x*ex p(4+3*x)-1512*x^2*exp(3*x)-5688*exp(2*x)*x^3-12*x^3*exp(4*x)-132*x^5*exp(2 *x)-4928*x^3*exp(4)+2484*x*exp(3*x)+15066*exp(2*x)*x^2-21060*x*exp(2*x)-10 8*x^6*exp(x)+14220*x^2*exp(4)-7772*exp(x)*x^4-64260*exp(x)*x^2+29004*exp(x )*x^3+78300*exp(x)*x+6*x^4*exp(8)-32*x*exp(12)+54*exp(2*x+8)-108*exp(4+3*x )-540*exp(x+8)+60*exp(12)-108*x*exp(4*x)+1620*exp(4+2*x)+11340*x*exp(4+x)- 8100*exp(4+x)+81*exp(4*x)+948*x^4*exp(4)-96*x^5*exp(4)+1350*exp(8)+exp(16) +4*x^6*exp(4)+1236*x^5*exp(x)+54*x^2*exp(4*x)+456*x^3*exp(3*x)-21600*x*...
Leaf count of result is larger than twice the leaf count of optimal. 1050 vs. \(2 (19) = 38\).
Time = 0.29 (sec) , antiderivative size = 1050, normalized size of antiderivative = 50.00 \[ \text {the integral} =\text {Too large to display} \]
integrate((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x ^2-56*x)*exp(4)-40*x^3+440*x^2-1400*x+1000)*exp(x)^3+((12*x^3-108*x^2+240* x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+180 *x^2-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x) +(4*x^4-60*x^3+300*x^2-500*x)*exp(4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500 *x^2+25000*x-12500)*log(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x-12) *exp(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x ^2-792*x+240)*exp(4)+120*x^4-1680*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-2 4*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+120*x^ 5-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-18 0*x)*exp(4)^2+(-12*x^5+228*x^4-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x ^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)+(-12*x^ 3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12 *x^7-348*x^6+4236*x^5-27900*x^4+106500*x^3-232500*x^2+262500*x-112500)*log (x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x-72)*exp(4 )-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2 +(36*x^4-480*x^3+2196*x^2-3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+4 0080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^2+864*x-180) *exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6 +2640*x^5-23400*x^4+106080*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x ^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4)^2+(12*x^6-31 2*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-1 8300*x^5+111540*x^4-393300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2- 60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^2+(-12*x^6+324*x ^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280* x^6+40608*x^5-190200*x^4+552000*x^3-960000*x^2+900000*x-337500)*log(x)+(4* x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-192*x^2+288*x-108)* exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84 *x^2-156*x+36)*exp(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*ex p(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800*x+27000)*exp(x)^3+( (-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+( -12*x^6+288*x^5-2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7- 1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+351000*x-135000)*exp(x) ^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368 *x^3+4392*x^2-6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-503 88*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-600*x^7+7720*x^6-55480*x^5 +242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(- 8*x^3+52*x^2-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp (4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^3-137100*x^2+153000*x-6750 0)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^ 3-1260000*x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3- 100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^2-1250*x)*exp(x)^2+(5*x^5-10 0*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2 -3125*x),x, algorithm=\
(x^8 - 32*x^7 + 444*x^6 - 3488*x^5 + (x^4 - 20*x^3 + 150*x^2 + 4*(x - 5)*e ^(3*x) + 6*(x^2 - 10*x + 25)*e^(2*x) + 4*(x^3 - 15*x^2 + 75*x - 125)*e^x - 500*x + e^(4*x) + 625)*log(x)^4 + 16885*x^4 - 4*(x^5 - 23*x^4 + 210*x^3 - 950*x^2 + (x^3 - 15*x^2 + 75*x - 125)*e^4 + (x - 3)*e^(4*x) + (4*x^2 - 32 *x + e^4 + 60)*e^(3*x) + 3*(2*x^3 - 26*x^2 + (x - 5)*e^4 + 110*x - 150)*e^ (2*x) + (4*x^4 - 72*x^3 + 480*x^2 + 3*(x^2 - 10*x + 25)*e^4 - 1400*x + 150 0)*e^x + 2125*x - 1875)*log(x)^3 - 50700*x^3 + 6*(x^6 - 26*x^5 + 279*x^4 - 1580*x^3 + 4975*x^2 + (x^2 - 10*x + 25)*e^8 + 2*(x^4 - 18*x^3 + 120*x^2 - 350*x + 375)*e^4 + (x^2 - 6*x + 9)*e^(4*x) + 2*(2*x^3 - 22*x^2 + (x - 3)* e^4 + 78*x - 90)*e^(3*x) + (6*x^4 - 96*x^3 + 564*x^2 + 6*(x^2 - 8*x + 15)* e^4 - 1440*x + e^8 + 1350)*e^(2*x) + 2*(2*x^5 - 42*x^4 + 348*x^3 - 1420*x^ 2 + (x - 5)*e^8 + 3*(x^3 - 13*x^2 + 55*x - 75)*e^4 + 2850*x - 2250)*e^x - 8250*x + 5625)*log(x)^2 + 87750*x^2 + 4*(x^2 - 8*x + 15)*e^12 + 6*(x^4 - 1 6*x^3 + 94*x^2 - 240*x + 225)*e^8 + 4*(x^6 - 24*x^5 + 237*x^4 - 1232*x^3 + 3555*x^2 - 5400*x + 3375)*e^4 + (x^4 - 12*x^3 + 54*x^2 - 108*x)*e^(4*x) + 4*(x^5 - 17*x^4 + 114*x^3 - 378*x^2 + (x^3 - 9*x^2 + 27*x - 27)*e^4 + 540 *x)*e^(3*x) + 6*(x^6 - 22*x^5 + 199*x^4 - 948*x^3 + 2430*x^2 + (x^2 - 6*x + 9)*e^8 + 2*(x^4 - 14*x^3 + 72*x^2 - 162*x + 135)*e^4 - 2700*x)*e^(2*x) + 4*(x^7 - 27*x^6 + 309*x^5 - 1943*x^4 + 7170*x^3 - 14850*x^2 + (x - 3)*e^1 2 + 3*(x^3 - 11*x^2 + 39*x - 45)*e^8 + 3*(x^5 - 19*x^4 + 142*x^3 - 522*...
Leaf count of result is larger than twice the leaf count of optimal. 1107 vs. \(2 (17) = 34\).
Time = 1.49 (sec) , antiderivative size = 1107, normalized size of antiderivative = 52.71 \[ \text {the integral} =\text {Too large to display} \]
integrate((((4-4*x)*exp(x)**5+(4*x*exp(4)-20*x**2+120*x-100)*exp(x)**4+((1 2*x**2-56*x)*exp(4)-40*x**3+440*x**2-1400*x+1000)*exp(x)**3+((12*x**3-108* x**2+240*x)*exp(4)-40*x**4+640*x**3-3600*x**2+8000*x-5000)*exp(x)**2+((4*x **4-48*x**3+180*x**2-200*x)*exp(4)-20*x**5+420*x**4-3400*x**3+13000*x**2-2 2500*x+12500)*exp(x)+(4*x**4-60*x**3+300*x**2-500*x)*exp(4)-4*x**6+104*x** 5-1100*x**4+6000*x**3-17500*x**2+25000*x-12500)*ln(x)**3+((12*x**2-48*x+36 )*exp(x)**5+((-12*x**2+48*x-12)*exp(4)+60*x**3-540*x**2+1380*x-900)*exp(x) **4+(-12*x*exp(4)**2+(-36*x**3+324*x**2-792*x+240)*exp(4)+120*x**4-1680*x* *3+8160*x**2-15600*x+9000)*exp(x)**3+((-24*x**2+108*x)*exp(4)**2+(-36*x**4 +504*x**3-2484*x**2+4680*x-1800)*exp(4)+120*x**5-2280*x**4+16560*x**3-5640 0*x**2+87000*x-45000)*exp(x)**2+((-12*x**3+96*x**2-180*x)*exp(4)**2+(-12*x **5+228*x**4-1740*x**3+6540*x**2-11400*x+6000)*exp(4)+60*x**6-1440*x**5+13 980*x**4-69600*x**3+184500*x**2-240000*x+112500)*exp(x)+(-12*x**3+120*x**2 -300*x)*exp(4)**2+(-36*x**4+600*x**3-3600*x**2+9000*x-7500)*exp(4)+12*x**7 -348*x**6+4236*x**5-27900*x**4+106500*x**3-232500*x**2+262500*x-112500)*ln (x)**2+((-12*x**3+84*x**2-180*x+108)*exp(x)**5+((12*x**3-96*x**2+204*x-72) *exp(4)-60*x**4+720*x**3-3000*x**2+5040*x-2700)*exp(x)**4+((24*x**2-84*x+1 2)*exp(4)**2+(36*x**4-480*x**3+2196*x**2-3720*x+1440)*exp(4)-120*x**5+2040 *x**4-13200*x**3+40080*x**2-55800*x+27000)*exp(x)**3+(12*x*exp(4)**3+(48*x **3-396*x**2+864*x-180)*exp(4)**2+(36*x**5-684*x**4+5004*x**3-17028*x**2+2 5200*x-10800)*exp(4)-120*x**6+2640*x**5-23400*x**4+106080*x**3-256200*x**2 +306000*x-135000)*exp(x)**2+((12*x**2-48*x)*exp(4)**3+(24*x**4-300*x**3+13 32*x**2-2340*x+900)*exp(4)**2+(12*x**6-312*x**5+3336*x**4-18384*x**3+53580 *x**2-75000*x+36000)*exp(4)-60*x**7+1620*x**6-18300*x**5+111540*x**4-39330 0*x**3+793500*x**2-832500*x+337500)*exp(x)+(12*x**2-60*x)*exp(4)**3+(12*x* *4-120*x**3+240*x**2+600*x-1500)*exp(4)**2+(-12*x**6+324*x**5-3504*x**4+19 320*x**3-56700*x**2+82500*x-45000)*exp(4)-12*x**8+384*x**7-5280*x**6+40608 *x**5-190200*x**4+552000*x**3-960000*x**2+900000*x-337500)*ln(x)+(4*x**4-4 0*x**3+144*x**2-216*x+108)*exp(x)**5+((-4*x**4+48*x**3-192*x**2+288*x-108) *exp(4)+20*x**5-300*x**4+1720*x**3-4680*x**2+5940*x-2700)*exp(x)**4+((-12* x**3+84*x**2-156*x+36)*exp(4)**2+(-12*x**5+212*x**4-1404*x**3+4236*x**2-55 44*x+2160)*exp(4)+40*x**6-800*x**5+6440*x**4-26560*x**3+58680*x**2-64800*x +27000)*exp(x)**3+((-12*x**2+40*x-4)*exp(4)**3+(-24*x**4+288*x**3-1188*x** 2+1800*x-540)*exp(4)**2+(-12*x**6+288*x**5-2760*x**4+13320*x**3-33444*x**2 +39960*x-16200)*exp(4)+40*x**7-1000*x**6+10440*x**5-58760*x**4+191480*x**3 -358200*x**2+351000*x-135000)*exp(x)**2+(-4*x*exp(4)**4+(-12*x**3+92*x**2- 192*x+40)*exp(4)**3+(-12*x**5+204*x**4-1368*x**3+4392*x**2-6300*x+2700)*ex p(4)**2+(-4*x**7+132*x**6-1776*x**5+12584*x**4-50388*x**3+112740*x**2-1278 00*x+54000)*exp(4)+20*x**8-600*x**7+7720*x**6-55480*x**5+242640*x**4-65780 0*x**3+1071000*x**2-945000*x+337500)*exp(x)-4*x*exp(4)**4+(-8*x**3+52*x**2 -40*x-100)*exp(4)**3+(-36*x**4+528*x**3-2760*x**2+6000*x-4500)*exp(4)**2+( 8*x**7-228*x**6+2712*x**5-17380*x**4+64440*x**3-137100*x**2+153000*x-67500 )*exp(4)+4*x**9-140*x**8+2144*x**7-18816*x**6+104008*x**5-374200*x**4+8720 00*x**3-1260000*x**2+1012500*x-337500)/(x*exp(x)**5+(5*x**2-25*x)*exp(x)** 4+(10*x**3-100*x**2+250*x)*exp(x)**3+(10*x**4-150*x**3+750*x**2-1250*x)*ex p(x)**2+(5*x**5-100*x**4+750*x**3-2500*x**2+3125*x)*exp(x)+x**6-25*x**5+25 0*x**4-1250*x**3+3125*x**2-3125*x),x)
x**4 - 12*x**3 + 54*x**2 - 108*x + (12 - 4*x)*log(x)**3 + (6*x**2 - 36*x + 54)*log(x)**2 + (-4*x**3 + 36*x**2 - 108*x)*log(x) + log(x)**4 + 108*log( x) + (4*x**6*exp(4) - 12*x**5*exp(4)*log(x) - 96*x**5*exp(4) + 12*x**4*exp (4)*log(x)**2 + 252*x**4*exp(4)*log(x) + 6*x**4*exp(8) + 948*x**4*exp(4) - 4*x**3*exp(4)*log(x)**3 - 216*x**3*exp(4)*log(x)**2 - 2088*x**3*exp(4)*lo g(x) - 12*x**3*exp(8)*log(x) - 96*x**3*exp(8) - 4928*x**3*exp(4) + 60*x**2 *exp(4)*log(x)**3 + 6*x**2*exp(8)*log(x)**2 + 1440*x**2*exp(4)*log(x)**2 + 156*x**2*exp(8)*log(x) + 8520*x**2*exp(4)*log(x) + 4*x**2*exp(12) + 14220 *x**2*exp(4) + 564*x**2*exp(8) - 300*x*exp(4)*log(x)**3 - 4200*x*exp(4)*lo g(x)**2 - 60*x*exp(8)*log(x)**2 - 660*x*exp(8)*log(x) - 17100*x*exp(4)*log (x) - 4*x*exp(12)*log(x) - 32*x*exp(12) - 1440*x*exp(8) - 21600*x*exp(4) + (4*x**3*exp(4) - 12*x**2*exp(4)*log(x) - 36*x**2*exp(4) + 12*x*exp(4)*log (x)**2 + 72*x*exp(4)*log(x) + 108*x*exp(4) - 4*exp(4)*log(x)**3 - 36*exp(4 )*log(x)**2 - 108*exp(4)*log(x) - 108*exp(4))*exp(3*x) + (12*x**4*exp(4) - 36*x**3*exp(4)*log(x) - 168*x**3*exp(4) + 36*x**2*exp(4)*log(x)**2 + 396* x**2*exp(4)*log(x) + 6*x**2*exp(8) + 864*x**2*exp(4) - 12*x*exp(4)*log(x)* *3 - 288*x*exp(4)*log(x)**2 - 1404*x*exp(4)*log(x) - 12*x*exp(8)*log(x) - 36*x*exp(8) - 1944*x*exp(4) + 60*exp(4)*log(x)**3 + 6*exp(8)*log(x)**2 + 5 40*exp(4)*log(x)**2 + 1620*exp(4)*log(x) + 36*exp(8)*log(x) + 1620*exp(4) + 54*exp(8))*exp(2*x) + (12*x**5*exp(4) - 36*x**4*exp(4)*log(x) - 228*x...
Leaf count of result is larger than twice the leaf count of optimal. 1075 vs. \(2 (19) = 38\).
Time = 0.74 (sec) , antiderivative size = 1075, normalized size of antiderivative = 51.19 \[ \text {the integral} =\text {Too large to display} \]
integrate((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x ^2-56*x)*exp(4)-40*x^3+440*x^2-1400*x+1000)*exp(x)^3+((12*x^3-108*x^2+240* x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+180 *x^2-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x) +(4*x^4-60*x^3+300*x^2-500*x)*exp(4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500 *x^2+25000*x-12500)*log(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x-12) *exp(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x ^2-792*x+240)*exp(4)+120*x^4-1680*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-2 4*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+120*x^ 5-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-18 0*x)*exp(4)^2+(-12*x^5+228*x^4-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x ^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)+(-12*x^ 3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12 *x^7-348*x^6+4236*x^5-27900*x^4+106500*x^3-232500*x^2+262500*x-112500)*log (x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x-72)*exp(4 )-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2 +(36*x^4-480*x^3+2196*x^2-3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+4 0080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^2+864*x-180) *exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6 +2640*x^5-23400*x^4+106080*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x ^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4)^2+(12*x^6-31 2*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-1 8300*x^5+111540*x^4-393300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2- 60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^2+(-12*x^6+324*x ^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280* x^6+40608*x^5-190200*x^4+552000*x^3-960000*x^2+900000*x-337500)*log(x)+(4* x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-192*x^2+288*x-108)* exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84 *x^2-156*x+36)*exp(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*ex p(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800*x+27000)*exp(x)^3+( (-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+( -12*x^6+288*x^5-2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7- 1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+351000*x-135000)*exp(x) ^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368 *x^3+4392*x^2-6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-503 88*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-600*x^7+7720*x^6-55480*x^5 +242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(- 8*x^3+52*x^2-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp (4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^3-137100*x^2+153000*x-6750 0)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^ 3-1260000*x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3- 100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^2-1250*x)*exp(x)^2+(5*x^5-10 0*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2 -3125*x),x, algorithm=\
(x^8 - 32*x^7 + 4*x^6*(e^4 + 111) - 32*x^5*(3*e^4 + 109) + x^4*(6*e^8 + 94 8*e^4 + 16885) + (x^4 - 20*x^3 + 150*x^2 - 500*x + 625)*log(x)^4 - 4*x^3*( 24*e^8 + 1232*e^4 + 12675) - 4*(x^5 - 23*x^4 + x^3*(e^4 + 210) - 5*x^2*(3* e^4 + 190) + 25*x*(3*e^4 + 85) - 125*e^4 - 1875)*log(x)^3 + 2*x^2*(2*e^12 + 282*e^8 + 7110*e^4 + 43875) + 6*(x^6 - 26*x^5 + x^4*(2*e^4 + 279) - 4*x^ 3*(9*e^4 + 395) + x^2*(e^8 + 240*e^4 + 4975) - 10*x*(e^8 + 70*e^4 + 825) + 25*e^8 + 750*e^4 + 5625)*log(x)^2 - 4*x*(8*e^12 + 360*e^8 + 5400*e^4 + 16 875) + (x^4 - 4*(x - 3)*log(x)^3 + log(x)^4 - 12*x^3 + 6*(x^2 - 6*x + 9)*l og(x)^2 + 54*x^2 - 4*(x^3 - 9*x^2 + 27*x - 27)*log(x) - 108*x)*e^(4*x) + 4 *(x^5 + (x - 5)*log(x)^4 - 17*x^4 + x^3*(e^4 + 114) - (4*x^2 - 32*x + e^4 + 60)*log(x)^3 - 9*x^2*(e^4 + 42) + 3*(2*x^3 - 22*x^2 + x*(e^4 + 78) - 3*e ^4 - 90)*log(x)^2 + 27*x*(e^4 + 20) - (4*x^4 - 56*x^3 + 3*x^2*(e^4 + 96) - 18*x*(e^4 + 36) + 27*e^4 + 540)*log(x) - 27*e^4)*e^(3*x) + 6*(x^6 - 22*x^ 5 + x^4*(2*e^4 + 199) + (x^2 - 10*x + 25)*log(x)^4 - 4*x^3*(7*e^4 + 237) - 2*(2*x^3 - 26*x^2 + x*(e^4 + 110) - 5*e^4 - 150)*log(x)^3 + x^2*(e^8 + 14 4*e^4 + 2430) + (6*x^4 - 96*x^3 + 6*x^2*(e^4 + 94) - 48*x*(e^4 + 30) + e^8 + 90*e^4 + 1350)*log(x)^2 - 6*x*(e^8 + 54*e^4 + 450) - 2*(2*x^5 - 38*x^4 + x^3*(3*e^4 + 284) - 3*x^2*(11*e^4 + 348) + x*(e^8 + 117*e^4 + 1890) - 3* e^8 - 135*e^4 - 1350)*log(x) + 9*e^8 + 270*e^4)*e^(2*x) + 4*(x^7 - 27*x^6 + 3*x^5*(e^4 + 103) - x^4*(57*e^4 + 1943) + (x^3 - 15*x^2 + 75*x - 125)...
Leaf count of result is larger than twice the leaf count of optimal. 6815 vs. \(2 (19) = 38\).
Time = 0.99 (sec) , antiderivative size = 6815, normalized size of antiderivative = 324.52 \[ \text {the integral} =\text {Too large to display} \]
integrate((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x ^2-56*x)*exp(4)-40*x^3+440*x^2-1400*x+1000)*exp(x)^3+((12*x^3-108*x^2+240* x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+180 *x^2-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x) +(4*x^4-60*x^3+300*x^2-500*x)*exp(4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500 *x^2+25000*x-12500)*log(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x-12) *exp(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x ^2-792*x+240)*exp(4)+120*x^4-1680*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-2 4*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+120*x^ 5-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-18 0*x)*exp(4)^2+(-12*x^5+228*x^4-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x ^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)+(-12*x^ 3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12 *x^7-348*x^6+4236*x^5-27900*x^4+106500*x^3-232500*x^2+262500*x-112500)*log (x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x-72)*exp(4 )-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2 +(36*x^4-480*x^3+2196*x^2-3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+4 0080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^2+864*x-180) *exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6 +2640*x^5-23400*x^4+106080*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x ^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4)^2+(12*x^6-31 2*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-1 8300*x^5+111540*x^4-393300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2- 60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^2+(-12*x^6+324*x ^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280* x^6+40608*x^5-190200*x^4+552000*x^3-960000*x^2+900000*x-337500)*log(x)+(4* x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-192*x^2+288*x-108)* exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84 *x^2-156*x+36)*exp(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*ex p(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800*x+27000)*exp(x)^3+( (-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+( -12*x^6+288*x^5-2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7- 1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+351000*x-135000)*exp(x) ^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368 *x^3+4392*x^2-6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-503 88*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-600*x^7+7720*x^6-55480*x^5 +242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(- 8*x^3+52*x^2-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp (4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^3-137100*x^2+153000*x-6750 0)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^ 3-1260000*x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3- 100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^2-1250*x)*exp(x)^2+(5*x^5-10 0*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2 -3125*x),x, algorithm=\
(x^19 + 4*x^18*e^x - 4*x^18*log(x) - 16*x^17*e^x*log(x) + 6*x^17*log(x)^2 + 24*x^16*e^x*log(x)^2 - 4*x^16*log(x)^3 - 16*x^15*e^x*log(x)^3 + x^15*log (x)^4 + 4*x^14*e^x*log(x)^4 - 74*x^18 + 4*x^17*e^4 + 6*x^17*e^(2*x) - 276* x^17*e^x + 284*x^17*log(x) - 12*x^16*e^4*log(x) - 24*x^16*e^(2*x)*log(x) + 1056*x^16*e^x*log(x) - 408*x^16*log(x)^2 + 12*x^15*e^4*log(x)^2 + 36*x^15 *e^(2*x)*log(x)^2 - 1512*x^15*e^x*log(x)^2 + 260*x^15*log(x)^3 - 4*x^14*e^ 4*log(x)^3 - 24*x^14*e^(2*x)*log(x)^3 + 960*x^14*e^x*log(x)^3 - 62*x^14*lo g(x)^4 + 6*x^13*e^(2*x)*log(x)^4 - 228*x^13*e^x*log(x)^4 + 2544*x^17 - 264 *x^16*e^4 + 4*x^16*e^(3*x) - 384*x^16*e^(2*x) + 12*x^16*e^(x + 4) + 8796*x ^16*e^x - 9324*x^16*log(x) + 756*x^15*e^4*log(x) - 16*x^15*e^(3*x)*log(x) + 1464*x^15*e^(2*x)*log(x) - 36*x^15*e^(x + 4)*log(x) - 32016*x^15*e^x*log (x) + 12762*x^15*log(x)^2 - 720*x^14*e^4*log(x)^2 + 24*x^14*e^(3*x)*log(x) ^2 - 2088*x^14*e^(2*x)*log(x)^2 + 36*x^14*e^(x + 4)*log(x)^2 + 43488*x^14* e^x*log(x)^2 - 7728*x^14*log(x)^3 + 228*x^13*e^4*log(x)^3 - 16*x^13*e^(3*x )*log(x)^3 + 1320*x^13*e^(2*x)*log(x)^3 - 12*x^13*e^(x + 4)*log(x)^3 - 261 12*x^13*e^x*log(x)^3 + 1746*x^13*log(x)^4 + 4*x^12*e^(3*x)*log(x)^4 - 312* x^12*e^(2*x)*log(x)^4 + 5844*x^12*e^x*log(x)^4 - 53888*x^16 + 6*x^15*e^8 + 8004*x^15*e^4 + x^15*e^(4*x) - 236*x^15*e^(3*x) + 11274*x^15*e^(2*x) + 12 *x^15*e^(2*x + 4) - 732*x^15*e^(x + 4) - 171572*x^15*e^x + 187580*x^15*log (x) - 12*x^14*e^8*log(x) - 21744*x^14*e^4*log(x) - 4*x^14*e^(4*x)*log(x...
Timed out. \[ \text {the integral} =\text {Too large to display} \]
int(-(log(x)^2*(exp(3*x)*(15600*x + 12*x*exp(8) + exp(4)*(792*x - 324*x^2 + 36*x^3 - 240) - 8160*x^2 + 1680*x^3 - 120*x^4 - 9000) - exp(5*x)*(12*x^2 - 48*x + 36) - 262500*x + exp(8)*(300*x - 120*x^2 + 12*x^3) + exp(4*x)*(e xp(4)*(12*x^2 - 48*x + 12) - 1380*x + 540*x^2 - 60*x^3 + 900) - exp(2*x)*( 87000*x + exp(8)*(108*x - 24*x^2) - exp(4)*(2484*x^2 - 4680*x - 504*x^3 + 36*x^4 + 1800) - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 - 45000) + exp (4)*(3600*x^2 - 9000*x - 600*x^3 + 36*x^4 + 7500) + exp(x)*(240000*x + exp (8)*(180*x - 96*x^2 + 12*x^3) + exp(4)*(11400*x - 6540*x^2 + 1740*x^3 - 22 8*x^4 + 12*x^5 - 6000) - 184500*x^2 + 69600*x^3 - 13980*x^4 + 1440*x^5 - 6 0*x^6 - 112500) + 232500*x^2 - 106500*x^3 + 27900*x^4 - 4236*x^5 + 348*x^6 - 12*x^7 + 112500) - 1012500*x + exp(3*x)*(64800*x + exp(8)*(156*x - 84*x ^2 + 12*x^3 - 36) + exp(4)*(5544*x - 4236*x^2 + 1404*x^3 - 212*x^4 + 12*x^ 5 - 2160) - 58680*x^2 + 26560*x^3 - 6440*x^4 + 800*x^5 - 40*x^6 - 27000) + 4*x*exp(16) - exp(4)*(153000*x - 137100*x^2 + 64440*x^3 - 17380*x^4 + 271 2*x^5 - 228*x^6 + 8*x^7 - 67500) + exp(4*x)*(exp(4)*(192*x^2 - 288*x - 48* x^3 + 4*x^4 + 108) - 5940*x + 4680*x^2 - 1720*x^3 + 300*x^4 - 20*x^5 + 270 0) + exp(12)*(40*x - 52*x^2 + 8*x^3 + 100) - exp(5*x)*(144*x^2 - 216*x - 4 0*x^3 + 4*x^4 + 108) - log(x)*(900000*x - exp(4)*(56700*x^2 - 82500*x - 19 320*x^3 + 3504*x^4 - 324*x^5 + 12*x^6 + 45000) - exp(12)*(60*x - 12*x^2) - exp(5*x)*(180*x - 84*x^2 + 12*x^3 - 108) + exp(2*x)*(306000*x + 12*x*exp( 12) + exp(8)*(864*x - 396*x^2 + 48*x^3 - 180) + exp(4)*(25200*x - 17028*x^ 2 + 5004*x^3 - 684*x^4 + 36*x^5 - 10800) - 256200*x^2 + 106080*x^3 - 23400 *x^4 + 2640*x^5 - 120*x^6 - 135000) + exp(3*x)*(exp(8)*(24*x^2 - 84*x + 12 ) - 55800*x + exp(4)*(2196*x^2 - 3720*x - 480*x^3 + 36*x^4 + 1440) + 40080 *x^2 - 13200*x^3 + 2040*x^4 - 120*x^5 + 27000) + exp(x)*(exp(4)*(53580*x^2 - 75000*x - 18384*x^3 + 3336*x^4 - 312*x^5 + 12*x^6 + 36000) - 832500*x - exp(12)*(48*x - 12*x^2) + exp(8)*(1332*x^2 - 2340*x - 300*x^3 + 24*x^4 + 900) + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x^6 - 60*x^ 7 + 337500) + exp(8)*(600*x + 240*x^2 - 120*x^3 + 12*x^4 - 1500) - 960000* x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x^6 + 384*x^7 - 12*x^8 + exp(4*x)*(5040*x + exp(4)*(204*x - 96*x^2 + 12*x^3 - 72) - 3000*x^2 + 720* x^3 - 60*x^4 - 2700) - 337500) + exp(8)*(2760*x^2 - 6000*x - 528*x^3 + 36* x^4 + 4500) + exp(x)*(945000*x + 4*x*exp(16) + exp(4)*(127800*x - 112740*x ^2 + 50388*x^3 - 12584*x^4 + 1776*x^5 - 132*x^6 + 4*x^7 - 54000) + exp(12) *(192*x - 92*x^2 + 12*x^3 - 40) + exp(8)*(6300*x - 4392*x^2 + 1368*x^3 - 2 04*x^4 + 12*x^5 - 2700) - 1071000*x^2 + 657800*x^3 - 242640*x^4 + 55480*x^ 5 - 7720*x^6 + 600*x^7 - 20*x^8 - 337500) + 1260000*x^2 - 872000*x^3 + 374 200*x^4 - 104008*x^5 + 18816*x^6 - 2144*x^7 + 140*x^8 - 4*x^9 + log(x)^3*( exp(3*x)*(1400*x + exp(4)*(56*x - 12*x^2) - 440*x^2 + 40*x^3 - 1000) - exp (4*x)*(120*x + 4*x*exp(4) - 20*x^2 - 100) - 25000*x + exp(4)*(500*x - 300* x^2 + 60*x^3 - 4*x^4) + exp(5*x)*(4*x - 4) + 17500*x^2 - 6000*x^3 + 1100*x ^4 - 104*x^5 + 4*x^6 - exp(2*x)*(8000*x + exp(4)*(240*x - 108*x^2 + 12*x^3 ) - 3600*x^2 + 640*x^3 - 40*x^4 - 5000) + exp(x)*(22500*x + exp(4)*(200*x - 180*x^2 + 48*x^3 - 4*x^4) - 13000*x^2 + 3400*x^3 - 420*x^4 + 20*x^5 - 12 500) + 12500) + exp(2*x)*(exp(4)*(33444*x^2 - 39960*x - 13320*x^3 + 2760*x ^4 - 288*x^5 + 12*x^6 + 16200) - 351000*x + exp(12)*(12*x^2 - 40*x + 4) + exp(8)*(1188*x^2 - 1800*x - 288*x^3 + 24*x^4 + 540) + 358200*x^2 - 191480* x^3 + 58760*x^4 - 10440*x^5 + 1000*x^6 - 40*x^7 + 135000) + 337500)/(x*exp (5*x) - exp(4*x)*(25*x - 5*x^2) - 3125*x + exp(3*x)*(250*x - 100*x^2 + 10* x^3) + exp(x)*(3125*x - 2500*x^2 + 750*x^3 - 100*x^4 + 5*x^5) - exp(2*x)*( 1250*x - 750*x^2 + 150*x^3 - 10*x^4) + 3125*x^2 - 1250*x^3 + 250*x^4 - 25* x^5 + x^6),x)
int(-(log(x)^2*(exp(3*x)*(15600*x + 12*x*exp(8) + exp(4)*(792*x - 324*x^2 + 36*x^3 - 240) - 8160*x^2 + 1680*x^3 - 120*x^4 - 9000) - exp(5*x)*(12*x^2 - 48*x + 36) - 262500*x + exp(8)*(300*x - 120*x^2 + 12*x^3) + exp(4*x)*(e xp(4)*(12*x^2 - 48*x + 12) - 1380*x + 540*x^2 - 60*x^3 + 900) - exp(2*x)*( 87000*x + exp(8)*(108*x - 24*x^2) - exp(4)*(2484*x^2 - 4680*x - 504*x^3 + 36*x^4 + 1800) - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 - 45000) + exp (4)*(3600*x^2 - 9000*x - 600*x^3 + 36*x^4 + 7500) + exp(x)*(240000*x + exp (8)*(180*x - 96*x^2 + 12*x^3) + exp(4)*(11400*x - 6540*x^2 + 1740*x^3 - 22 8*x^4 + 12*x^5 - 6000) - 184500*x^2 + 69600*x^3 - 13980*x^4 + 1440*x^5 - 6 0*x^6 - 112500) + 232500*x^2 - 106500*x^3 + 27900*x^4 - 4236*x^5 + 348*x^6 - 12*x^7 + 112500) - 1012500*x + exp(3*x)*(64800*x + exp(8)*(156*x - 84*x ^2 + 12*x^3 - 36) + exp(4)*(5544*x - 4236*x^2 + 1404*x^3 - 212*x^4 + 12*x^ 5 - 2160) - 58680*x^2 + 26560*x^3 - 6440*x^4 + 800*x^5 - 40*x^6 - 27000) + 4*x*exp(16) - exp(4)*(153000*x - 137100*x^2 + 64440*x^3 - 17380*x^4 + 271 2*x^5 - 228*x^6 + 8*x^7 - 67500) + exp(4*x)*(exp(4)*(192*x^2 - 288*x - 48* x^3 + 4*x^4 + 108) - 5940*x + 4680*x^2 - 1720*x^3 + 300*x^4 - 20*x^5 + 270 0) + exp(12)*(40*x - 52*x^2 + 8*x^3 + 100) - exp(5*x)*(144*x^2 - 216*x - 4 0*x^3 + 4*x^4 + 108) - log(x)*(900000*x - exp(4)*(56700*x^2 - 82500*x - 19 320*x^3 + 3504*x^4 - 324*x^5 + 12*x^6 + 45000) - exp(12)*(60*x - 12*x^2) - exp(5*x)*(180*x - 84*x^2 + 12*x^3 - 108) + exp(2*x)*(306000*x + 12*x*e...