Integrand size = 493, antiderivative size = 31 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x}{2-\frac {x^2}{\left (-\left (-23+e^{1+2 x}-x\right )^2+x\right )^2}} \]
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\[ \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 {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 \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {156621970562+2 e^{8+16 x}+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8-16 e^{7+14 x} (23+x)+8 e^{6+12 x} \left (3703+321 x+7 x^2\right )-16 e^{5+10 x} \left (85169+11040 x+480 x^2+7 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )-4 e^{3+6 x} \left (180217604+38691060 x+3343579 x^2+145234 x^3+3174 x^4+28 x^5\right )+2 e^{2+4 x} \left (4145004892+1064515164 x+114633771 x^2+6618384 x^3+216145 x^4+3792 x^5+28 x^6\right )-4 e^{1+2 x} \left (13619301788+4067768776 x+524020523 x^2+37712318 x^3+1637528 x^4+42930 x^5+630 x^6+4 x^7\right )}{\left (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 )\right )^2} \, dx \\ & = \int \left (\frac {1}{2}-\frac {x^2 (-3+8 x)}{2 \left (559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4\right )}+\frac {x^3 \left (2191118-285752 e^{1+2 x}+12422 e^{2+4 x}-180 e^{3+6 x}+374715 x-36992 e^{1+2 x} x+1084 e^{2+4 x} x-8 e^{3+6 x} x+24390 x^2-1620 e^{1+2 x} x^2+24 e^{2+4 x} x^2+716 x^3-24 e^{1+2 x} x^3+8 x^4\right )}{\left (559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4\right )^2}\right ) \, dx \\ & = \frac {x}{2}-\frac {1}{2} \int \frac {x^2 (-3+8 x)}{559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4} \, dx+\int \frac {x^3 \left (2191118-285752 e^{1+2 x}+12422 e^{2+4 x}-180 e^{3+6 x}+374715 x-36992 e^{1+2 x} x+1084 e^{2+4 x} x-8 e^{3+6 x} x+24390 x^2-1620 e^{1+2 x} x^2+24 e^{2+4 x} x^2+716 x^3-24 e^{1+2 x} x^3+8 x^4\right )}{\left (559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4\right )^2} \, dx \\ & = \frac {x}{2}-\frac {1}{2} \int \frac {x^2 (-3+8 x)}{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 )} \, dx+\int \frac {x^3 \left (2191118+374715 x+24390 x^2+716 x^3+8 x^4-4 e^{3+6 x} (45+2 x)+2 e^{2+4 x} \left (6211+542 x+12 x^2\right )-4 e^{1+2 x} \left (71438+9248 x+405 x^2+6 x^3\right )\right )}{\left (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 )\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(115\) vs. \(2(31)=62\).
Time = 10.27 (sec) , antiderivative size = 115, normalized size of antiderivative = 3.71 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x \left (529+e^{2+4 x}+45 x+x^2-2 e^{1+2 x} (23+x)\right )^2}{559682+2 e^{4+8 x}+95220 x+6165 x^2+180 x^3+2 x^4-8 e^{3+6 x} (23+x)+4 e^{2+4 x} \left (1587+137 x+3 x^2\right )-8 e^{1+2 x} \left (12167+1564 x+68 x^2+x^3\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(123\) vs. \(2(30)=60\).
Time = 0.32 (sec) , antiderivative size = 124, normalized size of antiderivative = 4.00
method | result | size |
risch | \(\frac {x}{2}+\frac {x^{3}}{4 \,{\mathrm e}^{8 x +4}-16 \,{\mathrm e}^{6 x +3} x +24 \,{\mathrm e}^{4 x +2} x^{2}-16 \,{\mathrm e}^{1+2 x} x^{3}+4 x^{4}-368 \,{\mathrm e}^{6 x +3}+1096 \,{\mathrm e}^{4 x +2} x -1088 \,{\mathrm e}^{1+2 x} x^{2}+360 x^{3}+12696 \,{\mathrm e}^{4 x +2}-25024 x \,{\mathrm e}^{1+2 x}+12330 x^{2}-194672 \,{\mathrm e}^{1+2 x}+190440 x +1119364}\) | \(124\) |
parallelrisch | \(\frac {559682 x -97336 x \,{\mathrm e}^{1+2 x}+180 x^{4}+6166 x^{3}+95220 x^{2}+2 x^{5}+2 \,{\mathrm e}^{8 x +4} x -8 \,{\mathrm e}^{6 x +3} x^{2}+12 \,{\mathrm e}^{4 x +2} x^{3}-8 \,{\mathrm e}^{1+2 x} x^{4}-184 \,{\mathrm e}^{6 x +3} x +548 \,{\mathrm e}^{4 x +2} x^{2}-544 \,{\mathrm e}^{1+2 x} x^{3}+6348 \,{\mathrm e}^{4 x +2} x -12512 \,{\mathrm e}^{1+2 x} x^{2}}{4 \,{\mathrm e}^{8 x +4}-16 \,{\mathrm e}^{6 x +3} x +24 \,{\mathrm e}^{4 x +2} x^{2}-16 \,{\mathrm e}^{1+2 x} x^{3}+4 x^{4}-368 \,{\mathrm e}^{6 x +3}+1096 \,{\mathrm e}^{4 x +2} x -1088 \,{\mathrm e}^{1+2 x} x^{2}+360 x^{3}+12696 \,{\mathrm e}^{4 x +2}-25024 x \,{\mathrm e}^{1+2 x}+12330 x^{2}-194672 \,{\mathrm e}^{1+2 x}+190440 x +1119364}\) | \(267\) |
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Leaf count of result is larger than twice the leaf count of optimal. 173 vs. \(2 (30) = 60\).
Time = 0.25 (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} \]
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Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (20) = 40\).
Time = 0.44 (sec) , antiderivative size = 88, normalized size of antiderivative = 2.84 \[ \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx=\frac {x^{3}}{4 x^{4} + 360 x^{3} + 12330 x^{2} + 190440 x + \left (- 16 x - 368\right ) e^{6 x + 3} + \left (24 x^{2} + 1096 x + 12696\right ) e^{4 x + 2} + \left (- 16 x^{3} - 1088 x^{2} - 25024 x - 194672\right ) e^{2 x + 1} + 4 e^{8 x + 4} + 1119364} + \frac {x}{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 204 vs. \(2 (30) = 60\).
Time = 1.05 (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} \]
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Leaf count of result is larger than twice the leaf count of optimal. 242 vs. \(2 (30) = 60\).
Time = 3.08 (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 )}} \]
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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 \]
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