Integrand size = 716, antiderivative size = 30 \[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx=\left (6+\frac {1}{16} \left (-x+\frac {e^5}{-3+\frac {1}{x}+x}+3 \log (x)\right )^2\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(329\) vs. \(2(30)=60\).
Time = 0.32 (sec) , antiderivative size = 329, normalized size of antiderivative = 10.97 \[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx=\frac {1}{256} \left (-12 e^5 x-4 \left (-48+e^5\right ) x^2+x^4+\frac {e^{20} (-8+21 x)}{\left (1-3 x+x^2\right )^4}+\frac {2 e^5 \left (208-2 e^{10}-618 x+9 e^5 (13+2 x)\right )}{1-3 x+x^2}+\frac {e^{10} \left (-240+e^{10}+702 x-4 e^5 (7+6 x)\right )}{\left (1-3 x+x^2\right )^2}+\frac {e^{15} \left (32-84 x+e^5 (7+6 x)\right )}{\left (1-3 x+x^2\right )^3}+108 e^5 \log (x)+\frac {12 \left (e^{15} x^3-3 e^{10} x^3 \left (1-3 x+x^2\right )-x \left (96+x^2\right ) \left (1-3 x+x^2\right )^3+3 e^5 \left (1-3 x+x^2\right )^2 \left (-3+41 x-3 x^2+x^3\right )\right ) \log (x)}{\left (1-3 x+x^2\right )^3}+\frac {54 \left (32-192 x+\left (353-2 e^5+e^{10}\right ) x^2+6 \left (-33+e^5\right ) x^3+\left (43-2 e^5\right ) x^4-6 x^5+x^6\right ) \log ^2(x)}{\left (1-3 x+x^2\right )^2}-\frac {108 x \left (1-e^5-3 x+x^2\right ) \log ^3(x)}{1-3 x+x^2}+81 \log ^4(x)\right ) \]
Integrate[(-288*x + 4416*x^2 - 28803*x^3 + 104206*x^4 - 229260*x^5 + 31826 9*x^6 - 283473*x^7 + 164104*x^8 - 61968*x^9 + 15115*x^10 - 2343*x^11 + 236 *x^12 - 18*x^13 + x^14 + E^20*(x^4 - x^6) + E^15*(3*x^3 - 22*x^4 + 48*x^5 - 29*x^6 + 2*x^8) + E^10*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 171*x^7 + 45*x^8 - 18*x^9) + E^5*(288*x - 3648*x^2 + 18729*x^3 - 49936*x ^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 253*x^10 + 36*x^11 - 2*x^12) + (864 - 13248*x + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961317*x^5 + 864729*x^6 - 512136*x^7 + 203472*x^8 - 55395*x^9 + 10719*x^1 0 - 1548*x^11 + 162*x^12 - 9*x^13 + E^15*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7) + E^10*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^ 9) + E^5*(288*x - 2646*x^2 + 9027*x^3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x^9 - 189*x^10 + 9*x^11))*Log[x] + (-81*x + 124 2*x^2 - 8100*x^3 + 29295*x^4 - 64395*x^5 + 89208*x^6 - 79056*x^7 + 45225*x ^8 - 16605*x^9 + 3780*x^10 - 486*x^11 + 27*x^12 + E^10*(27*x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 162*x^7 - 27*x^8) + E^5*(81*x - 1026*x^2 + 5265*x^3 - 14013*x^4 + 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9))*Log[x ]^2 + (81 - 1242*x + 8100*x^2 - 29295*x^3 + 64395*x^4 - 89208*x^5 + 79056* x^6 - 45225*x^7 + 16605*x^8 - 3780*x^9 + 486*x^10 - 27*x^11 + E^5*(27*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9))*Log[x ]^3)/(64*x - 960*x^2 + 6080*x^3 - 21120*x^4 + 43840*x^5 - 55872*x^6 + 4384 0*x^7 - 21120*x^8 + 6080*x^9 - 960*x^10 + 64*x^11),x]
(-12*E^5*x - 4*(-48 + E^5)*x^2 + x^4 + (E^20*(-8 + 21*x))/(1 - 3*x + x^2)^ 4 + (2*E^5*(208 - 2*E^10 - 618*x + 9*E^5*(13 + 2*x)))/(1 - 3*x + x^2) + (E ^10*(-240 + E^10 + 702*x - 4*E^5*(7 + 6*x)))/(1 - 3*x + x^2)^2 + (E^15*(32 - 84*x + E^5*(7 + 6*x)))/(1 - 3*x + x^2)^3 + 108*E^5*Log[x] + (12*(E^15*x ^3 - 3*E^10*x^3*(1 - 3*x + x^2) - x*(96 + x^2)*(1 - 3*x + x^2)^3 + 3*E^5*( 1 - 3*x + x^2)^2*(-3 + 41*x - 3*x^2 + x^3))*Log[x])/(1 - 3*x + x^2)^3 + (5 4*(32 - 192*x + (353 - 2*E^5 + E^10)*x^2 + 6*(-33 + E^5)*x^3 + (43 - 2*E^5 )*x^4 - 6*x^5 + x^6)*Log[x]^2)/(1 - 3*x + x^2)^2 - (108*x*(1 - E^5 - 3*x + x^2)*Log[x]^3)/(1 - 3*x + x^2) + 81*Log[x]^4)/256
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 27.24 (sec) , antiderivative size = 6740, normalized size of antiderivative = 224.67, number of steps used = 7, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2026, 2463, 27, 25, 7239, 7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {x^{14}-18 x^{13}+236 x^{12}-2343 x^{11}+15115 x^{10}-61968 x^9+164104 x^8-283473 x^7+318269 x^6-229260 x^5+104206 x^4-28803 x^3+4416 x^2+e^{20} \left (x^4-x^6\right )+e^{15} \left (2 x^8-29 x^6+48 x^5-22 x^4+3 x^3\right )+e^{10} \left (-18 x^9+45 x^8+171 x^7-435 x^6-315 x^5+1047 x^4-585 x^3+96 x^2\right )-288 x+\left (-27 x^{11}+486 x^{10}-3780 x^9+16605 x^8-45225 x^7+79056 x^6-89208 x^5+64395 x^4-29295 x^3+8100 x^2+e^5 \left (-27 x^9+243 x^8-783 x^7+972 x^6-972 x^4+783 x^3-243 x^2+27 x\right )-1242 x+81\right ) \log ^3(x)+e^5 \left (-2 x^{12}+36 x^{11}-253 x^{10}+1494 x^9-8121 x^8+29295 x^7-61691 x^6+74007 x^5-49936 x^4+18729 x^3-3648 x^2+288 x\right )+\left (27 x^{12}-486 x^{11}+3780 x^{10}-16605 x^9+45225 x^8-79056 x^7+89208 x^6-64395 x^5+29295 x^4-8100 x^3+1242 x^2+e^{10} \left (-27 x^8+162 x^7-270 x^6+270 x^4-162 x^3+27 x^2\right )+e^5 \left (162 x^9-1755 x^8+7614 x^7-16929 x^6+20655 x^5-14013 x^4+5265 x^3-1026 x^2+81 x\right )-81 x\right ) \log ^2(x)+\left (-9 x^{13}+162 x^{12}-1548 x^{11}+10719 x^{10}-55395 x^9+203472 x^8-512136 x^7+864729 x^6-961317 x^5+689580 x^4-312894 x^3+86427 x^2+e^{15} \left (-9 x^7+27 x^6-27 x^4+9 x^3\right )+e^{10} \left (9 x^9-333 x^7+1215 x^6-1665 x^5+999 x^4-270 x^3+27 x^2\right )-13248 x+e^5 \left (9 x^{11}-189 x^{10}+1143 x^9-2808 x^8+2934 x^7-3078 x^6+9081 x^5-13797 x^4+9027 x^3-2646 x^2+288 x\right )+864\right ) \log (x)}{64 x^{11}-960 x^{10}+6080 x^9-21120 x^8+43840 x^7-55872 x^6+43840 x^5-21120 x^4+6080 x^3-960 x^2+64 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {x^{14}-18 x^{13}+236 x^{12}-2343 x^{11}+15115 x^{10}-61968 x^9+164104 x^8-283473 x^7+318269 x^6-229260 x^5+104206 x^4-28803 x^3+4416 x^2+e^{20} \left (x^4-x^6\right )+e^{15} \left (2 x^8-29 x^6+48 x^5-22 x^4+3 x^3\right )+e^{10} \left (-18 x^9+45 x^8+171 x^7-435 x^6-315 x^5+1047 x^4-585 x^3+96 x^2\right )-288 x+\left (-27 x^{11}+486 x^{10}-3780 x^9+16605 x^8-45225 x^7+79056 x^6-89208 x^5+64395 x^4-29295 x^3+8100 x^2+e^5 \left (-27 x^9+243 x^8-783 x^7+972 x^6-972 x^4+783 x^3-243 x^2+27 x\right )-1242 x+81\right ) \log ^3(x)+e^5 \left (-2 x^{12}+36 x^{11}-253 x^{10}+1494 x^9-8121 x^8+29295 x^7-61691 x^6+74007 x^5-49936 x^4+18729 x^3-3648 x^2+288 x\right )+\left (27 x^{12}-486 x^{11}+3780 x^{10}-16605 x^9+45225 x^8-79056 x^7+89208 x^6-64395 x^5+29295 x^4-8100 x^3+1242 x^2+e^{10} \left (-27 x^8+162 x^7-270 x^6+270 x^4-162 x^3+27 x^2\right )+e^5 \left (162 x^9-1755 x^8+7614 x^7-16929 x^6+20655 x^5-14013 x^4+5265 x^3-1026 x^2+81 x\right )-81 x\right ) \log ^2(x)+\left (-9 x^{13}+162 x^{12}-1548 x^{11}+10719 x^{10}-55395 x^9+203472 x^8-512136 x^7+864729 x^6-961317 x^5+689580 x^4-312894 x^3+86427 x^2+e^{15} \left (-9 x^7+27 x^6-27 x^4+9 x^3\right )+e^{10} \left (9 x^9-333 x^7+1215 x^6-1665 x^5+999 x^4-270 x^3+27 x^2\right )-13248 x+e^5 \left (9 x^{11}-189 x^{10}+1143 x^9-2808 x^8+2934 x^7-3078 x^6+9081 x^5-13797 x^4+9027 x^3-2646 x^2+288 x\right )+864\right ) \log (x)}{x \left (64 x^{10}-960 x^9+6080 x^8-21120 x^7+43840 x^6-55872 x^5+43840 x^4-21120 x^3+6080 x^2-960 x+64\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {x^{14}-18 x^{13}+236 x^{12}-2343 x^{11}+15115 x^{10}-61968 x^9+164104 x^8-283473 x^7+318269 x^6-229260 x^5+104206 x^4-28803 x^3+4416 x^2+e^{20} \left (x^4-x^6\right )+e^{15} \left (2 x^8-29 x^6+48 x^5-22 x^4+3 x^3\right )+e^{10} \left (-18 x^9+45 x^8+171 x^7-435 x^6-315 x^5+1047 x^4-585 x^3+96 x^2\right )-288 x+\left (-27 x^{11}+486 x^{10}-3780 x^9+16605 x^8-45225 x^7+79056 x^6-89208 x^5+64395 x^4-29295 x^3+8100 x^2+e^5 \left (-27 x^9+243 x^8-783 x^7+972 x^6-972 x^4+783 x^3-243 x^2+27 x\right )-1242 x+81\right ) \log ^3(x)+e^5 \left (-2 x^{12}+36 x^{11}-253 x^{10}+1494 x^9-8121 x^8+29295 x^7-61691 x^6+74007 x^5-49936 x^4+18729 x^3-3648 x^2+288 x\right )+\left (27 x^{12}-486 x^{11}+3780 x^{10}-16605 x^9+45225 x^8-79056 x^7+89208 x^6-64395 x^5+29295 x^4-8100 x^3+1242 x^2+e^{10} \left (-27 x^8+162 x^7-270 x^6+270 x^4-162 x^3+27 x^2\right )+e^5 \left (162 x^9-1755 x^8+7614 x^7-16929 x^6+20655 x^5-14013 x^4+5265 x^3-1026 x^2+81 x\right )-81 x\right ) \log ^2(x)+\left (-9 x^{13}+162 x^{12}-1548 x^{11}+10719 x^{10}-55395 x^9+203472 x^8-512136 x^7+864729 x^6-961317 x^5+689580 x^4-312894 x^3+86427 x^2+e^{15} \left (-9 x^7+27 x^6-27 x^4+9 x^3\right )+e^{10} \left (9 x^9-333 x^7+1215 x^6-1665 x^5+999 x^4-270 x^3+27 x^2\right )-13248 x+e^5 \left (9 x^{11}-189 x^{10}+1143 x^9-2808 x^8+2934 x^7-3078 x^6+9081 x^5-13797 x^4+9027 x^3-2646 x^2+288 x\right )+864\right ) \log (x)}{64 x \left (x^2-3 x+1\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{64} \int -\frac {-x^{14}+18 x^{13}-236 x^{12}+2343 x^{11}-15115 x^{10}+61968 x^9-164104 x^8+283473 x^7-318269 x^6+229260 x^5-104206 x^4+28803 x^3-4416 x^2+288 x-27 \left (-x^{11}+18 x^{10}-140 x^9+615 x^8-1675 x^7+2928 x^6-3304 x^5+2385 x^4-1085 x^3+300 x^2-46 x+e^5 \left (-x^9+9 x^8-29 x^7+36 x^6-36 x^4+29 x^3-9 x^2+x\right )+3\right ) \log ^3(x)+27 \left (-x^{12}+18 x^{11}-140 x^{10}+615 x^9-1675 x^8+2928 x^7-3304 x^6+2385 x^5-1085 x^4+300 x^3-46 x^2+3 x-e^{10} \left (-x^8+6 x^7-10 x^6+10 x^4-6 x^3+x^2\right )-e^5 \left (6 x^9-65 x^8+282 x^7-627 x^6+765 x^5-519 x^4+195 x^3-38 x^2+3 x\right )\right ) \log ^2(x)-e^{20} \left (x^4-x^6\right )-e^{15} \left (2 x^8-29 x^6+48 x^5-22 x^4+3 x^3\right )-3 e^{10} \left (-6 x^9+15 x^8+57 x^7-145 x^6-105 x^5+349 x^4-195 x^3+32 x^2\right )-e^5 \left (-2 x^{12}+36 x^{11}-253 x^{10}+1494 x^9-8121 x^8+29295 x^7-61691 x^6+74007 x^5-49936 x^4+18729 x^3-3648 x^2+288 x\right )-9 \left (-x^{13}+18 x^{12}-172 x^{11}+1191 x^{10}-6155 x^9+22608 x^8-56904 x^7+96081 x^6-106813 x^5+76620 x^4-34766 x^3+9603 x^2-1472 x+e^{15} \left (-x^7+3 x^6-3 x^4+x^3\right )+e^{10} \left (x^9-37 x^7+135 x^6-185 x^5+111 x^4-30 x^3+3 x^2\right )+e^5 \left (x^{11}-21 x^{10}+127 x^9-312 x^8+326 x^7-342 x^6+1009 x^5-1533 x^4+1003 x^3-294 x^2+32 x\right )+96\right ) \log (x)}{x \left (x^2-3 x+1\right )^5}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{64} \int \frac {-x^{14}+18 x^{13}-236 x^{12}+2343 x^{11}-15115 x^{10}+61968 x^9-164104 x^8+283473 x^7-318269 x^6+229260 x^5-104206 x^4+28803 x^3-4416 x^2+288 x-27 \left (-x^{11}+18 x^{10}-140 x^9+615 x^8-1675 x^7+2928 x^6-3304 x^5+2385 x^4-1085 x^3+300 x^2-46 x+e^5 \left (-x^9+9 x^8-29 x^7+36 x^6-36 x^4+29 x^3-9 x^2+x\right )+3\right ) \log ^3(x)+27 \left (-x^{12}+18 x^{11}-140 x^{10}+615 x^9-1675 x^8+2928 x^7-3304 x^6+2385 x^5-1085 x^4+300 x^3-46 x^2+3 x-e^{10} \left (-x^8+6 x^7-10 x^6+10 x^4-6 x^3+x^2\right )-e^5 \left (6 x^9-65 x^8+282 x^7-627 x^6+765 x^5-519 x^4+195 x^3-38 x^2+3 x\right )\right ) \log ^2(x)-e^{20} \left (x^4-x^6\right )-e^{15} \left (2 x^8-29 x^6+48 x^5-22 x^4+3 x^3\right )-3 e^{10} \left (-6 x^9+15 x^8+57 x^7-145 x^6-105 x^5+349 x^4-195 x^3+32 x^2\right )-e^5 \left (-2 x^{12}+36 x^{11}-253 x^{10}+1494 x^9-8121 x^8+29295 x^7-61691 x^6+74007 x^5-49936 x^4+18729 x^3-3648 x^2+288 x\right )-9 \left (-x^{13}+18 x^{12}-172 x^{11}+1191 x^{10}-6155 x^9+22608 x^8-56904 x^7+96081 x^6-106813 x^5+76620 x^4-34766 x^3+9603 x^2-1472 x+e^{15} \left (-x^7+3 x^6-3 x^4+x^3\right )+e^{10} \left (x^9-37 x^7+135 x^6-185 x^5+111 x^4-30 x^3+3 x^2\right )+e^5 \left (x^{11}-21 x^{10}+127 x^9-312 x^8+326 x^7-342 x^6+1009 x^5-1533 x^4+1003 x^3-294 x^2+32 x\right )+96\right ) \log (x)}{x \left (x^2-3 x+1\right )^5}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{64} \int \frac {\left (-x^5+9 x^4-\left (29+e^5\right ) x^3+39 x^2+\left (-19+e^5\right ) x+3\right ) \left (-27 \left (x^2-3 x+1\right )^3 \log ^3(x)+27 x \left (x^2-3 x+1\right )^2 \left (x^2-3 x-e^5+1\right ) \log ^2(x)-9 \left (x^2-3 x+1\right ) \left (x^6-6 x^5+\left (43-2 e^5\right ) x^4+6 \left (-33+e^5\right ) x^3+\left (353-2 e^5+e^{10}\right ) x^2-192 x+32\right ) \log (x)+x \left (\left (x^2+96\right ) \left (x^2-3 x+1\right )^3-3 e^5 \left (x^2+32\right ) \left (x^2-3 x+1\right )^2+3 e^{10} x^2 \left (x^2-3 x+1\right )-e^{15} x^2\right )\right )}{x \left (x^2-3 x+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{64} \int \left (\frac {27 \left (x^5-9 x^4+29 \left (1+\frac {e^5}{29}\right ) x^3-39 x^2+19 \left (1-\frac {e^5}{19}\right ) x-3\right ) \log ^3(x)}{x \left (x^2-3 x+1\right )^2}+\frac {27 \left (x^2-3 x-e^5+1\right ) \left (-x^5+9 x^4-29 \left (1+\frac {e^5}{29}\right ) x^3+39 x^2-19 \left (1-\frac {e^5}{19}\right ) x+3\right ) \log ^2(x)}{\left (x^2-3 x+1\right )^3}+\frac {9 \left (-x^5+9 x^4-29 \left (1+\frac {e^5}{29}\right ) x^3+39 x^2-19 \left (1-\frac {e^5}{19}\right ) x+3\right ) \left (-x^6+6 x^5-43 \left (1-\frac {2 e^5}{43}\right ) x^4+198 \left (1-\frac {e^5}{33}\right ) x^3-353 \left (1+\frac {1}{353} e^5 \left (-2+e^5\right )\right ) x^2+192 x-32\right ) \log (x)}{x \left (x^2-3 x+1\right )^4}+\frac {\left (x^2-3 x-e^5+1\right ) \left (-x^5+9 x^4-29 \left (1+\frac {e^5}{29}\right ) x^3+39 x^2-19 \left (1-\frac {e^5}{19}\right ) x+3\right ) \left (x^6-6 x^5+107 \left (1-\frac {2 e^5}{107}\right ) x^4-582 \left (1-\frac {e^5}{97}\right ) x^3+1057 \left (1+\frac {e^5 \left (-2+e^5\right )}{1057}\right ) x^2-576 x+96\right )}{\left (x^2-3 x+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{64} \left (\frac {x^4}{4}-3 \log (x) x^3+\frac {27}{2} \log ^2(x) x^2+\left (48-e^5\right ) x^2+\frac {216 e^5 \log ^3(x) x}{5 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {162 e^5 \log ^3(x) x}{5 \left (-2 x-\sqrt {5}+3\right )}+\frac {216 e^5 \log ^3(x) x}{5 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {162 e^5 \log ^3(x) x}{5 \left (-2 x+\sqrt {5}+3\right )}-27 \log ^3(x) x-\frac {324 e^5 \left (1+e^5\right ) \log ^2(x) x}{5 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}+\frac {54 e^5 \left (7-e^5\right ) \log ^2(x) x}{5 \left (-2 x-\sqrt {5}+3\right )}+\frac {378 \left (9-\sqrt {5}\right ) e^{10} \log ^2(x) x}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {972 e^{10} \log ^2(x) x}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {324 e^5 \left (1+e^5\right ) \log ^2(x) x}{5 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {54 e^5 \left (7-e^5\right ) \log ^2(x) x}{5 \left (-2 x+\sqrt {5}+3\right )}+\frac {378 \left (9+\sqrt {5}\right ) e^{10} \log ^2(x) x}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {972 e^{10} \log ^2(x) x}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {36 e^5 \left (71+13 e^5-e^{10}\right ) \log (x) x}{5 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}+\frac {216 e^{10} \left (7+3 e^5\right ) \log (x) x}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {108 \left (9-\sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log (x) x}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {108 e^5 \left (19-2 e^5\right ) \log (x) x}{5 \left (-2 x-\sqrt {5}+3\right )}-\frac {648 \left (15-\sqrt {5}\right ) e^{15} \log (x) x}{125 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}+\frac {504 e^{15} \log (x) x}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}+\frac {756 e^{10} \log (x) x}{5 \sqrt {5} \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {648 e^{10} \log (x) x}{5 \sqrt {5} \left (3-\sqrt {5}\right )^2 \left (-2 x-\sqrt {5}+3\right )}+\frac {36 e^5 \left (71+13 e^5-e^{10}\right ) \log (x) x}{5 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {216 e^{10} \left (7+3 e^5\right ) \log (x) x}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {108 \left (9+\sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log (x) x}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {108 e^5 \left (19-2 e^5\right ) \log (x) x}{5 \left (-2 x+\sqrt {5}+3\right )}-\frac {648 \left (15+\sqrt {5}\right ) e^{15} \log (x) x}{125 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {504 e^{15} \log (x) x}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {756 e^{10} \log (x) x}{5 \sqrt {5} \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {648 e^{10} \log (x) x}{5 \sqrt {5} \left (3+\sqrt {5}\right )^2 \left (-2 x+\sqrt {5}+3\right )}-9 \left (32-e^5\right ) \log (x) x-6 \left (48-e^5\right ) x+9 \left (32-e^5\right ) x+\frac {81 \log ^4(x)}{4}+\frac {189 \left (5-3 \sqrt {5}\right ) e^{10} \log ^2(x)}{25 \left (-2 x-\sqrt {5}+3\right )^2}+\frac {162 e^{10} \log ^2(x)}{5 \sqrt {5} \left (-2 x-\sqrt {5}+3\right )^2}+\frac {189 \left (5+3 \sqrt {5}\right ) e^{10} \log ^2(x)}{25 \left (-2 x+\sqrt {5}+3\right )^2}-\frac {162 e^{10} \log ^2(x)}{5 \sqrt {5} \left (-2 x+\sqrt {5}+3\right )^2}+432 \log ^2(x)+\frac {3}{250} e^5 \left (1125-\sqrt {5} \left (5325+60 e^5+22 e^{10}\right )\right ) \log \left (-2 x-\sqrt {5}+3\right )+\frac {18 e^5 \left (71+13 e^5-e^{10}\right ) \log \left (-2 x-\sqrt {5}+3\right )}{5 \left (3-\sqrt {5}\right )}+\frac {108 e^{10} \left (7+3 e^5\right ) \log \left (-2 x-\sqrt {5}+3\right )}{25 \left (3-\sqrt {5}\right )}-\frac {54 \left (9-\sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log \left (-2 x-\sqrt {5}+3\right )}{25 \left (3-\sqrt {5}\right )}-\frac {54}{5} e^5 \left (19-2 e^5\right ) \log \left (-2 x-\sqrt {5}+3\right )-\frac {324 \left (15-\sqrt {5}\right ) e^{15} \log \left (-2 x-\sqrt {5}+3\right )}{125 \left (3-\sqrt {5}\right )}+\frac {252 e^{15} \log \left (-2 x-\sqrt {5}+3\right )}{25 \left (3-\sqrt {5}\right )}-\frac {216 e^{15} \log \left (-2 x-\sqrt {5}+3\right )}{25 \left (3-\sqrt {5}\right )^2}+\frac {168 e^{15} \log \left (-2 x-\sqrt {5}+3\right )}{25 \left (3-\sqrt {5}\right )^3}+\frac {378 e^{10} \log \left (-2 x-\sqrt {5}+3\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right )}-\frac {324 e^{10} \log \left (-2 x-\sqrt {5}+3\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right )^2}-\frac {18 e^5 \left (71+13 e^5-e^{10}\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5}}-\frac {108 e^{10} \left (7+3 e^5\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{25 \sqrt {5}}-\frac {324 e^5 \left (1+e^5\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \left (3+\sqrt {5}\right )}+\frac {54}{5} e^5 \left (7-e^5\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )+\frac {486 e^{10} \left (6-e^5\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{25 \sqrt {5}}+\frac {162 e^5 \left (19-2 e^5\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5}}+\frac {144 e^{15} \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5}}+\frac {378 \left (9+\sqrt {5}\right ) e^{10} \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )}-\frac {972 e^{10} \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )}+\frac {3}{250} e^5 \left (1125+\sqrt {5} \left (5325+60 e^5+22 e^{10}\right )\right ) \log \left (-2 x+\sqrt {5}+3\right )+\frac {18 e^5 \left (71+13 e^5-e^{10}\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \left (3+\sqrt {5}\right )}+\frac {108 e^{10} \left (7+3 e^5\right ) \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )}+\frac {36 e^{10} \left (7+3 e^5\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right )^2}-\frac {54 \left (9+\sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )}-\frac {54 e^{10} \left (6-e^5\right ) \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right )}-\frac {54}{5} e^5 \left (19-2 e^5\right ) \log \left (-2 x+\sqrt {5}+3\right )-\frac {324 \left (5+6 \sqrt {5}\right ) e^{15} \log \left (-2 x+\sqrt {5}+3\right )}{125 \left (3+\sqrt {5}\right )^2}-\frac {324 \left (15+\sqrt {5}\right ) e^{15} \log \left (-2 x+\sqrt {5}+3\right )}{125 \left (3+\sqrt {5}\right )}+\frac {252 e^{15} \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )}+\frac {504 e^{15} \log \left (-2 x+\sqrt {5}+3\right )}{25 \sqrt {5} \left (3+\sqrt {5}\right )^2}-\frac {216 e^{15} \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )^2}+\frac {168 e^{15} \log \left (-2 x+\sqrt {5}+3\right )}{25 \left (3+\sqrt {5}\right )^3}-\frac {378 e^{10} \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right )}+\frac {324 e^{10} \log \left (-2 x+\sqrt {5}+3\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right )^2}-\frac {378 e^{10} \log \left (1-\frac {3-\sqrt {5}}{2 x}\right ) \log (x)}{5 \sqrt {5} \left (3-\sqrt {5}\right )}+\frac {324 e^{10} \log \left (1-\frac {3-\sqrt {5}}{2 x}\right ) \log (x)}{5 \sqrt {5} \left (3-\sqrt {5}\right )^2}+\frac {378 e^{10} \log \left (1-\frac {3+\sqrt {5}}{2 x}\right ) \log (x)}{5 \sqrt {5} \left (3+\sqrt {5}\right )}-\frac {324 e^{10} \log \left (1-\frac {3+\sqrt {5}}{2 x}\right ) \log (x)}{5 \sqrt {5} \left (3+\sqrt {5}\right )^2}-\frac {36 e^{10} \left (7+3 e^5\right ) \log (x)}{5 \sqrt {5} \left (-2 x-\sqrt {5}+3\right )^2}-\frac {54 \left (5-3 \sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log (x)}{25 \left (-2 x-\sqrt {5}+3\right )^2}-\frac {324 \left (5-6 \sqrt {5}\right ) e^{15} \log (x)}{125 \left (-2 x-\sqrt {5}+3\right )^2}-\frac {504 e^{15} \log (x)}{25 \sqrt {5} \left (-2 x-\sqrt {5}+3\right )^2}+\frac {36 e^{10} \left (7+3 e^5\right ) \log (x)}{5 \sqrt {5} \left (-2 x+\sqrt {5}+3\right )^2}-\frac {54 \left (5+3 \sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log (x)}{25 \left (-2 x+\sqrt {5}+3\right )^2}-\frac {324 \left (5+6 \sqrt {5}\right ) e^{15} \log (x)}{125 \left (-2 x+\sqrt {5}+3\right )^2}+\frac {504 e^{15} \log (x)}{25 \sqrt {5} \left (-2 x+\sqrt {5}+3\right )^2}-\frac {216 \left (3-\sqrt {5}\right ) e^{15} \log (x)}{25 \left (-2 x-\sqrt {5}+3\right )^3}+\frac {168 e^{15} \log (x)}{25 \left (-2 x-\sqrt {5}+3\right )^3}-\frac {216 \left (3+\sqrt {5}\right ) e^{15} \log (x)}{25 \left (-2 x+\sqrt {5}+3\right )^3}+\frac {168 e^{15} \log (x)}{25 \left (-2 x+\sqrt {5}+3\right )^3}-\frac {36 e^{10} \left (7+3 e^5\right ) \log (x)}{5 \sqrt {5} \left (3+\sqrt {5}\right )^2}+\frac {36 e^{10} \left (7+3 e^5\right ) \log (x)}{5 \sqrt {5} \left (3-\sqrt {5}\right )^2}+\frac {54 e^{10} \left (6-e^5\right ) \log (x)}{5 \sqrt {5} \left (3+\sqrt {5}\right )}-\frac {54 e^{10} \left (6-e^5\right ) \log (x)}{5 \sqrt {5} \left (3-\sqrt {5}\right )}+\frac {324 \left (5+6 \sqrt {5}\right ) e^{15} \log (x)}{125 \left (3+\sqrt {5}\right )^2}-\frac {504 e^{15} \log (x)}{25 \sqrt {5} \left (3+\sqrt {5}\right )^2}+\frac {216 e^{15} \log (x)}{25 \left (3+\sqrt {5}\right )^2}-\frac {168 e^{15} \log (x)}{25 \left (3+\sqrt {5}\right )^3}+\frac {324 \left (5-6 \sqrt {5}\right ) e^{15} \log (x)}{125 \left (3-\sqrt {5}\right )^2}+\frac {504 e^{15} \log (x)}{25 \sqrt {5} \left (3-\sqrt {5}\right )^2}+\frac {216 e^{15} \log (x)}{25 \left (3-\sqrt {5}\right )^2}-\frac {168 e^{15} \log (x)}{25 \left (3-\sqrt {5}\right )^3}-\frac {9}{5} e^5 \left (15+\sqrt {5} \left (49-e^5\right )\right ) \log \left (\frac {1}{2} \left (3+\sqrt {5}\right )\right ) \log \left (2 x-\sqrt {5}-3\right )-\frac {9}{5} e^5 \left (15-\sqrt {5} \left (49-e^5\right )\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )+\frac {18 e^5 \left (71+13 e^5-e^{10}\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{5 \sqrt {5}}+\frac {108 e^{10} \left (7+3 e^5\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{25 \sqrt {5}}-\frac {324 e^5 \left (1+e^5\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{5 \left (3-\sqrt {5}\right )}+\frac {54}{5} e^5 \left (7-e^5\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )-\frac {486 e^{10} \left (6-e^5\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{25 \sqrt {5}}-\frac {162 e^5 \left (19-2 e^5\right ) \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{5 \sqrt {5}}-\frac {144 e^{15} \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{5 \sqrt {5}}+\frac {378 \left (9-\sqrt {5}\right ) e^{10} \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{25 \left (3-\sqrt {5}\right )}-\frac {972 e^{10} \log \left (\frac {1}{2} \left (3-\sqrt {5}\right )\right ) \log \left (2 x+\sqrt {5}-3\right )}{25 \left (3-\sqrt {5}\right )}-\frac {18 e^{10} \left (7+3 e^5\right ) \log \left (2 \left (9-4 \sqrt {5}\right )-\left (7-3 \sqrt {5}\right ) x\right )}{5 \sqrt {5} \left (7-3 \sqrt {5}\right )}-\frac {27 \left (5-3 \sqrt {5}\right ) e^{10} \left (6-e^5\right ) \log \left (2 \left (9-4 \sqrt {5}\right )-\left (7-3 \sqrt {5}\right ) x\right )}{25 \left (7-3 \sqrt {5}\right )}-\frac {162 \left (5-6 \sqrt {5}\right ) e^{15} \log \left (2 \left (9-4 \sqrt {5}\right )-\left (7-3 \sqrt {5}\right ) x\right )}{125 \left (7-3 \sqrt {5}\right )}-\frac {252 e^{15} \log \left (2 \left (9-4 \sqrt {5}\right )-\left (7-3 \sqrt {5}\right ) x\right )}{25 \sqrt {5} \left (7-3 \sqrt {5}\right )}-\frac {162 e^5 \left (1+e^5\right ) \log ^2(x) \log \left (1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {81 e^5 \left (7-e^5\right ) \log ^2(x) \log \left (1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {243 e^{10} \log ^2(x) \log \left (1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {324 e^5 \log ^2(x) \log \left (1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \left (3-\sqrt {5}\right )}-\frac {162 e^5 \log ^2(x) \log \left (1-\frac {2 x}{3-\sqrt {5}}\right )}{\sqrt {5}}-\frac {243}{5} e^5 \log ^2(x) \log \left (1-\frac {2 x}{3-\sqrt {5}}\right )+\frac {162 e^5 \left (1+e^5\right ) \log ^2(x) \log \left (1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {81 e^5 \left (7-e^5\right ) \log ^2(x) \log \left (1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {243 e^{10} \log ^2(x) \log \left (1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {324 e^5 \log ^2(x) \log \left (1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \left (3+\sqrt {5}\right )}+\frac {162 e^5 \log ^2(x) \log \left (1-\frac {2 x}{3+\sqrt {5}}\right )}{\sqrt {5}}-\frac {243}{5} e^5 \log ^2(x) \log \left (1-\frac {2 x}{3+\sqrt {5}}\right )+\frac {378 e^{10} \operatorname {PolyLog}\left (2,\frac {3-\sqrt {5}}{2 x}\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right )}-\frac {324 e^{10} \operatorname {PolyLog}\left (2,\frac {3-\sqrt {5}}{2 x}\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right )^2}-\frac {378 e^{10} \operatorname {PolyLog}\left (2,\frac {3+\sqrt {5}}{2 x}\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right )}+\frac {324 e^{10} \operatorname {PolyLog}\left (2,\frac {3+\sqrt {5}}{2 x}\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right )^2}-\frac {324 e^5 \left (1+e^5\right ) \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {162 e^5 \left (7-e^5\right ) \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {486 e^{10} \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {648 e^5 \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3-\sqrt {5}}\right )}{5 \left (3-\sqrt {5}\right )}-\frac {324 e^5 \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3-\sqrt {5}}\right )}{\sqrt {5}}-\frac {486}{5} e^5 \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3-\sqrt {5}}\right )+\frac {324 e^5 \left (1+e^5\right ) \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {162 e^5 \left (7-e^5\right ) \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {486 e^{10} \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {648 e^5 \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3+\sqrt {5}}\right )}{5 \left (3+\sqrt {5}\right )}+\frac {324 e^5 \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3+\sqrt {5}}\right )}{\sqrt {5}}-\frac {486}{5} e^5 \log (x) \operatorname {PolyLog}\left (2,\frac {2 x}{3+\sqrt {5}}\right )+\frac {9}{5} e^5 \left (15-\sqrt {5} \left (49-e^5\right )\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )-\frac {18 e^5 \left (71+13 e^5-e^{10}\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {108 e^{10} \left (7+3 e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{25 \sqrt {5}}+\frac {324 e^5 \left (1+e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \left (3-\sqrt {5}\right )}-\frac {54}{5} e^5 \left (7-e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )+\frac {486 e^{10} \left (6-e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{25 \sqrt {5}}+\frac {162 e^5 \left (19-2 e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {144 e^{15} \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {378 \left (9-\sqrt {5}\right ) e^{10} \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{25 \left (3-\sqrt {5}\right )}+\frac {972 e^{10} \operatorname {PolyLog}\left (2,1-\frac {2 x}{3-\sqrt {5}}\right )}{25 \left (3-\sqrt {5}\right )}+\frac {9}{5} e^5 \left (15+\sqrt {5} \left (49-e^5\right )\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )+\frac {18 e^5 \left (71+13 e^5-e^{10}\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {108 e^{10} \left (7+3 e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{25 \sqrt {5}}+\frac {324 e^5 \left (1+e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \left (3+\sqrt {5}\right )}-\frac {54}{5} e^5 \left (7-e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )-\frac {486 e^{10} \left (6-e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{25 \sqrt {5}}-\frac {162 e^5 \left (19-2 e^5\right ) \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {144 e^{15} \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {378 \left (9+\sqrt {5}\right ) e^{10} \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{25 \left (3+\sqrt {5}\right )}+\frac {972 e^{10} \operatorname {PolyLog}\left (2,1-\frac {2 x}{3+\sqrt {5}}\right )}{25 \left (3+\sqrt {5}\right )}+\frac {324 e^5 \left (1+e^5\right ) \operatorname {PolyLog}\left (3,\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {162 e^5 \left (7-e^5\right ) \operatorname {PolyLog}\left (3,\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {486 e^{10} \operatorname {PolyLog}\left (3,\frac {2 x}{3-\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {648 e^5 \operatorname {PolyLog}\left (3,\frac {2 x}{3-\sqrt {5}}\right )}{5 \left (3-\sqrt {5}\right )}+\frac {324 e^5 \operatorname {PolyLog}\left (3,\frac {2 x}{3-\sqrt {5}}\right )}{\sqrt {5}}+\frac {486}{5} e^5 \operatorname {PolyLog}\left (3,\frac {2 x}{3-\sqrt {5}}\right )-\frac {324 e^5 \left (1+e^5\right ) \operatorname {PolyLog}\left (3,\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {162 e^5 \left (7-e^5\right ) \operatorname {PolyLog}\left (3,\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}+\frac {486 e^{10} \operatorname {PolyLog}\left (3,\frac {2 x}{3+\sqrt {5}}\right )}{5 \sqrt {5}}-\frac {648 e^5 \operatorname {PolyLog}\left (3,\frac {2 x}{3+\sqrt {5}}\right )}{5 \left (3+\sqrt {5}\right )}-\frac {324 e^5 \operatorname {PolyLog}\left (3,\frac {2 x}{3+\sqrt {5}}\right )}{\sqrt {5}}+\frac {486}{5} e^5 \operatorname {PolyLog}\left (3,\frac {2 x}{3+\sqrt {5}}\right )+\frac {36 e^{10} \left (7+3 e^5\right )}{5 \sqrt {5} \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {54 e^{10} \left (6-e^5\right )}{5 \sqrt {5} \left (-2 x-\sqrt {5}+3\right )}+\frac {324 \left (5-6 \sqrt {5}\right ) e^{15}}{125 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}+\frac {504 e^{15}}{25 \sqrt {5} \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}+\frac {216 e^{15}}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )}-\frac {168 e^{15}}{25 \left (3-\sqrt {5}\right )^2 \left (-2 x-\sqrt {5}+3\right )}-\frac {36 e^{10} \left (7+3 e^5\right )}{5 \sqrt {5} \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {54 e^{10} \left (6-e^5\right )}{5 \sqrt {5} \left (-2 x+\sqrt {5}+3\right )}+\frac {324 \left (5+6 \sqrt {5}\right ) e^{15}}{125 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {504 e^{15}}{25 \sqrt {5} \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}+\frac {216 e^{15}}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )}-\frac {168 e^{15}}{25 \left (3+\sqrt {5}\right )^2 \left (-2 x+\sqrt {5}+3\right )}+\frac {e^5 \left (-6 \left (2575-180 e^5-11 e^{10}\right ) x-149 e^{10}+2655 e^5+5200\right )}{50 \left (x^2-3 x+1\right )}-\frac {84 e^{15}}{25 \left (3-\sqrt {5}\right ) \left (-2 x-\sqrt {5}+3\right )^2}+\frac {108 e^{15}}{25 \left (-2 x-\sqrt {5}+3\right )^2}-\frac {84 e^{15}}{25 \left (3+\sqrt {5}\right ) \left (-2 x+\sqrt {5}+3\right )^2}+\frac {108 e^{15}}{25 \left (-2 x+\sqrt {5}+3\right )^2}-\frac {e^{10} \left (-54 \left (65-3 e^5\right ) x-5 e^{10}+122 e^5+1200\right )}{20 \left (x^2-3 x+1\right )^2}+\frac {e^{15} \left (-6 \left (14-e^5\right ) x+7 e^5+32\right )}{4 \left (x^2-3 x+1\right )^3}-\frac {e^{20} (8-21 x)}{4 \left (x^2-3 x+1\right )^4}\right )\) |
Int[(-288*x + 4416*x^2 - 28803*x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283473*x^7 + 164104*x^8 - 61968*x^9 + 15115*x^10 - 2343*x^11 + 236*x^12 - 18*x^13 + x^14 + E^20*(x^4 - x^6) + E^15*(3*x^3 - 22*x^4 + 48*x^5 - 29*x ^6 + 2*x^8) + E^10*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 171* x^7 + 45*x^8 - 18*x^9) + E^5*(288*x - 3648*x^2 + 18729*x^3 - 49936*x^4 + 7 4007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 253*x^10 + 36*x^1 1 - 2*x^12) + (864 - 13248*x + 86427*x^2 - 312894*x^3 + 689580*x^4 - 96131 7*x^5 + 864729*x^6 - 512136*x^7 + 203472*x^8 - 55395*x^9 + 10719*x^10 - 15 48*x^11 + 162*x^12 - 9*x^13 + E^15*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7) + E^1 0*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^9) + E ^5*(288*x - 2646*x^2 + 9027*x^3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x ^7 - 2808*x^8 + 1143*x^9 - 189*x^10 + 9*x^11))*Log[x] + (-81*x + 1242*x^2 - 8100*x^3 + 29295*x^4 - 64395*x^5 + 89208*x^6 - 79056*x^7 + 45225*x^8 - 1 6605*x^9 + 3780*x^10 - 486*x^11 + 27*x^12 + E^10*(27*x^2 - 162*x^3 + 270*x ^4 - 270*x^6 + 162*x^7 - 27*x^8) + E^5*(81*x - 1026*x^2 + 5265*x^3 - 14013 *x^4 + 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9))*Log[x]^2 + (81 - 1242*x + 8100*x^2 - 29295*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x^9 + 486*x^10 - 27*x^11 + E^5*(27*x - 243*x^ 2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9))*Log[x]^3)/( 64*x - 960*x^2 + 6080*x^3 - 21120*x^4 + 43840*x^5 - 55872*x^6 + 43840*x^7 - 21120*x^8 + 6080*x^9 - 960*x^10 + 64*x^11),x]
((108*E^15)/(25*(3 - Sqrt[5] - 2*x)^2) - (84*E^15)/(25*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)^2) - (168*E^15)/(25*(3 - Sqrt[5])^2*(3 - Sqrt[5] - 2*x)) + (216*E^15)/(25*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (504*E^15)/(25*Sqrt[5] *(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (324*(5 - 6*Sqrt[5])*E^15)/(125*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) - (54*E^10*(6 - E^5))/(5*Sqrt[5]*(3 - Sqrt[ 5] - 2*x)) + (36*E^10*(7 + 3*E^5))/(5*Sqrt[5]*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (108*E^15)/(25*(3 + Sqrt[5] - 2*x)^2) - (84*E^15)/(25*(3 + Sqrt[5 ])*(3 + Sqrt[5] - 2*x)^2) - (168*E^15)/(25*(3 + Sqrt[5])^2*(3 + Sqrt[5] - 2*x)) + (216*E^15)/(25*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) - (504*E^15)/(25 *Sqrt[5]*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (324*(5 + 6*Sqrt[5])*E^15)/( 125*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (54*E^10*(6 - E^5))/(5*Sqrt[5]*(3 + Sqrt[5] - 2*x)) - (36*E^10*(7 + 3*E^5))/(5*Sqrt[5]*(3 + Sqrt[5])*(3 + S qrt[5] - 2*x)) + 9*(32 - E^5)*x - 6*(48 - E^5)*x + (48 - E^5)*x^2 + x^4/4 - (E^20*(8 - 21*x))/(4*(1 - 3*x + x^2)^4) + (E^15*(32 + 7*E^5 - 6*(14 - E^ 5)*x))/(4*(1 - 3*x + x^2)^3) - (E^10*(1200 + 122*E^5 - 5*E^10 - 54*(65 - 3 *E^5)*x))/(20*(1 - 3*x + x^2)^2) + (E^5*(5200 + 2655*E^5 - 149*E^10 - 6*(2 575 - 180*E^5 - 11*E^10)*x))/(50*(1 - 3*x + x^2)) - (324*E^10*Log[3 - Sqrt [5] - 2*x])/(5*Sqrt[5]*(3 - Sqrt[5])^2) + (378*E^10*Log[3 - Sqrt[5] - 2*x] )/(5*Sqrt[5]*(3 - Sqrt[5])) + (168*E^15*Log[3 - Sqrt[5] - 2*x])/(25*(3 - S qrt[5])^3) - (216*E^15*Log[3 - Sqrt[5] - 2*x])/(25*(3 - Sqrt[5])^2) + (...
3.8.3.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(627\) vs. \(2(45)=90\).
Time = 0.85 (sec) , antiderivative size = 628, normalized size of antiderivative = 20.93
| method | result | size |
| risch | \(\frac {81 \ln \left (x \right )^{4}}{256}+\frac {27 x \left (-x^{2}+{\mathrm e}^{5}+3 x -1\right ) \ln \left (x \right )^{3}}{64 \left (x^{2}-3 x +1\right )}+\frac {27 \left (x^{6}-2 x^{4} {\mathrm e}^{5}-6 x^{5}+x^{2} {\mathrm e}^{10}+6 x^{3} {\mathrm e}^{5}+43 x^{4}-2 x^{2} {\mathrm e}^{5}-198 x^{3}+353 x^{2}-192 x +32\right ) \ln \left (x \right )^{2}}{128 \left (x^{2}-3 x +1\right )^{2}}+\frac {3 \left (-x^{9}+3 x^{7} {\mathrm e}^{5}+9 x^{8}-3 x^{5} {\mathrm e}^{10}-27 x^{6} {\mathrm e}^{5}-126 x^{7}+x^{3} {\mathrm e}^{15}+9 x^{4} {\mathrm e}^{10}+210 x^{5} {\mathrm e}^{5}+909 x^{6}-3 x^{3} {\mathrm e}^{10}-864 x^{4} {\mathrm e}^{5}-2910 x^{5}+1464 x^{3} {\mathrm e}^{5}+4329 x^{4}-846 x^{2} {\mathrm e}^{5}-2881 x^{3}+177 x \,{\mathrm e}^{5}+864 x^{2}-9 \,{\mathrm e}^{5}-96 x \right ) \ln \left (x \right )}{64 \left (x^{2}-3 x +1\right ) \left (x^{4}-6 x^{3}+11 x^{2}-6 x +1\right )}+\frac {72 x \,{\mathrm e}^{10}-1356 x^{7} {\mathrm e}^{5}+23744 x^{2} {\mathrm e}^{5}-42588 x^{5} {\mathrm e}^{5}-88 x^{8} {\mathrm e}^{5}+69596 x^{4} {\mathrm e}^{5}-56448 x^{3} {\mathrm e}^{5}+108 \ln \left (-x \right ) {\mathrm e}^{5}+12488 x^{6} {\mathrm e}^{5}-288 x^{3} {\mathrm e}^{10}-6 \,{\mathrm e}^{10}-12 x^{11}+x^{12}-4992 x \,{\mathrm e}^{5}+250 x^{10}-2448 x^{9}-27792 x^{7}+11331 x^{8}+11137 x^{4}-2304 x^{3}+192 x^{2}+37498 x^{6}-27660 x^{5}+416 \,{\mathrm e}^{5}-324 x^{5} {\mathrm e}^{10}+12 x^{5} {\mathrm e}^{15}+948 x^{4} {\mathrm e}^{10}-4 x^{4} {\mathrm e}^{15}+{\mathrm e}^{20} x^{4}-4 \,{\mathrm e}^{5} x^{10}-4 \,{\mathrm e}^{15} x^{6}+108 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{8}-1296 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{7}+6264 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{6}+36 x^{7} {\mathrm e}^{10}-90 x^{6} {\mathrm e}^{10}+36 \,{\mathrm e}^{5} x^{9}-15552 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{5}+21060 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{4}-15552 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{3}+6264 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{2}-1296 \,{\mathrm e}^{5} \ln \left (-x \right ) x -156 x^{2} {\mathrm e}^{10}}{256 \left (x^{4}-6 x^{3}+11 x^{2}-6 x +1\right ) \left (x^{2}-3 x +1\right )^{2}}\) | \(628\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(971\) |
int((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x)*exp(5 )-27*x^11+486*x^10-3780*x^9+16605*x^8-45225*x^7+79056*x^6-89208*x^5+64395* x^4-29295*x^3+8100*x^2-1242*x+81)*ln(x)^3+((-27*x^8+162*x^7-270*x^6+270*x^ 4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+20655*x^5- 14013*x^4+5265*x^3-1026*x^2+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10-16605* x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+1242*x^2-81 *x)*ln(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+1215*x^6 -1665*x^5+999*x^4-270*x^3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x^9-2808* x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+288*x)*exp(5)-9 *x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^7+864729 *x^6-961317*x^5+689580*x^4-312894*x^3+86427*x^2-13248*x+864)*ln(x)+(-x^6+x ^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+(-18*x^9+45*x^8+1 71*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12+36*x^11- 253*x^10+1494*x^9-8121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^4+18729*x ^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^11+15115*x^10-61968 *x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803*x^3+4416 *x^2-288*x)/(64*x^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872*x^6+43840 *x^5-21120*x^4+6080*x^3-960*x^2+64*x),x,method=_RETURNVERBOSE)
81/256*ln(x)^4+27/64*x*(-x^2+exp(5)+3*x-1)/(x^2-3*x+1)*ln(x)^3+27/128*(x^6 -2*x^4*exp(5)-6*x^5+x^2*exp(5)^2+6*x^3*exp(5)+43*x^4-2*x^2*exp(5)-198*x^3+ 353*x^2-192*x+32)/(x^2-3*x+1)^2*ln(x)^2+3/64*(-x^9+3*x^7*exp(5)+9*x^8-3*x^ 5*exp(5)^2-27*x^6*exp(5)-126*x^7+x^3*exp(5)^3+9*x^4*exp(5)^2+210*x^5*exp(5 )+909*x^6-3*x^3*exp(5)^2-864*x^4*exp(5)-2910*x^5+1464*x^3*exp(5)+4329*x^4- 846*x^2*exp(5)-2881*x^3+177*x*exp(5)+864*x^2-9*exp(5)-96*x)/(x^2-3*x+1)/(x ^4-6*x^3+11*x^2-6*x+1)*ln(x)+1/256*(-4*x^6*exp(5)^3+x^4*exp(5)^4-1356*x^7* exp(5)+23744*x^2*exp(5)+12*x^5*exp(5)^3-324*x^5*exp(5)^2-42588*x^5*exp(5)- 288*x^3*exp(5)^2-88*x^8*exp(5)+69596*x^4*exp(5)-156*x^2*exp(5)^2+948*x^4*e xp(5)^2-90*x^6*exp(5)^2-56448*x^3*exp(5)+108*ln(-x)*exp(5)+12488*x^6*exp(5 )-4*x^4*exp(5)^3-12*x^11+x^12+72*x*exp(5)^2-4992*x*exp(5)+250*x^10-2448*x^ 9-27792*x^7+11331*x^8+11137*x^4-2304*x^3+192*x^2+37498*x^6-27660*x^5+416*e xp(5)-6*exp(5)^2-4*exp(5)*x^10+36*exp(5)^2*x^7+108*exp(5)*ln(-x)*x^8-1296* exp(5)*ln(-x)*x^7+6264*exp(5)*ln(-x)*x^6+36*exp(5)*x^9-15552*exp(5)*ln(-x) *x^5+21060*exp(5)*ln(-x)*x^4-15552*exp(5)*ln(-x)*x^3+6264*exp(5)*ln(-x)*x^ 2-1296*exp(5)*ln(-x)*x)/(x^4-6*x^3+11*x^2-6*x+1)/(x^2-3*x+1)^2
Leaf count of result is larger than twice the leaf count of optimal. 592 vs. \(2 (26) = 52\).
Time = 0.28 (sec) , antiderivative size = 592, normalized size of antiderivative = 19.73 \[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx=\frac {x^{12} - 12 \, x^{11} + 250 \, x^{10} - 2448 \, x^{9} + 11331 \, x^{8} - 27792 \, x^{7} + 37498 \, x^{6} - 27660 \, x^{5} + x^{4} e^{20} + 81 \, {\left (x^{8} - 12 \, x^{7} + 58 \, x^{6} - 144 \, x^{5} + 195 \, x^{4} - 144 \, x^{3} + 58 \, x^{2} - 12 \, x + 1\right )} \log \left (x\right )^{4} + 11137 \, x^{4} - 108 \, {\left (x^{9} - 12 \, x^{8} + 58 \, x^{7} - 144 \, x^{6} + 195 \, x^{5} - 144 \, x^{4} + 58 \, x^{3} - 12 \, x^{2} - {\left (x^{7} - 9 \, x^{6} + 30 \, x^{5} - 45 \, x^{4} + 30 \, x^{3} - 9 \, x^{2} + x\right )} e^{5} + x\right )} \log \left (x\right )^{3} - 2304 \, x^{3} + 54 \, {\left (x^{10} - 12 \, x^{9} + 90 \, x^{8} - 528 \, x^{7} + 2051 \, x^{6} - 4752 \, x^{5} + 6298 \, x^{4} - 4620 \, x^{3} + 1857 \, x^{2} + {\left (x^{6} - 6 \, x^{5} + 11 \, x^{4} - 6 \, x^{3} + x^{2}\right )} e^{10} - 2 \, {\left (x^{8} - 9 \, x^{7} + 30 \, x^{6} - 45 \, x^{5} + 30 \, x^{4} - 9 \, x^{3} + x^{2}\right )} e^{5} - 384 \, x + 32\right )} \log \left (x\right )^{2} + 192 \, x^{2} - 4 \, {\left (x^{6} - 3 \, x^{5} + x^{4}\right )} e^{15} + 6 \, {\left (6 \, x^{7} - 15 \, x^{6} - 54 \, x^{5} + 158 \, x^{4} - 48 \, x^{3} - 26 \, x^{2} + 12 \, x - 1\right )} e^{10} - 4 \, {\left (x^{10} - 9 \, x^{9} + 22 \, x^{8} + 339 \, x^{7} - 3122 \, x^{6} + 10647 \, x^{5} - 17399 \, x^{4} + 14112 \, x^{3} - 5936 \, x^{2} + 1248 \, x - 104\right )} e^{5} - 12 \, {\left (x^{11} - 12 \, x^{10} + 154 \, x^{9} - 1296 \, x^{8} + 5763 \, x^{7} - 13968 \, x^{6} + 18778 \, x^{5} - 13836 \, x^{4} + 5569 \, x^{3} - 1152 \, x^{2} - {\left (x^{5} - 3 \, x^{4} + x^{3}\right )} e^{15} + 3 \, {\left (x^{7} - 6 \, x^{6} + 11 \, x^{5} - 6 \, x^{4} + x^{3}\right )} e^{10} - 3 \, {\left (x^{9} - 9 \, x^{8} + 62 \, x^{7} - 333 \, x^{6} + 990 \, x^{5} - 1449 \, x^{4} + 961 \, x^{3} - 288 \, x^{2} + 32 \, x\right )} e^{5} + 96 \, x\right )} \log \left (x\right )}{256 \, {\left (x^{8} - 12 \, x^{7} + 58 \, x^{6} - 144 \, x^{5} + 195 \, x^{4} - 144 \, x^{3} + 58 \, x^{2} - 12 \, x + 1\right )}} \]
integrate((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x) *exp(5)-27*x^11+486*x^10-3780*x^9+16605*x^8-45225*x^7+79056*x^6-89208*x^5+ 64395*x^4-29295*x^3+8100*x^2-1242*x+81)*log(x)^3+((-27*x^8+162*x^7-270*x^6 +270*x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+206 55*x^5-14013*x^4+5265*x^3-1026*x^2+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10 -16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+1242 *x^2-81*x)*log(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+ 1215*x^6-1665*x^5+999*x^4-270*x^3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x ^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+288*x)* exp(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^ 7+864729*x^6-961317*x^5+689580*x^4-312894*x^3+86427*x^2-13248*x+864)*log(x )+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+(-18*x^9 +45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12 +36*x^11-253*x^10+1494*x^9-8121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^ 4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^11+15115*x ^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803 *x^3+4416*x^2-288*x)/(64*x^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872* x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x, algorithm=\
1/256*(x^12 - 12*x^11 + 250*x^10 - 2448*x^9 + 11331*x^8 - 27792*x^7 + 3749 8*x^6 - 27660*x^5 + x^4*e^20 + 81*(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x ^4 - 144*x^3 + 58*x^2 - 12*x + 1)*log(x)^4 + 11137*x^4 - 108*(x^9 - 12*x^8 + 58*x^7 - 144*x^6 + 195*x^5 - 144*x^4 + 58*x^3 - 12*x^2 - (x^7 - 9*x^6 + 30*x^5 - 45*x^4 + 30*x^3 - 9*x^2 + x)*e^5 + x)*log(x)^3 - 2304*x^3 + 54*( x^10 - 12*x^9 + 90*x^8 - 528*x^7 + 2051*x^6 - 4752*x^5 + 6298*x^4 - 4620*x ^3 + 1857*x^2 + (x^6 - 6*x^5 + 11*x^4 - 6*x^3 + x^2)*e^10 - 2*(x^8 - 9*x^7 + 30*x^6 - 45*x^5 + 30*x^4 - 9*x^3 + x^2)*e^5 - 384*x + 32)*log(x)^2 + 19 2*x^2 - 4*(x^6 - 3*x^5 + x^4)*e^15 + 6*(6*x^7 - 15*x^6 - 54*x^5 + 158*x^4 - 48*x^3 - 26*x^2 + 12*x - 1)*e^10 - 4*(x^10 - 9*x^9 + 22*x^8 + 339*x^7 - 3122*x^6 + 10647*x^5 - 17399*x^4 + 14112*x^3 - 5936*x^2 + 1248*x - 104)*e^ 5 - 12*(x^11 - 12*x^10 + 154*x^9 - 1296*x^8 + 5763*x^7 - 13968*x^6 + 18778 *x^5 - 13836*x^4 + 5569*x^3 - 1152*x^2 - (x^5 - 3*x^4 + x^3)*e^15 + 3*(x^7 - 6*x^6 + 11*x^5 - 6*x^4 + x^3)*e^10 - 3*(x^9 - 9*x^8 + 62*x^7 - 333*x^6 + 990*x^5 - 1449*x^4 + 961*x^3 - 288*x^2 + 32*x)*e^5 + 96*x)*log(x))/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 508 vs. \(2 (26) = 52\).
Time = 11.02 (sec) , antiderivative size = 508, normalized size of antiderivative = 16.93 \[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx=\frac {x^{4}}{256} + x^{2} \cdot \left (\frac {3}{4} - \frac {e^{5}}{64}\right ) - \frac {3 x e^{5}}{64} + \frac {81 \log {\left (x \right )}^{4}}{256} + \frac {27 e^{5} \log {\left (x \right )}}{64} + \frac {x^{7} \left (- 1236 e^{5} + 36 e^{10}\right ) + x^{6} \left (- 4 e^{15} - 90 e^{10} + 11540 e^{5}\right ) + x^{5} \left (- 324 e^{10} - 40824 e^{5} + 12 e^{15}\right ) + x^{4} \left (- 4 e^{15} + 68100 e^{5} + 948 e^{10} + e^{20}\right ) + x^{3} \left (- 55800 e^{5} - 288 e^{10}\right ) + x^{2} \left (- 156 e^{10} + 23604 e^{5}\right ) + x \left (- 4980 e^{5} + 72 e^{10}\right ) - 6 e^{10} + 416 e^{5}}{256 x^{8} - 3072 x^{7} + 14848 x^{6} - 36864 x^{5} + 49920 x^{4} - 36864 x^{3} + 14848 x^{2} - 3072 x + 256} + \frac {\left (- 3 x^{9} + 27 x^{8} - 378 x^{7} + 9 x^{7} e^{5} - 81 x^{6} e^{5} + 2727 x^{6} - 9 x^{5} e^{10} - 8730 x^{5} + 630 x^{5} e^{5} - 2592 x^{4} e^{5} + 12987 x^{4} + 27 x^{4} e^{10} - 9 x^{3} e^{10} - 8643 x^{3} + 4392 x^{3} e^{5} + 3 x^{3} e^{15} - 2538 x^{2} e^{5} + 2592 x^{2} - 288 x + 531 x e^{5} - 27 e^{5}\right ) \log {\left (x \right )}}{64 x^{6} - 576 x^{5} + 1920 x^{4} - 2880 x^{3} + 1920 x^{2} - 576 x + 64} + \frac {\left (27 x^{6} - 162 x^{5} - 54 x^{4} e^{5} + 1161 x^{4} - 5346 x^{3} + 162 x^{3} e^{5} - 54 x^{2} e^{5} + 9531 x^{2} + 27 x^{2} e^{10} - 5184 x + 864\right ) \log {\left (x \right )}^{2}}{128 x^{4} - 768 x^{3} + 1408 x^{2} - 768 x + 128} + \frac {\left (- 27 x^{3} + 81 x^{2} - 27 x + 27 x e^{5}\right ) \log {\left (x \right )}^{3}}{64 x^{2} - 192 x + 64} \]
integrate((((-27*x**9+243*x**8-783*x**7+972*x**6-972*x**4+783*x**3-243*x** 2+27*x)*exp(5)-27*x**11+486*x**10-3780*x**9+16605*x**8-45225*x**7+79056*x* *6-89208*x**5+64395*x**4-29295*x**3+8100*x**2-1242*x+81)*ln(x)**3+((-27*x* *8+162*x**7-270*x**6+270*x**4-162*x**3+27*x**2)*exp(5)**2+(162*x**9-1755*x **8+7614*x**7-16929*x**6+20655*x**5-14013*x**4+5265*x**3-1026*x**2+81*x)*e xp(5)+27*x**12-486*x**11+3780*x**10-16605*x**9+45225*x**8-79056*x**7+89208 *x**6-64395*x**5+29295*x**4-8100*x**3+1242*x**2-81*x)*ln(x)**2+((-9*x**7+2 7*x**6-27*x**4+9*x**3)*exp(5)**3+(9*x**9-333*x**7+1215*x**6-1665*x**5+999* x**4-270*x**3+27*x**2)*exp(5)**2+(9*x**11-189*x**10+1143*x**9-2808*x**8+29 34*x**7-3078*x**6+9081*x**5-13797*x**4+9027*x**3-2646*x**2+288*x)*exp(5)-9 *x**13+162*x**12-1548*x**11+10719*x**10-55395*x**9+203472*x**8-512136*x**7 +864729*x**6-961317*x**5+689580*x**4-312894*x**3+86427*x**2-13248*x+864)*l n(x)+(-x**6+x**4)*exp(5)**4+(2*x**8-29*x**6+48*x**5-22*x**4+3*x**3)*exp(5) **3+(-18*x**9+45*x**8+171*x**7-435*x**6-315*x**5+1047*x**4-585*x**3+96*x** 2)*exp(5)**2+(-2*x**12+36*x**11-253*x**10+1494*x**9-8121*x**8+29295*x**7-6 1691*x**6+74007*x**5-49936*x**4+18729*x**3-3648*x**2+288*x)*exp(5)+x**14-1 8*x**13+236*x**12-2343*x**11+15115*x**10-61968*x**9+164104*x**8-283473*x** 7+318269*x**6-229260*x**5+104206*x**4-28803*x**3+4416*x**2-288*x)/(64*x**1 1-960*x**10+6080*x**9-21120*x**8+43840*x**7-55872*x**6+43840*x**5-21120*x* *4+6080*x**3-960*x**2+64*x),x)
x**4/256 + x**2*(3/4 - exp(5)/64) - 3*x*exp(5)/64 + 81*log(x)**4/256 + 27* exp(5)*log(x)/64 + (x**7*(-1236*exp(5) + 36*exp(10)) + x**6*(-4*exp(15) - 90*exp(10) + 11540*exp(5)) + x**5*(-324*exp(10) - 40824*exp(5) + 12*exp(15 )) + x**4*(-4*exp(15) + 68100*exp(5) + 948*exp(10) + exp(20)) + x**3*(-558 00*exp(5) - 288*exp(10)) + x**2*(-156*exp(10) + 23604*exp(5)) + x*(-4980*e xp(5) + 72*exp(10)) - 6*exp(10) + 416*exp(5))/(256*x**8 - 3072*x**7 + 1484 8*x**6 - 36864*x**5 + 49920*x**4 - 36864*x**3 + 14848*x**2 - 3072*x + 256) + (-3*x**9 + 27*x**8 - 378*x**7 + 9*x**7*exp(5) - 81*x**6*exp(5) + 2727*x **6 - 9*x**5*exp(10) - 8730*x**5 + 630*x**5*exp(5) - 2592*x**4*exp(5) + 12 987*x**4 + 27*x**4*exp(10) - 9*x**3*exp(10) - 8643*x**3 + 4392*x**3*exp(5) + 3*x**3*exp(15) - 2538*x**2*exp(5) + 2592*x**2 - 288*x + 531*x*exp(5) - 27*exp(5))*log(x)/(64*x**6 - 576*x**5 + 1920*x**4 - 2880*x**3 + 1920*x**2 - 576*x + 64) + (27*x**6 - 162*x**5 - 54*x**4*exp(5) + 1161*x**4 - 5346*x* *3 + 162*x**3*exp(5) - 54*x**2*exp(5) + 9531*x**2 + 27*x**2*exp(10) - 5184 *x + 864)*log(x)**2/(128*x**4 - 768*x**3 + 1408*x**2 - 768*x + 128) + (-27 *x**3 + 81*x**2 - 27*x + 27*x*exp(5))*log(x)**3/(64*x**2 - 192*x + 64)
Leaf count of result is larger than twice the leaf count of optimal. 4571 vs. \(2 (26) = 52\).
Time = 0.51 (sec) , antiderivative size = 4571, normalized size of antiderivative = 152.37 \[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx=\text {Too large to display} \]
integrate((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x) *exp(5)-27*x^11+486*x^10-3780*x^9+16605*x^8-45225*x^7+79056*x^6-89208*x^5+ 64395*x^4-29295*x^3+8100*x^2-1242*x+81)*log(x)^3+((-27*x^8+162*x^7-270*x^6 +270*x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+206 55*x^5-14013*x^4+5265*x^3-1026*x^2+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10 -16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+1242 *x^2-81*x)*log(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+ 1215*x^6-1665*x^5+999*x^4-270*x^3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x ^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+288*x)* exp(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^ 7+864729*x^6-961317*x^5+689580*x^4-312894*x^3+86427*x^2-13248*x+864)*log(x )+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+(-18*x^9 +45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12 +36*x^11-253*x^10+1494*x^9-8121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^ 4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^11+15115*x ^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803 *x^3+4416*x^2-288*x)/(64*x^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872* x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x, algorithm=\
1/256*x^4 - 1/64*x^3 - 3/16000*sqrt(5)*(22*e^15 + 60*e^10 + 5325*e^5)*log( (2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 3/4*x^2 + 1/480000*(432*sqrt(5) *log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 + 18 432*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^20 - 1/4800 00*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373) /(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) )*e^20 - 11/240000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3 )) + 5*(432*x^7 - 4536*x^6 + 18432*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58 *x^2 - 12*x + 1))*e^15 - 29/480000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2 *x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 35280 *x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^ 4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^15 + 1/160000*(348*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(348*x^7 - 3654*x^6 + 14848*x^5 - 29 145*x^4 + 28420*x^3 - 13572*x^2 + 3216*x - 297)/(x^8 - 12*x^7 + 58*x^6 - 1 44*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^15 + 3/10000*(156*sqrt( 5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(156*x^7 - 1638*x^6 + 6656*x^5 - 13065*x^4 + 12640*x^3 - 6134*x^2 + 1452*x - 134)/(x^8 - 12*x...
\[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx =\text {Too large to display} \]
integrate((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x) *exp(5)-27*x^11+486*x^10-3780*x^9+16605*x^8-45225*x^7+79056*x^6-89208*x^5+ 64395*x^4-29295*x^3+8100*x^2-1242*x+81)*log(x)^3+((-27*x^8+162*x^7-270*x^6 +270*x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+206 55*x^5-14013*x^4+5265*x^3-1026*x^2+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10 -16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+1242 *x^2-81*x)*log(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+ 1215*x^6-1665*x^5+999*x^4-270*x^3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x ^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+288*x)* exp(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^ 7+864729*x^6-961317*x^5+689580*x^4-312894*x^3+86427*x^2-13248*x+864)*log(x )+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+(-18*x^9 +45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12 +36*x^11-253*x^10+1494*x^9-8121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^ 4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^11+15115*x ^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803 *x^3+4416*x^2-288*x)/(64*x^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872* x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x, algorithm=\
integrate(1/64*(x^14 - 18*x^13 + 236*x^12 - 2343*x^11 + 15115*x^10 - 61968 *x^9 + 164104*x^8 - 283473*x^7 + 318269*x^6 - 229260*x^5 + 104206*x^4 - 27 *(x^11 - 18*x^10 + 140*x^9 - 615*x^8 + 1675*x^7 - 2928*x^6 + 3304*x^5 - 23 85*x^4 + 1085*x^3 - 300*x^2 + (x^9 - 9*x^8 + 29*x^7 - 36*x^6 + 36*x^4 - 29 *x^3 + 9*x^2 - x)*e^5 + 46*x - 3)*log(x)^3 - 28803*x^3 + 27*(x^12 - 18*x^1 1 + 140*x^10 - 615*x^9 + 1675*x^8 - 2928*x^7 + 3304*x^6 - 2385*x^5 + 1085* x^4 - 300*x^3 + 46*x^2 - (x^8 - 6*x^7 + 10*x^6 - 10*x^4 + 6*x^3 - x^2)*e^1 0 + (6*x^9 - 65*x^8 + 282*x^7 - 627*x^6 + 765*x^5 - 519*x^4 + 195*x^3 - 38 *x^2 + 3*x)*e^5 - 3*x)*log(x)^2 + 4416*x^2 - (x^6 - x^4)*e^20 + (2*x^8 - 2 9*x^6 + 48*x^5 - 22*x^4 + 3*x^3)*e^15 - 3*(6*x^9 - 15*x^8 - 57*x^7 + 145*x ^6 + 105*x^5 - 349*x^4 + 195*x^3 - 32*x^2)*e^10 - (2*x^12 - 36*x^11 + 253* x^10 - 1494*x^9 + 8121*x^8 - 29295*x^7 + 61691*x^6 - 74007*x^5 + 49936*x^4 - 18729*x^3 + 3648*x^2 - 288*x)*e^5 - 9*(x^13 - 18*x^12 + 172*x^11 - 1191 *x^10 + 6155*x^9 - 22608*x^8 + 56904*x^7 - 96081*x^6 + 106813*x^5 - 76620* x^4 + 34766*x^3 - 9603*x^2 + (x^7 - 3*x^6 + 3*x^4 - x^3)*e^15 - (x^9 - 37* x^7 + 135*x^6 - 185*x^5 + 111*x^4 - 30*x^3 + 3*x^2)*e^10 - (x^11 - 21*x^10 + 127*x^9 - 312*x^8 + 326*x^7 - 342*x^6 + 1009*x^5 - 1533*x^4 + 1003*x^3 - 294*x^2 + 32*x)*e^5 + 1472*x - 96)*log(x) - 288*x)/(x^11 - 15*x^10 + 95* x^9 - 330*x^8 + 685*x^7 - 873*x^6 + 685*x^5 - 330*x^4 + 95*x^3 - 15*x^2 + x), x)
Timed out. \[ \int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} \left (x^4-x^6\right )+e^{15} \left (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8\right )+e^{10} \left (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9\right )+e^5 \left (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12}\right )+\left (864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} \left (9 x^3-27 x^4+27 x^6-9 x^7\right )+e^{10} \left (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9\right )+e^5 \left (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11}\right )\right ) \log (x)+\left (-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} \left (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8\right )+e^5 \left (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9\right )\right ) \log ^2(x)+\left (81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 \left (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9\right )\right ) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx=\int \frac {{\mathrm {e}}^{20}\,\left (x^4-x^6\right )-288\,x+{\mathrm {e}}^{15}\,\left (2\,x^8-29\,x^6+48\,x^5-22\,x^4+3\,x^3\right )+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^{10}\,\left (-27\,x^8+162\,x^7-270\,x^6+270\,x^4-162\,x^3+27\,x^2\right )-81\,x+{\mathrm {e}}^5\,\left (162\,x^9-1755\,x^8+7614\,x^7-16929\,x^6+20655\,x^5-14013\,x^4+5265\,x^3-1026\,x^2+81\,x\right )+1242\,x^2-8100\,x^3+29295\,x^4-64395\,x^5+89208\,x^6-79056\,x^7+45225\,x^8-16605\,x^9+3780\,x^{10}-486\,x^{11}+27\,x^{12}\right )+{\mathrm {e}}^5\,\left (-2\,x^{12}+36\,x^{11}-253\,x^{10}+1494\,x^9-8121\,x^8+29295\,x^7-61691\,x^6+74007\,x^5-49936\,x^4+18729\,x^3-3648\,x^2+288\,x\right )+{\ln \left (x\right )}^3\,\left ({\mathrm {e}}^5\,\left (-27\,x^9+243\,x^8-783\,x^7+972\,x^6-972\,x^4+783\,x^3-243\,x^2+27\,x\right )-1242\,x+8100\,x^2-29295\,x^3+64395\,x^4-89208\,x^5+79056\,x^6-45225\,x^7+16605\,x^8-3780\,x^9+486\,x^{10}-27\,x^{11}+81\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^5\,\left (9\,x^{11}-189\,x^{10}+1143\,x^9-2808\,x^8+2934\,x^7-3078\,x^6+9081\,x^5-13797\,x^4+9027\,x^3-2646\,x^2+288\,x\right )-13248\,x+{\mathrm {e}}^{10}\,\left (9\,x^9-333\,x^7+1215\,x^6-1665\,x^5+999\,x^4-270\,x^3+27\,x^2\right )+86427\,x^2-312894\,x^3+689580\,x^4-961317\,x^5+864729\,x^6-512136\,x^7+203472\,x^8-55395\,x^9+10719\,x^{10}-1548\,x^{11}+162\,x^{12}-9\,x^{13}+{\mathrm {e}}^{15}\,\left (-9\,x^7+27\,x^6-27\,x^4+9\,x^3\right )+864\right )+4416\,x^2-28803\,x^3+104206\,x^4-229260\,x^5+318269\,x^6-283473\,x^7+164104\,x^8-61968\,x^9+15115\,x^{10}-2343\,x^{11}+236\,x^{12}-18\,x^{13}+x^{14}+{\mathrm {e}}^{10}\,\left (-18\,x^9+45\,x^8+171\,x^7-435\,x^6-315\,x^5+1047\,x^4-585\,x^3+96\,x^2\right )}{64\,x^{11}-960\,x^{10}+6080\,x^9-21120\,x^8+43840\,x^7-55872\,x^6+43840\,x^5-21120\,x^4+6080\,x^3-960\,x^2+64\,x} \,d x \]
int((exp(20)*(x^4 - x^6) - 288*x + exp(15)*(3*x^3 - 22*x^4 + 48*x^5 - 29*x ^6 + 2*x^8) + log(x)^2*(exp(10)*(27*x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 16 2*x^7 - 27*x^8) - 81*x + exp(5)*(81*x - 1026*x^2 + 5265*x^3 - 14013*x^4 + 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9) + 1242*x^2 - 8100*x ^3 + 29295*x^4 - 64395*x^5 + 89208*x^6 - 79056*x^7 + 45225*x^8 - 16605*x^9 + 3780*x^10 - 486*x^11 + 27*x^12) + exp(5)*(288*x - 3648*x^2 + 18729*x^3 - 49936*x^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 25 3*x^10 + 36*x^11 - 2*x^12) + log(x)^3*(exp(5)*(27*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9) - 1242*x + 8100*x^2 - 2929 5*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x ^9 + 486*x^10 - 27*x^11 + 81) + log(x)*(exp(5)*(288*x - 2646*x^2 + 9027*x^ 3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x^9 - 189 *x^10 + 9*x^11) - 13248*x + exp(10)*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^9) + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961 317*x^5 + 864729*x^6 - 512136*x^7 + 203472*x^8 - 55395*x^9 + 10719*x^10 - 1548*x^11 + 162*x^12 - 9*x^13 + exp(15)*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7) + 864) + 4416*x^2 - 28803*x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283 473*x^7 + 164104*x^8 - 61968*x^9 + 15115*x^10 - 2343*x^11 + 236*x^12 - 18* x^13 + x^14 + exp(10)*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 1 71*x^7 + 45*x^8 - 18*x^9))/(64*x - 960*x^2 + 6080*x^3 - 21120*x^4 + 43840* x^5 - 55872*x^6 + 43840*x^7 - 21120*x^8 + 6080*x^9 - 960*x^10 + 64*x^11),x )
int((exp(20)*(x^4 - x^6) - 288*x + exp(15)*(3*x^3 - 22*x^4 + 48*x^5 - 29*x ^6 + 2*x^8) + log(x)^2*(exp(10)*(27*x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 16 2*x^7 - 27*x^8) - 81*x + exp(5)*(81*x - 1026*x^2 + 5265*x^3 - 14013*x^4 + 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9) + 1242*x^2 - 8100*x ^3 + 29295*x^4 - 64395*x^5 + 89208*x^6 - 79056*x^7 + 45225*x^8 - 16605*x^9 + 3780*x^10 - 486*x^11 + 27*x^12) + exp(5)*(288*x - 3648*x^2 + 18729*x^3 - 49936*x^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 25 3*x^10 + 36*x^11 - 2*x^12) + log(x)^3*(exp(5)*(27*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9) - 1242*x + 8100*x^2 - 2929 5*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x ^9 + 486*x^10 - 27*x^11 + 81) + log(x)*(exp(5)*(288*x - 2646*x^2 + 9027*x^ 3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x^9 - 189 *x^10 + 9*x^11) - 13248*x + exp(10)*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^9) + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961 317*x^5 + 864729*x^6 - 512136*x^7 + 203472*x^8 - 55395*x^9 + 10719*x^10 - 1548*x^11 + 162*x^12 - 9*x^13 + exp(15)*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7) + 864) + 4416*x^2 - 28803*x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283 473*x^7 + 164104*x^8 - 61968*x^9 + 15115*x^10 - 2343*x^11 + 236*x^12 - 18* x^13 + x^14 + exp(10)*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 1 71*x^7 + 45*x^8 - 18*x^9))/(64*x - 960*x^2 + 6080*x^3 - 21120*x^4 + 438...