Integrand size = 493, antiderivative size = 31 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x}{2-\frac {x^2}{\left (-\left (-23+e^{1+2 x}-x\right )^2+x\right )^2}} \] Output:
x/(2-x^2/(x-(exp(1+2*x)-x-23)^2)^2)
Leaf count is larger than twice the leaf count of optimal. \(115\) vs. \(2(31)=62\).
Time = 10.18 (sec) , antiderivative size = 115, normalized size of antiderivative = 3.71 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x \left (529+e^{2+4 x}+45 x+x^2-2 e^{1+2 x} (23+x)\right )^2}{559682+2 e^{4+8 x}+95220 x+6165 x^2+180 x^3+2 x^4-8 e^{3+6 x} (23+x)+4 e^{2+4 x} \left (1587+137 x+3 x^2\right )-8 e^{1+2 x} \left (12167+1564 x+68 x^2+x^3\right )} \] Input:
Integrate[(156621970562 + 2*E^(8 + 16*x) + E^(7 + 14*x)*(-368 - 16*x) + 53 292920040*x + 7984703253*x^2 + 687869280*x^3 + 37265659*x^4 + 1300140*x^5 + 28529*x^6 + 360*x^7 + 2*x^8 + E^(6 + 12*x)*(29624 + 2568*x + 56*x^2) + E ^(5 + 10*x)*(-1362704 - 176640*x - 7680*x^2 - 112*x^3) + E^(4 + 8*x)*(3917 7740 + 6750040*x + 438853*x^2 + 12752*x^3 + 140*x^4) + E^(3 + 6*x)*(-72087 0416 - 154764240*x - 13374316*x^2 - 580936*x^3 - 12696*x^4 - 112*x^5) + E^ (2 + 4*x)*(8290009784 + 2129030328*x + 229267542*x^2 + 13236768*x^3 + 4322 90*x^4 + 7584*x^5 + 56*x^6) + E^(1 + 2*x)*(-54477207152 - 16271075104*x - 2096082092*x^2 - 150849272*x^3 - 6550112*x^4 - 171720*x^5 - 2520*x^6 - 16* x^7))/(313243941124 + 4*E^(8 + 16*x) + E^(7 + 14*x)*(-736 - 32*x) + 106585 840080*x + 15967727460*x^2 + 1375548120*x^3 + 74525153*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + E^(6 + 12*x)*(59248 + 5136*x + 112*x^2) + E ^(5 + 10*x)*(-2725408 - 353280*x - 15360*x^2 - 224*x^3) + E^(4 + 8*x)*(783 55480 + 13500080*x + 877700*x^2 + 25520*x^3 + 280*x^4) + E^(3 + 6*x)*(-144 1740832 - 309528480*x - 26748080*x^2 - 1162960*x^3 - 25440*x^4 - 224*x^5) + E^(2 + 4*x)*(16580019568 + 4258060656*x + 458516040*x^2 + 26497832*x^3 + 866760*x^4 + 15216*x^5 + 112*x^6) + E^(1 + 2*x)*(-108954414304 - 32542150 208*x - 4191872176*x^2 - 301868192*x^3 - 13124704*x^4 - 344528*x^5 - 5056* x^6 - 32*x^7)),x]
Output:
(x*(529 + E^(2 + 4*x) + 45*x + x^2 - 2*E^(1 + 2*x)*(23 + x))^2)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))
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.
| \(\displaystyle \int \frac {2 x^8+360 x^7+28529 x^6+1300140 x^5+37265659 x^4+687869280 x^3+7984703253 x^2+e^{12 x+6} \left (56 x^2+2568 x+29624\right )+e^{10 x+5} \left (-112 x^3-7680 x^2-176640 x-1362704\right )+e^{8 x+4} \left (140 x^4+12752 x^3+438853 x^2+6750040 x+39177740\right )+e^{6 x+3} \left (-112 x^5-12696 x^4-580936 x^3-13374316 x^2-154764240 x-720870416\right )+e^{4 x+2} \left (56 x^6+7584 x^5+432290 x^4+13236768 x^3+229267542 x^2+2129030328 x+8290009784\right )+e^{2 x+1} \left (-16 x^7-2520 x^6-171720 x^5-6550112 x^4-150849272 x^3-2096082092 x^2-16271075104 x-54477207152\right )+53292920040 x+2 e^{16 x+8}+e^{14 x+7} (-16 x-368)+156621970562}{4 x^8+720 x^7+57060 x^6+2600280 x^5+74525153 x^4+1375548120 x^3+15967727460 x^2+e^{12 x+6} \left (112 x^2+5136 x+59248\right )+e^{10 x+5} \left (-224 x^3-15360 x^2-353280 x-2725408\right )+e^{8 x+4} \left (280 x^4+25520 x^3+877700 x^2+13500080 x+78355480\right )+e^{6 x+3} \left (-224 x^5-25440 x^4-1162960 x^3-26748080 x^2-309528480 x-1441740832\right )+e^{4 x+2} \left (112 x^6+15216 x^5+866760 x^4+26497832 x^3+458516040 x^2+4258060656 x+16580019568\right )+e^{2 x+1} \left (-32 x^7-5056 x^6-344528 x^5-13124704 x^4-301868192 x^3-4191872176 x^2-32542150208 x-108954414304\right )+106585840080 x+4 e^{16 x+8}+e^{14 x+7} (-32 x-736)+313243941124} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {2 x^8+360 x^7+28529 x^6+1300140 x^5+37265659 x^4+687869280 x^3+7984703253 x^2+e^{12 x+6} \left (56 x^2+2568 x+29624\right )+e^{10 x+5} \left (-112 x^3-7680 x^2-176640 x-1362704\right )+e^{8 x+4} \left (140 x^4+12752 x^3+438853 x^2+6750040 x+39177740\right )+e^{6 x+3} \left (-112 x^5-12696 x^4-580936 x^3-13374316 x^2-154764240 x-720870416\right )+e^{4 x+2} \left (56 x^6+7584 x^5+432290 x^4+13236768 x^3+229267542 x^2+2129030328 x+8290009784\right )+e^{2 x+1} \left (-16 x^7-2520 x^6-171720 x^5-6550112 x^4-150849272 x^3-2096082092 x^2-16271075104 x-54477207152\right )+53292920040 x+2 e^{16 x+8}+e^{14 x+7} (-16 x-368)+156621970562}{\left (2 x^4-8 e^{2 x+1} x^3+180 x^3-544 e^{2 x+1} x^2+12 e^{4 x+2} x^2+6165 x^2-12512 e^{2 x+1} x+548 e^{4 x+2} x-8 e^{6 x+3} x+95220 x-97336 e^{2 x+1}+6348 e^{4 x+2}-184 e^{6 x+3}+2 e^{8 x+4}+559682\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (8 x^4-24 e^{2 x+1} x^3+716 x^3-1620 e^{2 x+1} x^2+24 e^{4 x+2} x^2+24390 x^2-36992 e^{2 x+1} x+1084 e^{4 x+2} x-8 e^{6 x+3} x+374715 x-285752 e^{2 x+1}+12422 e^{4 x+2}-180 e^{6 x+3}+2191118\right ) x^3}{\left (2 x^4-8 e^{2 x+1} x^3+180 x^3-544 e^{2 x+1} x^2+12 e^{4 x+2} x^2+6165 x^2-12512 e^{2 x+1} x+548 e^{4 x+2} x-8 e^{6 x+3} x+95220 x-97336 e^{2 x+1}+6348 e^{4 x+2}-184 e^{6 x+3}+2 e^{8 x+4}+559682\right )^2}-\frac {(8 x-3) x^2}{2 \left (2 x^4-8 e^{2 x+1} x^3+180 x^3-544 e^{2 x+1} x^2+12 e^{4 x+2} x^2+6165 x^2-12512 e^{2 x+1} x+548 e^{4 x+2} x-8 e^{6 x+3} x+95220 x-97336 e^{2 x+1}+6348 e^{4 x+2}-184 e^{6 x+3}+2 e^{8 x+4}+559682\right )}+\frac {1}{2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {\left (8 x^4-24 e^{2 x+1} x^3+716 x^3-1620 e^{2 x+1} x^2+24 e^{4 x+2} x^2+24390 x^2-36992 e^{2 x+1} x+1084 e^{4 x+2} x-8 e^{6 x+3} x+374715 x-285752 e^{2 x+1}+12422 e^{4 x+2}-180 e^{6 x+3}+2191118\right ) x^3}{\left (2 x^4-8 e^{2 x+1} x^3+180 x^3-544 e^{2 x+1} x^2+12 e^{4 x+2} x^2+6165 x^2-12512 e^{2 x+1} x+548 e^{4 x+2} x-8 e^{6 x+3} x+95220 x-97336 e^{2 x+1}+6348 e^{4 x+2}-184 e^{6 x+3}+2 e^{8 x+4}+559682\right )^2}-\frac {(8 x-3) x^2}{2 \left (2 x^4-8 e^{2 x+1} x^3+180 x^3-544 e^{2 x+1} x^2+12 e^{4 x+2} x^2+6165 x^2-12512 e^{2 x+1} x+548 e^{4 x+2} x-8 e^{6 x+3} x+95220 x-97336 e^{2 x+1}+6348 e^{4 x+2}-184 e^{6 x+3}+2 e^{8 x+4}+559682\right )}+\frac {1}{2}\right )dx\) |
Input:
Int[(156621970562 + 2*E^(8 + 16*x) + E^(7 + 14*x)*(-368 - 16*x) + 53292920 040*x + 7984703253*x^2 + 687869280*x^3 + 37265659*x^4 + 1300140*x^5 + 2852 9*x^6 + 360*x^7 + 2*x^8 + E^(6 + 12*x)*(29624 + 2568*x + 56*x^2) + E^(5 + 10*x)*(-1362704 - 176640*x - 7680*x^2 - 112*x^3) + E^(4 + 8*x)*(39177740 + 6750040*x + 438853*x^2 + 12752*x^3 + 140*x^4) + E^(3 + 6*x)*(-720870416 - 154764240*x - 13374316*x^2 - 580936*x^3 - 12696*x^4 - 112*x^5) + E^(2 + 4 *x)*(8290009784 + 2129030328*x + 229267542*x^2 + 13236768*x^3 + 432290*x^4 + 7584*x^5 + 56*x^6) + E^(1 + 2*x)*(-54477207152 - 16271075104*x - 209608 2092*x^2 - 150849272*x^3 - 6550112*x^4 - 171720*x^5 - 2520*x^6 - 16*x^7))/ (313243941124 + 4*E^(8 + 16*x) + E^(7 + 14*x)*(-736 - 32*x) + 106585840080 *x + 15967727460*x^2 + 1375548120*x^3 + 74525153*x^4 + 2600280*x^5 + 57060 *x^6 + 720*x^7 + 4*x^8 + E^(6 + 12*x)*(59248 + 5136*x + 112*x^2) + E^(5 + 10*x)*(-2725408 - 353280*x - 15360*x^2 - 224*x^3) + E^(4 + 8*x)*(78355480 + 13500080*x + 877700*x^2 + 25520*x^3 + 280*x^4) + E^(3 + 6*x)*(-144174083 2 - 309528480*x - 26748080*x^2 - 1162960*x^3 - 25440*x^4 - 224*x^5) + E^(2 + 4*x)*(16580019568 + 4258060656*x + 458516040*x^2 + 26497832*x^3 + 86676 0*x^4 + 15216*x^5 + 112*x^6) + E^(1 + 2*x)*(-108954414304 - 32542150208*x - 4191872176*x^2 - 301868192*x^3 - 13124704*x^4 - 344528*x^5 - 5056*x^6 - 32*x^7)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(123\) vs. \(2(30)=60\).
Time = 10.18 (sec) , antiderivative size = 124, normalized size of antiderivative = 4.00
| method | result | size |
| risch | \(\frac {x}{2}+\frac {x^{3}}{4 \,{\mathrm e}^{8 x +4}-16 \,{\mathrm e}^{6 x +3} x +24 \,{\mathrm e}^{4 x +2} x^{2}-16 x^{3} {\mathrm e}^{1+2 x}+4 x^{4}-368 \,{\mathrm e}^{6 x +3}+1096 \,{\mathrm e}^{4 x +2} x -1088 x^{2} {\mathrm e}^{1+2 x}+360 x^{3}+12696 \,{\mathrm e}^{4 x +2}-25024 x \,{\mathrm e}^{1+2 x}+12330 x^{2}-194672 \,{\mathrm e}^{1+2 x}+190440 x +1119364}\) | \(124\) |
| parallelrisch | \(\frac {559682 x +6348 \,{\mathrm e}^{4 x +2} x +2 \,{\mathrm e}^{8 x +4} x -8 \,{\mathrm e}^{6 x +3} x^{2}+12 \,{\mathrm e}^{4 x +2} x^{3}-184 \,{\mathrm e}^{6 x +3} x +548 \,{\mathrm e}^{4 x +2} x^{2}-97336 x \,{\mathrm e}^{1+2 x}+180 x^{4}+6166 x^{3}+95220 x^{2}+2 x^{5}-8 x^{4} {\mathrm e}^{1+2 x}-12512 x^{2} {\mathrm e}^{1+2 x}-544 x^{3} {\mathrm e}^{1+2 x}}{4 \,{\mathrm e}^{8 x +4}-16 \,{\mathrm e}^{6 x +3} x +24 \,{\mathrm e}^{4 x +2} x^{2}-16 x^{3} {\mathrm e}^{1+2 x}+4 x^{4}-368 \,{\mathrm e}^{6 x +3}+1096 \,{\mathrm e}^{4 x +2} x -1088 x^{2} {\mathrm e}^{1+2 x}+360 x^{3}+12696 \,{\mathrm e}^{4 x +2}-25024 x \,{\mathrm e}^{1+2 x}+12330 x^{2}-194672 \,{\mathrm e}^{1+2 x}+190440 x +1119364}\) | \(267\) |
Input:
int((2*exp(1+2*x)^8+(-16*x-368)*exp(1+2*x)^7+(56*x^2+2568*x+29624)*exp(1+2 *x)^6+(-112*x^3-7680*x^2-176640*x-1362704)*exp(1+2*x)^5+(140*x^4+12752*x^3 +438853*x^2+6750040*x+39177740)*exp(1+2*x)^4+(-112*x^5-12696*x^4-580936*x^ 3-13374316*x^2-154764240*x-720870416)*exp(1+2*x)^3+(56*x^6+7584*x^5+432290 *x^4+13236768*x^3+229267542*x^2+2129030328*x+8290009784)*exp(1+2*x)^2+(-16 *x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^2-16271075 104*x-54477207152)*exp(1+2*x)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37265659 *x^4+687869280*x^3+7984703253*x^2+53292920040*x+156621970562)/(4*exp(1+2*x )^8+(-32*x-736)*exp(1+2*x)^7+(112*x^2+5136*x+59248)*exp(1+2*x)^6+(-224*x^3 -15360*x^2-353280*x-2725408)*exp(1+2*x)^5+(280*x^4+25520*x^3+877700*x^2+13 500080*x+78355480)*exp(1+2*x)^4+(-224*x^5-25440*x^4-1162960*x^3-26748080*x ^2-309528480*x-1441740832)*exp(1+2*x)^3+(112*x^6+15216*x^5+866760*x^4+2649 7832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(1+2*x)^2+(-32*x^7-505 6*x^6-344528*x^5-13124704*x^4-301868192*x^3-4191872176*x^2-32542150208*x-1 08954414304)*exp(1+2*x)+4*x^8+720*x^7+57060*x^6+2600280*x^5+74525153*x^4+1 375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x,method=_RETUR NVERBOSE)
Output:
1/2*x+1/2*x^3/(2*exp(8*x+4)-8*exp(6*x+3)*x+12*exp(4*x+2)*x^2-8*x^3*exp(1+2 *x)+2*x^4-184*exp(6*x+3)+548*exp(4*x+2)*x-544*x^2*exp(1+2*x)+180*x^3+6348* exp(4*x+2)-12512*x*exp(1+2*x)+6165*x^2-97336*exp(1+2*x)+95220*x+559682)
Leaf count of result is larger than twice the leaf count of optimal. 173 vs. \(2 (30) = 60\).
Time = 0.09 (sec) , antiderivative size = 173, normalized size of antiderivative = 5.58 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x^{5} + 90 \, x^{4} + 3083 \, x^{3} + 47610 \, x^{2} + x e^{\left (8 \, x + 4\right )} - 4 \, {\left (x^{2} + 23 \, x\right )} e^{\left (6 \, x + 3\right )} + 2 \, {\left (3 \, x^{3} + 137 \, x^{2} + 1587 \, x\right )} e^{\left (4 \, x + 2\right )} - 4 \, {\left (x^{4} + 68 \, x^{3} + 1564 \, x^{2} + 12167 \, x\right )} e^{\left (2 \, x + 1\right )} + 279841 \, x}{2 \, x^{4} + 180 \, x^{3} + 6165 \, x^{2} - 8 \, {\left (x + 23\right )} e^{\left (6 \, x + 3\right )} + 4 \, {\left (3 \, x^{2} + 137 \, x + 1587\right )} e^{\left (4 \, x + 2\right )} - 8 \, {\left (x^{3} + 68 \, x^{2} + 1564 \, x + 12167\right )} e^{\left (2 \, x + 1\right )} + 95220 \, x + 2 \, e^{\left (8 \, x + 4\right )} + 559682} \] Input:
integrate((2*exp(1+2*x)^8+(-16*x-368)*exp(1+2*x)^7+(56*x^2+2568*x+29624)*e xp(1+2*x)^6+(-112*x^3-7680*x^2-176640*x-1362704)*exp(1+2*x)^5+(140*x^4+127 52*x^3+438853*x^2+6750040*x+39177740)*exp(1+2*x)^4+(-112*x^5-12696*x^4-580 936*x^3-13374316*x^2-154764240*x-720870416)*exp(1+2*x)^3+(56*x^6+7584*x^5+ 432290*x^4+13236768*x^3+229267542*x^2+2129030328*x+8290009784)*exp(1+2*x)^ 2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^2-16 271075104*x-54477207152)*exp(1+2*x)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37 265659*x^4+687869280*x^3+7984703253*x^2+53292920040*x+156621970562)/(4*exp (1+2*x)^8+(-32*x-736)*exp(1+2*x)^7+(112*x^2+5136*x+59248)*exp(1+2*x)^6+(-2 24*x^3-15360*x^2-353280*x-2725408)*exp(1+2*x)^5+(280*x^4+25520*x^3+877700* x^2+13500080*x+78355480)*exp(1+2*x)^4+(-224*x^5-25440*x^4-1162960*x^3-2674 8080*x^2-309528480*x-1441740832)*exp(1+2*x)^3+(112*x^6+15216*x^5+866760*x^ 4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(1+2*x)^2+(-32*x ^7-5056*x^6-344528*x^5-13124704*x^4-301868192*x^3-4191872176*x^2-325421502 08*x-108954414304)*exp(1+2*x)+4*x^8+720*x^7+57060*x^6+2600280*x^5+74525153 *x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x, algori thm="fricas")
Output:
(x^5 + 90*x^4 + 3083*x^3 + 47610*x^2 + x*e^(8*x + 4) - 4*(x^2 + 23*x)*e^(6 *x + 3) + 2*(3*x^3 + 137*x^2 + 1587*x)*e^(4*x + 2) - 4*(x^4 + 68*x^3 + 156 4*x^2 + 12167*x)*e^(2*x + 1) + 279841*x)/(2*x^4 + 180*x^3 + 6165*x^2 - 8*( x + 23)*e^(6*x + 3) + 4*(3*x^2 + 137*x + 1587)*e^(4*x + 2) - 8*(x^3 + 68*x ^2 + 1564*x + 12167)*e^(2*x + 1) + 95220*x + 2*e^(8*x + 4) + 559682)
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (20) = 40\).
Time = 0.47 (sec) , antiderivative size = 88, normalized size of antiderivative = 2.84 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x^{3}}{4 x^{4} + 360 x^{3} + 12330 x^{2} + 190440 x + \left (- 16 x - 368\right ) e^{6 x + 3} + \left (24 x^{2} + 1096 x + 12696\right ) e^{4 x + 2} + \left (- 16 x^{3} - 1088 x^{2} - 25024 x - 194672\right ) e^{2 x + 1} + 4 e^{8 x + 4} + 1119364} + \frac {x}{2} \] Input:
integrate((2*exp(1+2*x)**8+(-16*x-368)*exp(1+2*x)**7+(56*x**2+2568*x+29624 )*exp(1+2*x)**6+(-112*x**3-7680*x**2-176640*x-1362704)*exp(1+2*x)**5+(140* x**4+12752*x**3+438853*x**2+6750040*x+39177740)*exp(1+2*x)**4+(-112*x**5-1 2696*x**4-580936*x**3-13374316*x**2-154764240*x-720870416)*exp(1+2*x)**3+( 56*x**6+7584*x**5+432290*x**4+13236768*x**3+229267542*x**2+2129030328*x+82 90009784)*exp(1+2*x)**2+(-16*x**7-2520*x**6-171720*x**5-6550112*x**4-15084 9272*x**3-2096082092*x**2-16271075104*x-54477207152)*exp(1+2*x)+2*x**8+360 *x**7+28529*x**6+1300140*x**5+37265659*x**4+687869280*x**3+7984703253*x**2 +53292920040*x+156621970562)/(4*exp(1+2*x)**8+(-32*x-736)*exp(1+2*x)**7+(1 12*x**2+5136*x+59248)*exp(1+2*x)**6+(-224*x**3-15360*x**2-353280*x-2725408 )*exp(1+2*x)**5+(280*x**4+25520*x**3+877700*x**2+13500080*x+78355480)*exp( 1+2*x)**4+(-224*x**5-25440*x**4-1162960*x**3-26748080*x**2-309528480*x-144 1740832)*exp(1+2*x)**3+(112*x**6+15216*x**5+866760*x**4+26497832*x**3+4585 16040*x**2+4258060656*x+16580019568)*exp(1+2*x)**2+(-32*x**7-5056*x**6-344 528*x**5-13124704*x**4-301868192*x**3-4191872176*x**2-32542150208*x-108954 414304)*exp(1+2*x)+4*x**8+720*x**7+57060*x**6+2600280*x**5+74525153*x**4+1 375548120*x**3+15967727460*x**2+106585840080*x+313243941124),x)
Output:
x**3/(4*x**4 + 360*x**3 + 12330*x**2 + 190440*x + (-16*x - 368)*exp(6*x + 3) + (24*x**2 + 1096*x + 12696)*exp(4*x + 2) + (-16*x**3 - 1088*x**2 - 250 24*x - 194672)*exp(2*x + 1) + 4*exp(8*x + 4) + 1119364) + x/2
Leaf count of result is larger than twice the leaf count of optimal. 204 vs. \(2 (30) = 60\).
Time = 1.03 (sec) , antiderivative size = 204, normalized size of antiderivative = 6.58 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x^{5} + 90 \, x^{4} + 3083 \, x^{3} + 47610 \, x^{2} - 4 \, {\left (x^{2} e^{3} + 23 \, x e^{3}\right )} e^{\left (6 \, x\right )} + 2 \, {\left (3 \, x^{3} e^{2} + 137 \, x^{2} e^{2} + 1587 \, x e^{2}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (x^{4} e + 68 \, x^{3} e + 1564 \, x^{2} e + 12167 \, x e\right )} e^{\left (2 \, x\right )} + x e^{\left (8 \, x + 4\right )} + 279841 \, x}{2 \, x^{4} + 180 \, x^{3} + 6165 \, x^{2} - 8 \, {\left (x e^{3} + 23 \, e^{3}\right )} e^{\left (6 \, x\right )} + 4 \, {\left (3 \, x^{2} e^{2} + 137 \, x e^{2} + 1587 \, e^{2}\right )} e^{\left (4 \, x\right )} - 8 \, {\left (x^{3} e + 68 \, x^{2} e + 1564 \, x e + 12167 \, e\right )} e^{\left (2 \, x\right )} + 95220 \, x + 2 \, e^{\left (8 \, x + 4\right )} + 559682} \] Input:
integrate((2*exp(1+2*x)^8+(-16*x-368)*exp(1+2*x)^7+(56*x^2+2568*x+29624)*e xp(1+2*x)^6+(-112*x^3-7680*x^2-176640*x-1362704)*exp(1+2*x)^5+(140*x^4+127 52*x^3+438853*x^2+6750040*x+39177740)*exp(1+2*x)^4+(-112*x^5-12696*x^4-580 936*x^3-13374316*x^2-154764240*x-720870416)*exp(1+2*x)^3+(56*x^6+7584*x^5+ 432290*x^4+13236768*x^3+229267542*x^2+2129030328*x+8290009784)*exp(1+2*x)^ 2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^2-16 271075104*x-54477207152)*exp(1+2*x)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37 265659*x^4+687869280*x^3+7984703253*x^2+53292920040*x+156621970562)/(4*exp (1+2*x)^8+(-32*x-736)*exp(1+2*x)^7+(112*x^2+5136*x+59248)*exp(1+2*x)^6+(-2 24*x^3-15360*x^2-353280*x-2725408)*exp(1+2*x)^5+(280*x^4+25520*x^3+877700* x^2+13500080*x+78355480)*exp(1+2*x)^4+(-224*x^5-25440*x^4-1162960*x^3-2674 8080*x^2-309528480*x-1441740832)*exp(1+2*x)^3+(112*x^6+15216*x^5+866760*x^ 4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(1+2*x)^2+(-32*x ^7-5056*x^6-344528*x^5-13124704*x^4-301868192*x^3-4191872176*x^2-325421502 08*x-108954414304)*exp(1+2*x)+4*x^8+720*x^7+57060*x^6+2600280*x^5+74525153 *x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x, algori thm="maxima")
Output:
(x^5 + 90*x^4 + 3083*x^3 + 47610*x^2 - 4*(x^2*e^3 + 23*x*e^3)*e^(6*x) + 2* (3*x^3*e^2 + 137*x^2*e^2 + 1587*x*e^2)*e^(4*x) - 4*(x^4*e + 68*x^3*e + 156 4*x^2*e + 12167*x*e)*e^(2*x) + x*e^(8*x + 4) + 279841*x)/(2*x^4 + 180*x^3 + 6165*x^2 - 8*(x*e^3 + 23*e^3)*e^(6*x) + 4*(3*x^2*e^2 + 137*x*e^2 + 1587* e^2)*e^(4*x) - 8*(x^3*e + 68*x^2*e + 1564*x*e + 12167*e)*e^(2*x) + 95220*x + 2*e^(8*x + 4) + 559682)
Leaf count of result is larger than twice the leaf count of optimal. 242 vs. \(2 (30) = 60\).
Time = 2.78 (sec) , antiderivative size = 242, normalized size of antiderivative = 7.81 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {2 \, x^{5} - 8 \, x^{4} e^{\left (2 \, x + 1\right )} + 180 \, x^{4} + 12 \, x^{3} e^{\left (4 \, x + 2\right )} - 544 \, x^{3} e^{\left (2 \, x + 1\right )} + 6167 \, x^{3} - 8 \, x^{2} e^{\left (6 \, x + 3\right )} + 548 \, x^{2} e^{\left (4 \, x + 2\right )} - 12512 \, x^{2} e^{\left (2 \, x + 1\right )} + 95220 \, x^{2} + 2 \, x e^{\left (8 \, x + 4\right )} - 184 \, x e^{\left (6 \, x + 3\right )} + 6348 \, x e^{\left (4 \, x + 2\right )} - 97336 \, x e^{\left (2 \, x + 1\right )} + 559682 \, x}{2 \, {\left (2 \, x^{4} - 8 \, x^{3} e^{\left (2 \, x + 1\right )} + 180 \, x^{3} + 12 \, x^{2} e^{\left (4 \, x + 2\right )} - 544 \, x^{2} e^{\left (2 \, x + 1\right )} + 6165 \, x^{2} - 8 \, x e^{\left (6 \, x + 3\right )} + 548 \, x e^{\left (4 \, x + 2\right )} - 12512 \, x e^{\left (2 \, x + 1\right )} + 95220 \, x + 2 \, e^{\left (8 \, x + 4\right )} - 184 \, e^{\left (6 \, x + 3\right )} + 6348 \, e^{\left (4 \, x + 2\right )} - 97336 \, e^{\left (2 \, x + 1\right )} + 559682\right )}} \] Input:
integrate((2*exp(1+2*x)^8+(-16*x-368)*exp(1+2*x)^7+(56*x^2+2568*x+29624)*e xp(1+2*x)^6+(-112*x^3-7680*x^2-176640*x-1362704)*exp(1+2*x)^5+(140*x^4+127 52*x^3+438853*x^2+6750040*x+39177740)*exp(1+2*x)^4+(-112*x^5-12696*x^4-580 936*x^3-13374316*x^2-154764240*x-720870416)*exp(1+2*x)^3+(56*x^6+7584*x^5+ 432290*x^4+13236768*x^3+229267542*x^2+2129030328*x+8290009784)*exp(1+2*x)^ 2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^2-16 271075104*x-54477207152)*exp(1+2*x)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37 265659*x^4+687869280*x^3+7984703253*x^2+53292920040*x+156621970562)/(4*exp (1+2*x)^8+(-32*x-736)*exp(1+2*x)^7+(112*x^2+5136*x+59248)*exp(1+2*x)^6+(-2 24*x^3-15360*x^2-353280*x-2725408)*exp(1+2*x)^5+(280*x^4+25520*x^3+877700* x^2+13500080*x+78355480)*exp(1+2*x)^4+(-224*x^5-25440*x^4-1162960*x^3-2674 8080*x^2-309528480*x-1441740832)*exp(1+2*x)^3+(112*x^6+15216*x^5+866760*x^ 4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(1+2*x)^2+(-32*x ^7-5056*x^6-344528*x^5-13124704*x^4-301868192*x^3-4191872176*x^2-325421502 08*x-108954414304)*exp(1+2*x)+4*x^8+720*x^7+57060*x^6+2600280*x^5+74525153 *x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x, algori thm="giac")
Output:
1/2*(2*x^5 - 8*x^4*e^(2*x + 1) + 180*x^4 + 12*x^3*e^(4*x + 2) - 544*x^3*e^ (2*x + 1) + 6167*x^3 - 8*x^2*e^(6*x + 3) + 548*x^2*e^(4*x + 2) - 12512*x^2 *e^(2*x + 1) + 95220*x^2 + 2*x*e^(8*x + 4) - 184*x*e^(6*x + 3) + 6348*x*e^ (4*x + 2) - 97336*x*e^(2*x + 1) + 559682*x)/(2*x^4 - 8*x^3*e^(2*x + 1) + 1 80*x^3 + 12*x^2*e^(4*x + 2) - 544*x^2*e^(2*x + 1) + 6165*x^2 - 8*x*e^(6*x + 3) + 548*x*e^(4*x + 2) - 12512*x*e^(2*x + 1) + 95220*x + 2*e^(8*x + 4) - 184*e^(6*x + 3) + 6348*e^(4*x + 2) - 97336*e^(2*x + 1) + 559682)
Timed out. \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\int \frac {53292920040\,x+2\,{\mathrm {e}}^{16\,x+8}-{\mathrm {e}}^{14\,x+7}\,\left (16\,x+368\right )-{\mathrm {e}}^{6\,x+3}\,\left (112\,x^5+12696\,x^4+580936\,x^3+13374316\,x^2+154764240\,x+720870416\right )+{\mathrm {e}}^{12\,x+6}\,\left (56\,x^2+2568\,x+29624\right )-{\mathrm {e}}^{2\,x+1}\,\left (16\,x^7+2520\,x^6+171720\,x^5+6550112\,x^4+150849272\,x^3+2096082092\,x^2+16271075104\,x+54477207152\right )-{\mathrm {e}}^{10\,x+5}\,\left (112\,x^3+7680\,x^2+176640\,x+1362704\right )+{\mathrm {e}}^{4\,x+2}\,\left (56\,x^6+7584\,x^5+432290\,x^4+13236768\,x^3+229267542\,x^2+2129030328\,x+8290009784\right )+7984703253\,x^2+687869280\,x^3+37265659\,x^4+1300140\,x^5+28529\,x^6+360\,x^7+2\,x^8+{\mathrm {e}}^{8\,x+4}\,\left (140\,x^4+12752\,x^3+438853\,x^2+6750040\,x+39177740\right )+156621970562}{106585840080\,x+4\,{\mathrm {e}}^{16\,x+8}-{\mathrm {e}}^{14\,x+7}\,\left (32\,x+736\right )+{\mathrm {e}}^{4\,x+2}\,\left (112\,x^6+15216\,x^5+866760\,x^4+26497832\,x^3+458516040\,x^2+4258060656\,x+16580019568\right )+{\mathrm {e}}^{12\,x+6}\,\left (112\,x^2+5136\,x+59248\right )-{\mathrm {e}}^{6\,x+3}\,\left (224\,x^5+25440\,x^4+1162960\,x^3+26748080\,x^2+309528480\,x+1441740832\right )-{\mathrm {e}}^{2\,x+1}\,\left (32\,x^7+5056\,x^6+344528\,x^5+13124704\,x^4+301868192\,x^3+4191872176\,x^2+32542150208\,x+108954414304\right )-{\mathrm {e}}^{10\,x+5}\,\left (224\,x^3+15360\,x^2+353280\,x+2725408\right )+15967727460\,x^2+1375548120\,x^3+74525153\,x^4+2600280\,x^5+57060\,x^6+720\,x^7+4\,x^8+{\mathrm {e}}^{8\,x+4}\,\left (280\,x^4+25520\,x^3+877700\,x^2+13500080\,x+78355480\right )+313243941124} \,d x \] Input:
int((53292920040*x + 2*exp(16*x + 8) - exp(14*x + 7)*(16*x + 368) - exp(6* x + 3)*(154764240*x + 13374316*x^2 + 580936*x^3 + 12696*x^4 + 112*x^5 + 72 0870416) + exp(12*x + 6)*(2568*x + 56*x^2 + 29624) - exp(2*x + 1)*(1627107 5104*x + 2096082092*x^2 + 150849272*x^3 + 6550112*x^4 + 171720*x^5 + 2520* x^6 + 16*x^7 + 54477207152) - exp(10*x + 5)*(176640*x + 7680*x^2 + 112*x^3 + 1362704) + exp(4*x + 2)*(2129030328*x + 229267542*x^2 + 13236768*x^3 + 432290*x^4 + 7584*x^5 + 56*x^6 + 8290009784) + 7984703253*x^2 + 687869280* x^3 + 37265659*x^4 + 1300140*x^5 + 28529*x^6 + 360*x^7 + 2*x^8 + exp(8*x + 4)*(6750040*x + 438853*x^2 + 12752*x^3 + 140*x^4 + 39177740) + 1566219705 62)/(106585840080*x + 4*exp(16*x + 8) - exp(14*x + 7)*(32*x + 736) + exp(4 *x + 2)*(4258060656*x + 458516040*x^2 + 26497832*x^3 + 866760*x^4 + 15216* x^5 + 112*x^6 + 16580019568) + exp(12*x + 6)*(5136*x + 112*x^2 + 59248) - exp(6*x + 3)*(309528480*x + 26748080*x^2 + 1162960*x^3 + 25440*x^4 + 224*x ^5 + 1441740832) - exp(2*x + 1)*(32542150208*x + 4191872176*x^2 + 30186819 2*x^3 + 13124704*x^4 + 344528*x^5 + 5056*x^6 + 32*x^7 + 108954414304) - ex p(10*x + 5)*(353280*x + 15360*x^2 + 224*x^3 + 2725408) + 15967727460*x^2 + 1375548120*x^3 + 74525153*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + exp(8*x + 4)*(13500080*x + 877700*x^2 + 25520*x^3 + 280*x^4 + 78355480) + 313243941124),x)
Output:
int((53292920040*x + 2*exp(16*x + 8) - exp(14*x + 7)*(16*x + 368) - exp(6* x + 3)*(154764240*x + 13374316*x^2 + 580936*x^3 + 12696*x^4 + 112*x^5 + 72 0870416) + exp(12*x + 6)*(2568*x + 56*x^2 + 29624) - exp(2*x + 1)*(1627107 5104*x + 2096082092*x^2 + 150849272*x^3 + 6550112*x^4 + 171720*x^5 + 2520* x^6 + 16*x^7 + 54477207152) - exp(10*x + 5)*(176640*x + 7680*x^2 + 112*x^3 + 1362704) + exp(4*x + 2)*(2129030328*x + 229267542*x^2 + 13236768*x^3 + 432290*x^4 + 7584*x^5 + 56*x^6 + 8290009784) + 7984703253*x^2 + 687869280* x^3 + 37265659*x^4 + 1300140*x^5 + 28529*x^6 + 360*x^7 + 2*x^8 + exp(8*x + 4)*(6750040*x + 438853*x^2 + 12752*x^3 + 140*x^4 + 39177740) + 1566219705 62)/(106585840080*x + 4*exp(16*x + 8) - exp(14*x + 7)*(32*x + 736) + exp(4 *x + 2)*(4258060656*x + 458516040*x^2 + 26497832*x^3 + 866760*x^4 + 15216* x^5 + 112*x^6 + 16580019568) + exp(12*x + 6)*(5136*x + 112*x^2 + 59248) - exp(6*x + 3)*(309528480*x + 26748080*x^2 + 1162960*x^3 + 25440*x^4 + 224*x ^5 + 1441740832) - exp(2*x + 1)*(32542150208*x + 4191872176*x^2 + 30186819 2*x^3 + 13124704*x^4 + 344528*x^5 + 5056*x^6 + 32*x^7 + 108954414304) - ex p(10*x + 5)*(353280*x + 15360*x^2 + 224*x^3 + 2725408) + 15967727460*x^2 + 1375548120*x^3 + 74525153*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + exp(8*x + 4)*(13500080*x + 877700*x^2 + 25520*x^3 + 280*x^4 + 78355480) + 313243941124), x)
Time = 0.74 (sec) , antiderivative size = 282, normalized size of antiderivative = 9.10 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {2 e^{8 x} e^{4} x -46 e^{8 x} e^{4}-8 e^{6 x} e^{3} x^{2}+4232 e^{6 x} e^{3}+12 e^{4 x} e^{2} x^{3}+272 e^{4 x} e^{2} x^{2}-6256 e^{4 x} e^{2} x -146004 e^{4 x} e^{2}-8 e^{2 x} e \,x^{4}-360 e^{2 x} e \,x^{3}+190440 e^{2 x} e x +2238728 e^{2 x} e +2 x^{5}+134 x^{4}+2026 x^{3}-46575 x^{2}-1630378 x -12872686}{4 e^{8 x} e^{4}-16 e^{6 x} e^{3} x -368 e^{6 x} e^{3}+24 e^{4 x} e^{2} x^{2}+1096 e^{4 x} e^{2} x +12696 e^{4 x} e^{2}-16 e^{2 x} e \,x^{3}-1088 e^{2 x} e \,x^{2}-25024 e^{2 x} e x -194672 e^{2 x} e +4 x^{4}+360 x^{3}+12330 x^{2}+190440 x +1119364} \] Input:
int((2*exp(1+2*x)^8+(-16*x-368)*exp(1+2*x)^7+(56*x^2+2568*x+29624)*exp(1+2 *x)^6+(-112*x^3-7680*x^2-176640*x-1362704)*exp(1+2*x)^5+(140*x^4+12752*x^3 +438853*x^2+6750040*x+39177740)*exp(1+2*x)^4+(-112*x^5-12696*x^4-580936*x^ 3-13374316*x^2-154764240*x-720870416)*exp(1+2*x)^3+(56*x^6+7584*x^5+432290 *x^4+13236768*x^3+229267542*x^2+2129030328*x+8290009784)*exp(1+2*x)^2+(-16 *x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^2-16271075 104*x-54477207152)*exp(1+2*x)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37265659 *x^4+687869280*x^3+7984703253*x^2+53292920040*x+156621970562)/(4*exp(1+2*x )^8+(-32*x-736)*exp(1+2*x)^7+(112*x^2+5136*x+59248)*exp(1+2*x)^6+(-224*x^3 -15360*x^2-353280*x-2725408)*exp(1+2*x)^5+(280*x^4+25520*x^3+877700*x^2+13 500080*x+78355480)*exp(1+2*x)^4+(-224*x^5-25440*x^4-1162960*x^3-26748080*x ^2-309528480*x-1441740832)*exp(1+2*x)^3+(112*x^6+15216*x^5+866760*x^4+2649 7832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(1+2*x)^2+(-32*x^7-505 6*x^6-344528*x^5-13124704*x^4-301868192*x^3-4191872176*x^2-32542150208*x-1 08954414304)*exp(1+2*x)+4*x^8+720*x^7+57060*x^6+2600280*x^5+74525153*x^4+1 375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x)
Output:
(2*e**(8*x)*e**4*x - 46*e**(8*x)*e**4 - 8*e**(6*x)*e**3*x**2 + 4232*e**(6* x)*e**3 + 12*e**(4*x)*e**2*x**3 + 272*e**(4*x)*e**2*x**2 - 6256*e**(4*x)*e **2*x - 146004*e**(4*x)*e**2 - 8*e**(2*x)*e*x**4 - 360*e**(2*x)*e*x**3 + 1 90440*e**(2*x)*e*x + 2238728*e**(2*x)*e + 2*x**5 + 134*x**4 + 2026*x**3 - 46575*x**2 - 1630378*x - 12872686)/(2*(2*e**(8*x)*e**4 - 8*e**(6*x)*e**3*x - 184*e**(6*x)*e**3 + 12*e**(4*x)*e**2*x**2 + 548*e**(4*x)*e**2*x + 6348* e**(4*x)*e**2 - 8*e**(2*x)*e*x**3 - 544*e**(2*x)*e*x**2 - 12512*e**(2*x)*e *x - 97336*e**(2*x)*e + 2*x**4 + 180*x**3 + 6165*x**2 + 95220*x + 559682))