Integrand size = 427, antiderivative size = 32 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\left (e^{e^{x/2}}+\frac {2 x}{(3-x)^2 (4-x)^4}\right )^2 \log (x) \] Output:
(2*x/(3-x)^2/(4-x)^4+exp(exp(1/2*x)))^2*ln(x)
Time = 0.21 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.22 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\frac {\left (e^{e^{x/2}} (-4+x)^4 (-3+x)^2+2 x\right )^2 \log (x)}{(-4+x)^8 (-3+x)^4} \] Input:
Integrate[(48*x^2 - 28*x^3 + 4*x^4 + (96*x^2 + 104*x^3 - 40*x^4)*Log[x] + E^(2*E^(x/2))*(63700992 - 249495552*x + 452984832*x^2 - 505331712*x^3 + 38 6967552*x^4 - 215183872*x^5 + 89609472*x^6 - 28389312*x^7 + 6876012*x^8 - 1267047*x^9 + 174861*x^10 - 17526*x^11 + 1206*x^12 - 51*x^13 + x^14 + E^(x /2)*(63700992*x - 249495552*x^2 + 452984832*x^3 - 505331712*x^4 + 38696755 2*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 126704 7*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15)*Log[x]) + E^E^(x/2)*(110592*x - 248832*x^2 + 244224*x^3 - 136576*x^4 + 47600*x^5 - 1 0588*x^6 + 1468*x^7 - 116*x^8 + 4*x^9 + (110592*x - 64512*x^2 - 118272*x^3 + 168064*x^4 - 94224*x^5 + 28916*x^6 - 5116*x^7 + 492*x^8 - 20*x^9 + E^(x /2)*(55296*x^2 - 124416*x^3 + 122112*x^4 - 68288*x^5 + 23800*x^6 - 5294*x^ 7 + 734*x^8 - 58*x^9 + 2*x^10))*Log[x]))/(63700992*x - 249495552*x^2 + 452 984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1 206*x^13 - 51*x^14 + x^15),x]
Output:
((E^E^(x/2)*(-4 + x)^4*(-3 + x)^2 + 2*x)^2*Log[x])/((-4 + x)^8*(-3 + 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.
| \(\displaystyle \int \frac {4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )+110592 x\right ) \log (x)+110592 x\right )+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )}{x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )+110592 x\right ) \log (x)+110592 x\right )+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )}{x \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+63700992\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {495 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4) x}-\frac {495 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-3) x}-\frac {330 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^2 x}-\frac {165 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-3)^2 x}+\frac {210 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^3 x}-\frac {45 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-3)^3 x}-\frac {126 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^4 x}-\frac {9 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-3)^4 x}+\frac {70 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^5 x}-\frac {4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )}{(x-3)^5 x}-\frac {35 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^6 x}+\frac {15 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^7 x}-\frac {5 \left (4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )\right )}{(x-4)^8 x}+\frac {4 x^4-28 x^3+48 x^2+\left (-40 x^4+104 x^3+96 x^2\right ) \log (x)+e^{2 e^{x/2}} \left (x^{14}-51 x^{13}+1206 x^{12}-17526 x^{11}+174861 x^{10}-1267047 x^9+6876012 x^8-28389312 x^7+89609472 x^6-215183872 x^5+386967552 x^4-505331712 x^3+452984832 x^2-249495552 x+e^{x/2} \left (x^{15}-51 x^{14}+1206 x^{13}-17526 x^{12}+174861 x^{11}-1267047 x^{10}+6876012 x^9-28389312 x^8+89609472 x^7-215183872 x^6+386967552 x^5-505331712 x^4+452984832 x^3-249495552 x^2+63700992 x\right ) \log (x)+63700992\right )+e^{e^{x/2}} \left (4 x^9-116 x^8+1468 x^7-10588 x^6+47600 x^5-136576 x^4+244224 x^3-248832 x^2+110592 x+\left (-20 x^9+492 x^8-5116 x^7+28916 x^6-94224 x^5+168064 x^4-118272 x^3-64512 x^2+110592 x+e^{x/2} \left (2 x^{10}-58 x^9+734 x^8-5294 x^7+23800 x^6-68288 x^5+122112 x^4-124416 x^3+55296 x^2\right )\right ) \log (x)\right )}{(x-4)^9 x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (\left (e^{e^{x/2}} (x-3)^2 (x-4)^4+2 x\right ) \left (x^2-7 x+12\right )+x \left (-20 x^2+e^{\frac {x}{2}+e^{x/2}} (x-3)^3 (x-4)^5+52 x+48\right ) \log (x)\right )}{(3-x)^5 (4-x)^9 x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right )^2}{(x-4)^8 (x-3)^4 x}-\frac {20 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x^2 \log (x)}{(x-4)^9 (x-3)^5}+\frac {52 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) x \log (x)}{(x-4)^9 (x-3)^5}+\frac {e^{\frac {1}{2} \left (x+2 e^{x/2}\right )} \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(3-x)^2 (4-x)^4}+\frac {48 \left (e^{e^{x/2}} x^6-22 e^{e^{x/2}} x^5+201 e^{e^{x/2}} x^4-976 e^{e^{x/2}} x^3+2656 e^{e^{x/2}} x^2-3840 e^{e^{x/2}} x+2 x+2304 e^{e^{x/2}}\right ) \log (x)}{(x-4)^9 (x-3)^5}\right )dx\) |
Input:
Int[(48*x^2 - 28*x^3 + 4*x^4 + (96*x^2 + 104*x^3 - 40*x^4)*Log[x] + E^(2*E ^(x/2))*(63700992 - 249495552*x + 452984832*x^2 - 505331712*x^3 + 38696755 2*x^4 - 215183872*x^5 + 89609472*x^6 - 28389312*x^7 + 6876012*x^8 - 126704 7*x^9 + 174861*x^10 - 17526*x^11 + 1206*x^12 - 51*x^13 + x^14 + E^(x/2)*(6 3700992*x - 249495552*x^2 + 452984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 6876012*x^9 - 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15)*Log[x]) + E^E^(x /2)*(110592*x - 248832*x^2 + 244224*x^3 - 136576*x^4 + 47600*x^5 - 10588*x ^6 + 1468*x^7 - 116*x^8 + 4*x^9 + (110592*x - 64512*x^2 - 118272*x^3 + 168 064*x^4 - 94224*x^5 + 28916*x^6 - 5116*x^7 + 492*x^8 - 20*x^9 + E^(x/2)*(5 5296*x^2 - 124416*x^3 + 122112*x^4 - 68288*x^5 + 23800*x^6 - 5294*x^7 + 73 4*x^8 - 58*x^9 + 2*x^10))*Log[x]))/(63700992*x - 249495552*x^2 + 452984832 *x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 2838 9312*x^8 + 6876012*x^9 - 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^ 13 - 51*x^14 + x^15),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(118\) vs. \(2(28)=56\).
Time = 0.06 (sec) , antiderivative size = 119, normalized size of antiderivative = 3.72
\[\frac {4 x^{2} \ln \left (x \right )}{x^{12}-44 x^{11}+886 x^{10}-10796 x^{9}+88657 x^{8}-516896 x^{7}+2193856 x^{6}-6829568 x^{5}+15476224 x^{4}-24895488 x^{3}+26984448 x^{2}-17694720 x +5308416}+\ln \left (x \right ) {\mathrm e}^{2 \,{\mathrm e}^{\frac {x}{2}}}+\frac {4 x \ln \left (x \right ) {\mathrm e}^{{\mathrm e}^{\frac {x}{2}}}}{x^{6}-22 x^{5}+201 x^{4}-976 x^{3}+2656 x^{2}-3840 x +2304}\]
Input:
int((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012* x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+45 2984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*ln(x)+x^14-51*x^13+1206*x ^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+89609472*x ^6-215183872*x^5+386967552*x^4-505331712*x^3+452984832*x^2-249495552*x+637 00992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+23800*x^6-68288 *x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-5116*x^7+2 8916*x^6-94224*x^5+168064*x^4-118272*x^3-64512*x^2+110592*x)*ln(x)+4*x^9-1 16*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-248832*x^2+11059 2*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*ln(x)+4*x^4-28*x^3+48*x^2)/( x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9-283 89312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+452984832 *x^3-249495552*x^2+63700992*x),x)
Output:
4*x^2/(x^12-44*x^11+886*x^10-10796*x^9+88657*x^8-516896*x^7+2193856*x^6-68 29568*x^5+15476224*x^4-24895488*x^3+26984448*x^2-17694720*x+5308416)*ln(x) +ln(x)*exp(exp(1/2*x))^2+4*x/(x^6-22*x^5+201*x^4-976*x^3+2656*x^2-3840*x+2 304)*ln(x)*exp(exp(1/2*x))
Leaf count of result is larger than twice the leaf count of optimal. 178 vs. \(2 (24) = 48\).
Time = 0.09 (sec) , antiderivative size = 178, normalized size of antiderivative = 5.56 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\frac {4 \, x^{2} \log \left (x\right ) + {\left (x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416\right )} e^{\left (2 \, e^{\left (\frac {1}{2} \, x\right )}\right )} \log \left (x\right ) + 4 \, {\left (x^{7} - 22 \, x^{6} + 201 \, x^{5} - 976 \, x^{4} + 2656 \, x^{3} - 3840 \, x^{2} + 2304 \, x\right )} e^{\left (e^{\left (\frac {1}{2} \, x\right )}\right )} \log \left (x\right )}{x^{12} - 44 \, x^{11} + 886 \, x^{10} - 10796 \, x^{9} + 88657 \, x^{8} - 516896 \, x^{7} + 2193856 \, x^{6} - 6829568 \, x^{5} + 15476224 \, x^{4} - 24895488 \, x^{3} + 26984448 \, x^{2} - 17694720 \, x + 5308416} \] Input:
integrate((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+68 76012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712* x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^13 +1206*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+896 09472*x^6-215183872*x^5+386967552*x^4-505331712*x^3+452984832*x^2-24949555 2*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+23800*x^ 6-68288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-511 6*x^7+28916*x^6-94224*x^5+168064*x^4-118272*x^3-64512*x^2+110592*x)*log(x) +4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-248832*x ^2+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+ 48*x^2)/(x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+687601 2*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+ 452984832*x^3-249495552*x^2+63700992*x),x, algorithm="fricas")
Output:
(4*x^2*log(x) + (x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 51689 6*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448 *x^2 - 17694720*x + 5308416)*e^(2*e^(1/2*x))*log(x) + 4*(x^7 - 22*x^6 + 20 1*x^5 - 976*x^4 + 2656*x^3 - 3840*x^2 + 2304*x)*e^(e^(1/2*x))*log(x))/(x^1 2 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 17694720*x + 5308416)
Leaf count of result is larger than twice the leaf count of optimal. 170 vs. \(2 (24) = 48\).
Time = 0.49 (sec) , antiderivative size = 170, normalized size of antiderivative = 5.31 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\frac {4 x^{2} \log {\left (x \right )}}{x^{12} - 44 x^{11} + 886 x^{10} - 10796 x^{9} + 88657 x^{8} - 516896 x^{7} + 2193856 x^{6} - 6829568 x^{5} + 15476224 x^{4} - 24895488 x^{3} + 26984448 x^{2} - 17694720 x + 5308416} + \frac {4 x e^{e^{\frac {x}{2}}} \log {\left (x \right )} + \left (x^{6} \log {\left (x \right )} - 22 x^{5} \log {\left (x \right )} + 201 x^{4} \log {\left (x \right )} - 976 x^{3} \log {\left (x \right )} + 2656 x^{2} \log {\left (x \right )} - 3840 x \log {\left (x \right )} + 2304 \log {\left (x \right )}\right ) e^{2 e^{\frac {x}{2}}}}{x^{6} - 22 x^{5} + 201 x^{4} - 976 x^{3} + 2656 x^{2} - 3840 x + 2304} \] Input:
integrate((((x**15-51*x**14+1206*x**13-17526*x**12+174861*x**11-1267047*x* *10+6876012*x**9-28389312*x**8+89609472*x**7-215183872*x**6+386967552*x**5 -505331712*x**4+452984832*x**3-249495552*x**2+63700992*x)*exp(1/2*x)*ln(x) +x**14-51*x**13+1206*x**12-17526*x**11+174861*x**10-1267047*x**9+6876012*x **8-28389312*x**7+89609472*x**6-215183872*x**5+386967552*x**4-505331712*x* *3+452984832*x**2-249495552*x+63700992)*exp(exp(1/2*x))**2+(((2*x**10-58*x **9+734*x**8-5294*x**7+23800*x**6-68288*x**5+122112*x**4-124416*x**3+55296 *x**2)*exp(1/2*x)-20*x**9+492*x**8-5116*x**7+28916*x**6-94224*x**5+168064* x**4-118272*x**3-64512*x**2+110592*x)*ln(x)+4*x**9-116*x**8+1468*x**7-1058 8*x**6+47600*x**5-136576*x**4+244224*x**3-248832*x**2+110592*x)*exp(exp(1/ 2*x))+(-40*x**4+104*x**3+96*x**2)*ln(x)+4*x**4-28*x**3+48*x**2)/(x**15-51* x**14+1206*x**13-17526*x**12+174861*x**11-1267047*x**10+6876012*x**9-28389 312*x**8+89609472*x**7-215183872*x**6+386967552*x**5-505331712*x**4+452984 832*x**3-249495552*x**2+63700992*x),x)
Output:
4*x**2*log(x)/(x**12 - 44*x**11 + 886*x**10 - 10796*x**9 + 88657*x**8 - 51 6896*x**7 + 2193856*x**6 - 6829568*x**5 + 15476224*x**4 - 24895488*x**3 + 26984448*x**2 - 17694720*x + 5308416) + (4*x*exp(exp(x/2))*log(x) + (x**6* log(x) - 22*x**5*log(x) + 201*x**4*log(x) - 976*x**3*log(x) + 2656*x**2*lo g(x) - 3840*x*log(x) + 2304*log(x))*exp(2*exp(x/2)))/(x**6 - 22*x**5 + 201 *x**4 - 976*x**3 + 2656*x**2 - 3840*x + 2304)
Leaf count of result is larger than twice the leaf count of optimal. 586 vs. \(2 (24) = 48\).
Time = 0.17 (sec) , antiderivative size = 586, normalized size of antiderivative = 18.31 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx =\text {Too large to display} \] Input:
integrate((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+68 76012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712* x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^13 +1206*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+896 09472*x^6-215183872*x^5+386967552*x^4-505331712*x^3+452984832*x^2-24949555 2*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+23800*x^ 6-68288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-511 6*x^7+28916*x^6-94224*x^5+168064*x^4-118272*x^3-64512*x^2+110592*x)*log(x) +4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-248832*x ^2+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+ 48*x^2)/(x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+687601 2*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+ 452984832*x^3-249495552*x^2+63700992*x),x, algorithm="maxima")
Output:
1/35*(2552760*x^11 - 103386780*x^10 + 1900104360*x^9 - 20917102710*x^8 + 1 53240991512*x^7 - 784453702788*x^6 + 2863076933592*x^5 - 7449941242557*x^4 + 13543600742564*x^3 - 16382097148104*x^2 + 11865447305280*x - 3898411992 288)/(x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 219 3856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 1769 4720*x + 5308416) - (153720*x^11 - 6225660*x^10 + 114418920*x^9 - 12595688 70*x^8 + 9227739864*x^7 - 47237587236*x^6 + 172406409624*x^5 - 44861442822 9*x^4 + 815557399108*x^3 - 986483638730*x^2 + 714503737040*x - 23475136380 0)/(x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 21938 56*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 176947 20*x + 5308416) + 4/7*(138600*x^11 - 5613300*x^10 + 103164600*x^9 - 113567 6850*x^8 + 8320093320*x^7 - 42591267180*x^6 + 155448402120*x^5 - 404488418 895*x^4 + 735338638540*x^3 - 889452461150*x^2 + 644224680940*x - 211661065 722)/(x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 219 3856*x^6 - 6829568*x^5 + 15476224*x^4 - 24895488*x^3 + 26984448*x^2 - 1769 4720*x + 5308416) + 1/35*(55440*x^11 - 2245320*x^10 + 41265840*x^9 - 45427 0740*x^8 + 3328037328*x^7 - 17036506872*x^6 + 62179360848*x^5 - 1617953675 58*x^4 + 294135455416*x^3 + 140*x^2*log(x) + 35*(x^12 - 44*x^11 + 886*x^10 - 10796*x^9 + 88657*x^8 - 516896*x^7 + 2193856*x^6 - 6829568*x^5 + 154762 24*x^4 - 24895488*x^3 + 26984448*x^2 - 17694720*x + 5308416)*e^(2*e^(1/...
\[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\int { \frac {4 \, x^{4} - 28 \, x^{3} + 48 \, x^{2} + {\left (x^{14} - 51 \, x^{13} + 1206 \, x^{12} - 17526 \, x^{11} + 174861 \, x^{10} - 1267047 \, x^{9} + 6876012 \, x^{8} - 28389312 \, x^{7} + 89609472 \, x^{6} - 215183872 \, x^{5} + 386967552 \, x^{4} - 505331712 \, x^{3} + {\left (x^{15} - 51 \, x^{14} + 1206 \, x^{13} - 17526 \, x^{12} + 174861 \, x^{11} - 1267047 \, x^{10} + 6876012 \, x^{9} - 28389312 \, x^{8} + 89609472 \, x^{7} - 215183872 \, x^{6} + 386967552 \, x^{5} - 505331712 \, x^{4} + 452984832 \, x^{3} - 249495552 \, x^{2} + 63700992 \, x\right )} e^{\left (\frac {1}{2} \, x\right )} \log \left (x\right ) + 452984832 \, x^{2} - 249495552 \, x + 63700992\right )} e^{\left (2 \, e^{\left (\frac {1}{2} \, x\right )}\right )} + 2 \, {\left (2 \, x^{9} - 58 \, x^{8} + 734 \, x^{7} - 5294 \, x^{6} + 23800 \, x^{5} - 68288 \, x^{4} + 122112 \, x^{3} - 124416 \, x^{2} - {\left (10 \, x^{9} - 246 \, x^{8} + 2558 \, x^{7} - 14458 \, x^{6} + 47112 \, x^{5} - 84032 \, x^{4} + 59136 \, x^{3} + 32256 \, x^{2} - {\left (x^{10} - 29 \, x^{9} + 367 \, x^{8} - 2647 \, x^{7} + 11900 \, x^{6} - 34144 \, x^{5} + 61056 \, x^{4} - 62208 \, x^{3} + 27648 \, x^{2}\right )} e^{\left (\frac {1}{2} \, x\right )} - 55296 \, x\right )} \log \left (x\right ) + 55296 \, x\right )} e^{\left (e^{\left (\frac {1}{2} \, x\right )}\right )} - 8 \, {\left (5 \, x^{4} - 13 \, x^{3} - 12 \, x^{2}\right )} \log \left (x\right )}{x^{15} - 51 \, x^{14} + 1206 \, x^{13} - 17526 \, x^{12} + 174861 \, x^{11} - 1267047 \, x^{10} + 6876012 \, x^{9} - 28389312 \, x^{8} + 89609472 \, x^{7} - 215183872 \, x^{6} + 386967552 \, x^{5} - 505331712 \, x^{4} + 452984832 \, x^{3} - 249495552 \, x^{2} + 63700992 \, x} \,d x } \] Input:
integrate((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+68 76012*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712* x^4+452984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^13 +1206*x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+896 09472*x^6-215183872*x^5+386967552*x^4-505331712*x^3+452984832*x^2-24949555 2*x+63700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+23800*x^ 6-68288*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-511 6*x^7+28916*x^6-94224*x^5+168064*x^4-118272*x^3-64512*x^2+110592*x)*log(x) +4*x^9-116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-248832*x ^2+110592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+ 48*x^2)/(x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+687601 2*x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+ 452984832*x^3-249495552*x^2+63700992*x),x, algorithm="giac")
Output:
integrate((4*x^4 - 28*x^3 + 48*x^2 + (x^14 - 51*x^13 + 1206*x^12 - 17526*x ^11 + 174861*x^10 - 1267047*x^9 + 6876012*x^8 - 28389312*x^7 + 89609472*x^ 6 - 215183872*x^5 + 386967552*x^4 - 505331712*x^3 + (x^15 - 51*x^14 + 1206 *x^13 - 17526*x^12 + 174861*x^11 - 1267047*x^10 + 6876012*x^9 - 28389312*x ^8 + 89609472*x^7 - 215183872*x^6 + 386967552*x^5 - 505331712*x^4 + 452984 832*x^3 - 249495552*x^2 + 63700992*x)*e^(1/2*x)*log(x) + 452984832*x^2 - 2 49495552*x + 63700992)*e^(2*e^(1/2*x)) + 2*(2*x^9 - 58*x^8 + 734*x^7 - 529 4*x^6 + 23800*x^5 - 68288*x^4 + 122112*x^3 - 124416*x^2 - (10*x^9 - 246*x^ 8 + 2558*x^7 - 14458*x^6 + 47112*x^5 - 84032*x^4 + 59136*x^3 + 32256*x^2 - (x^10 - 29*x^9 + 367*x^8 - 2647*x^7 + 11900*x^6 - 34144*x^5 + 61056*x^4 - 62208*x^3 + 27648*x^2)*e^(1/2*x) - 55296*x)*log(x) + 55296*x)*e^(e^(1/2*x )) - 8*(5*x^4 - 13*x^3 - 12*x^2)*log(x))/(x^15 - 51*x^14 + 1206*x^13 - 175 26*x^12 + 174861*x^11 - 1267047*x^10 + 6876012*x^9 - 28389312*x^8 + 896094 72*x^7 - 215183872*x^6 + 386967552*x^5 - 505331712*x^4 + 452984832*x^3 - 2 49495552*x^2 + 63700992*x), x)
Time = 1.69 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.59 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\frac {\ln \left (x\right )\,{\left (2\,x+2304\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}-3840\,x\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}+2656\,x^2\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}-976\,x^3\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}+201\,x^4\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}-22\,x^5\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}+x^6\,{\mathrm {e}}^{\sqrt {{\mathrm {e}}^x}}\right )}^2}{{\left (x-3\right )}^4\,{\left (x-4\right )}^8} \] Input:
int((exp(exp(x/2))*(110592*x + log(x)*(110592*x - 64512*x^2 - 118272*x^3 + 168064*x^4 - 94224*x^5 + 28916*x^6 - 5116*x^7 + 492*x^8 - 20*x^9 + exp(x/ 2)*(55296*x^2 - 124416*x^3 + 122112*x^4 - 68288*x^5 + 23800*x^6 - 5294*x^7 + 734*x^8 - 58*x^9 + 2*x^10)) - 248832*x^2 + 244224*x^3 - 136576*x^4 + 47 600*x^5 - 10588*x^6 + 1468*x^7 - 116*x^8 + 4*x^9) + log(x)*(96*x^2 + 104*x ^3 - 40*x^4) + exp(2*exp(x/2))*(452984832*x^2 - 249495552*x - 505331712*x^ 3 + 386967552*x^4 - 215183872*x^5 + 89609472*x^6 - 28389312*x^7 + 6876012* x^8 - 1267047*x^9 + 174861*x^10 - 17526*x^11 + 1206*x^12 - 51*x^13 + x^14 + exp(x/2)*log(x)*(63700992*x - 249495552*x^2 + 452984832*x^3 - 505331712* x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^7 - 28389312*x^8 + 687601 2*x^9 - 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^ 15) + 63700992) + 48*x^2 - 28*x^3 + 4*x^4)/(63700992*x - 249495552*x^2 + 4 52984832*x^3 - 505331712*x^4 + 386967552*x^5 - 215183872*x^6 + 89609472*x^ 7 - 28389312*x^8 + 6876012*x^9 - 1267047*x^10 + 174861*x^11 - 17526*x^12 + 1206*x^13 - 51*x^14 + x^15),x)
Output:
(log(x)*(2*x + 2304*exp(exp(x)^(1/2)) - 3840*x*exp(exp(x)^(1/2)) + 2656*x^ 2*exp(exp(x)^(1/2)) - 976*x^3*exp(exp(x)^(1/2)) + 201*x^4*exp(exp(x)^(1/2) ) - 22*x^5*exp(exp(x)^(1/2)) + x^6*exp(exp(x)^(1/2)))^2)/((x - 3)^4*(x - 4 )^8)
Time = 0.24 (sec) , antiderivative size = 429, normalized size of antiderivative = 13.41 \[ \int \frac {48 x^2-28 x^3+4 x^4+\left (96 x^2+104 x^3-40 x^4\right ) \log (x)+e^{2 e^{x/2}} \left (63700992-249495552 x+452984832 x^2-505331712 x^3+386967552 x^4-215183872 x^5+89609472 x^6-28389312 x^7+6876012 x^8-1267047 x^9+174861 x^{10}-17526 x^{11}+1206 x^{12}-51 x^{13}+x^{14}+e^{x/2} \left (63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}\right ) \log (x)\right )+e^{e^{x/2}} \left (110592 x-248832 x^2+244224 x^3-136576 x^4+47600 x^5-10588 x^6+1468 x^7-116 x^8+4 x^9+\left (110592 x-64512 x^2-118272 x^3+168064 x^4-94224 x^5+28916 x^6-5116 x^7+492 x^8-20 x^9+e^{x/2} \left (55296 x^2-124416 x^3+122112 x^4-68288 x^5+23800 x^6-5294 x^7+734 x^8-58 x^9+2 x^{10}\right )\right ) \log (x)\right )}{63700992 x-249495552 x^2+452984832 x^3-505331712 x^4+386967552 x^5-215183872 x^6+89609472 x^7-28389312 x^8+6876012 x^9-1267047 x^{10}+174861 x^{11}-17526 x^{12}+1206 x^{13}-51 x^{14}+x^{15}} \, dx=\frac {-1337720832+4459069440 x +11088 x^{11}-223272 x^{10}+2720592 x^{9}+196411392 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right )-6800080896 x^{2}+1721051136 x^{5}+130257792 x^{7}+6273662976 x^{3}-22341564 x^{8}-552851712 x^{6}+148 \,\mathrm {log}\left (x \right ) x^{2}-252 x^{12}-3900008448 x^{4}+37 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{12}-1628 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{11}+32782 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{10}-399452 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{9}+3280309 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{8}-19125152 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{7}+81172672 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{6}-252694016 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{5}+572620288 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{4}-921133056 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{3}+998424576 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{2}-654704640 e^{2 e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x +148 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{7}-3256 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{6}+29748 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{5}-144448 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{4}+393088 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{3}-568320 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x^{2}+340992 e^{e^{\frac {x}{2}}} \mathrm {log}\left (x \right ) x}{37 x^{12}-1628 x^{11}+32782 x^{10}-399452 x^{9}+3280309 x^{8}-19125152 x^{7}+81172672 x^{6}-252694016 x^{5}+572620288 x^{4}-921133056 x^{3}+998424576 x^{2}-654704640 x +196411392} \] Input:
int((((x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012* x^9-28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+45 2984832*x^3-249495552*x^2+63700992*x)*exp(1/2*x)*log(x)+x^14-51*x^13+1206* x^12-17526*x^11+174861*x^10-1267047*x^9+6876012*x^8-28389312*x^7+89609472* x^6-215183872*x^5+386967552*x^4-505331712*x^3+452984832*x^2-249495552*x+63 700992)*exp(exp(1/2*x))^2+(((2*x^10-58*x^9+734*x^8-5294*x^7+23800*x^6-6828 8*x^5+122112*x^4-124416*x^3+55296*x^2)*exp(1/2*x)-20*x^9+492*x^8-5116*x^7+ 28916*x^6-94224*x^5+168064*x^4-118272*x^3-64512*x^2+110592*x)*log(x)+4*x^9 -116*x^8+1468*x^7-10588*x^6+47600*x^5-136576*x^4+244224*x^3-248832*x^2+110 592*x)*exp(exp(1/2*x))+(-40*x^4+104*x^3+96*x^2)*log(x)+4*x^4-28*x^3+48*x^2 )/(x^15-51*x^14+1206*x^13-17526*x^12+174861*x^11-1267047*x^10+6876012*x^9- 28389312*x^8+89609472*x^7-215183872*x^6+386967552*x^5-505331712*x^4+452984 832*x^3-249495552*x^2+63700992*x),x)
Output:
(37*e**(2*e**(x/2))*log(x)*x**12 - 1628*e**(2*e**(x/2))*log(x)*x**11 + 327 82*e**(2*e**(x/2))*log(x)*x**10 - 399452*e**(2*e**(x/2))*log(x)*x**9 + 328 0309*e**(2*e**(x/2))*log(x)*x**8 - 19125152*e**(2*e**(x/2))*log(x)*x**7 + 81172672*e**(2*e**(x/2))*log(x)*x**6 - 252694016*e**(2*e**(x/2))*log(x)*x* *5 + 572620288*e**(2*e**(x/2))*log(x)*x**4 - 921133056*e**(2*e**(x/2))*log (x)*x**3 + 998424576*e**(2*e**(x/2))*log(x)*x**2 - 654704640*e**(2*e**(x/2 ))*log(x)*x + 196411392*e**(2*e**(x/2))*log(x) + 148*e**(e**(x/2))*log(x)* x**7 - 3256*e**(e**(x/2))*log(x)*x**6 + 29748*e**(e**(x/2))*log(x)*x**5 - 144448*e**(e**(x/2))*log(x)*x**4 + 393088*e**(e**(x/2))*log(x)*x**3 - 5683 20*e**(e**(x/2))*log(x)*x**2 + 340992*e**(e**(x/2))*log(x)*x + 148*log(x)* x**2 - 252*x**12 + 11088*x**11 - 223272*x**10 + 2720592*x**9 - 22341564*x* *8 + 130257792*x**7 - 552851712*x**6 + 1721051136*x**5 - 3900008448*x**4 + 6273662976*x**3 - 6800080896*x**2 + 4459069440*x - 1337720832)/(37*(x**12 - 44*x**11 + 886*x**10 - 10796*x**9 + 88657*x**8 - 516896*x**7 + 2193856* x**6 - 6829568*x**5 + 15476224*x**4 - 24895488*x**3 + 26984448*x**2 - 1769 4720*x + 5308416))