Integrand size = 188, antiderivative size = 24 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=1+729 x^6 \left (-e^4+x\right )^4 (x-5 \log (x))^2 \]
Leaf count is larger than twice the leaf count of optimal. \(152\) vs. \(2(24)=48\).
Time = 0.24 (sec) , antiderivative size = 152, normalized size of antiderivative = 6.33 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=1458 \left (\frac {e^{16} x^8}{2}-2 e^{12} x^9+3 e^8 x^{10}-2 e^4 x^{11}+\frac {x^{12}}{2}-5 e^{16} x^7 \log (x)+20 e^{12} x^8 \log (x)-30 e^8 x^9 \log (x)+20 e^4 x^{10} \log (x)-5 x^{11} \log (x)+\frac {25}{2} e^{16} x^6 \log ^2(x)-50 e^{12} x^7 \log ^2(x)+75 e^8 x^8 \log ^2(x)-50 e^4 x^9 \log ^2(x)+\frac {25}{2} x^{10} \log ^2(x)\right ) \]
Integrate[-7290*x^10 + 8748*x^11 + E^16*(-7290*x^6 + 5832*x^7) + E^12*(291 60*x^7 - 26244*x^8) + E^8*(-43740*x^8 + 43740*x^9) + E^4*(29160*x^9 - 3207 6*x^10) + (36450*x^9 - 80190*x^10 + E^16*(36450*x^5 - 51030*x^6) + E^12*(- 145800*x^6 + 233280*x^7) + E^8*(218700*x^7 - 393660*x^8) + E^4*(-145800*x^ 8 + 291600*x^9))*Log[x] + (109350*E^16*x^5 - 510300*E^12*x^6 + 874800*E^8* x^7 - 656100*E^4*x^8 + 182250*x^9)*Log[x]^2,x]
1458*((E^16*x^8)/2 - 2*E^12*x^9 + 3*E^8*x^10 - 2*E^4*x^11 + x^12/2 - 5*E^1 6*x^7*Log[x] + 20*E^12*x^8*Log[x] - 30*E^8*x^9*Log[x] + 20*E^4*x^10*Log[x] - 5*x^11*Log[x] + (25*E^16*x^6*Log[x]^2)/2 - 50*E^12*x^7*Log[x]^2 + 75*E^ 8*x^8*Log[x]^2 - 50*E^4*x^9*Log[x]^2 + (25*x^10*Log[x]^2)/2)
Leaf count is larger than twice the leaf count of optimal. \(344\) vs. \(2(24)=48\).
Time = 0.58 (sec) , antiderivative size = 344, normalized size of antiderivative = 14.33, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {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.
| \(\displaystyle \int \left (8748 x^{11}-7290 x^{10}+e^4 \left (29160 x^9-32076 x^{10}\right )+e^8 \left (43740 x^9-43740 x^8\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^{16} \left (5832 x^7-7290 x^6\right )+\left (182250 x^9-656100 e^4 x^8+874800 e^8 x^7-510300 e^{12} x^6+109350 e^{16} x^5\right ) \log ^2(x)+\left (-80190 x^{10}+36450 x^9+e^4 \left (291600 x^9-145800 x^8\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^{12} \left (233280 x^7-145800 x^6\right )+e^{16} \left (36450 x^5-51030 x^6\right )\right ) \log (x)\right ) \, dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 729 x^{12}-2916 e^4 x^{11}-7290 x^{11} \log (x)-\frac {729}{2} \left (1+8 e^4\right ) x^{10}+4374 e^8 x^{10}+2916 e^4 x^{10}+\frac {729 x^{10}}{2}+18225 x^{10} \log ^2(x)+3645 \left (1+8 e^4\right ) x^{10} \log (x)-3645 x^{10} \log (x)+180 e^4 \left (10+27 e^4\right ) x^9-2916 e^{12} x^9-4860 e^8 x^9-1800 e^4 x^9-72900 e^4 x^9 \log ^2(x)-1620 e^4 \left (10+27 e^4\right ) x^9 \log (x)+16200 e^4 x^9 \log (x)-\frac {3645}{16} e^8 \left (15+16 e^4\right ) x^8+729 e^{16} x^8+3645 e^{12} x^8+\frac {54675 e^8 x^8}{16}+109350 e^8 x^8 \log ^2(x)+\frac {3645}{2} e^8 \left (15+16 e^4\right ) x^8 \log (x)-\frac {54675}{2} e^8 x^8 \log (x)+\frac {7290}{49} e^{12} \left (20+7 e^4\right ) x^7-\frac {7290 e^{16} x^7}{7}-\frac {145800 e^{12} x^7}{49}-72900 e^{12} x^7 \log ^2(x)-\frac {7290}{7} e^{12} \left (20+7 e^4\right ) x^7 \log (x)+\frac {145800}{7} e^{12} x^7 \log (x)+18225 e^{16} x^6 \log ^2(x)\) |
Int[-7290*x^10 + 8748*x^11 + E^16*(-7290*x^6 + 5832*x^7) + E^12*(29160*x^7 - 26244*x^8) + E^8*(-43740*x^8 + 43740*x^9) + E^4*(29160*x^9 - 32076*x^10 ) + (36450*x^9 - 80190*x^10 + E^16*(36450*x^5 - 51030*x^6) + E^12*(-145800 *x^6 + 233280*x^7) + E^8*(218700*x^7 - 393660*x^8) + E^4*(-145800*x^8 + 29 1600*x^9))*Log[x] + (109350*E^16*x^5 - 510300*E^12*x^6 + 874800*E^8*x^7 - 656100*E^4*x^8 + 182250*x^9)*Log[x]^2,x]
(-145800*E^12*x^7)/49 - (7290*E^16*x^7)/7 + (7290*E^12*(20 + 7*E^4)*x^7)/4 9 + (54675*E^8*x^8)/16 + 3645*E^12*x^8 + 729*E^16*x^8 - (3645*E^8*(15 + 16 *E^4)*x^8)/16 - 1800*E^4*x^9 - 4860*E^8*x^9 - 2916*E^12*x^9 + 180*E^4*(10 + 27*E^4)*x^9 + (729*x^10)/2 + 2916*E^4*x^10 + 4374*E^8*x^10 - (729*(1 + 8 *E^4)*x^10)/2 - 2916*E^4*x^11 + 729*x^12 + (145800*E^12*x^7*Log[x])/7 - (7 290*E^12*(20 + 7*E^4)*x^7*Log[x])/7 - (54675*E^8*x^8*Log[x])/2 + (3645*E^8 *(15 + 16*E^4)*x^8*Log[x])/2 + 16200*E^4*x^9*Log[x] - 1620*E^4*(10 + 27*E^ 4)*x^9*Log[x] - 3645*x^10*Log[x] + 3645*(1 + 8*E^4)*x^10*Log[x] - 7290*x^1 1*Log[x] + 18225*E^16*x^6*Log[x]^2 - 72900*E^12*x^7*Log[x]^2 + 109350*E^8* x^8*Log[x]^2 - 72900*E^4*x^9*Log[x]^2 + 18225*x^10*Log[x]^2
3.5.61.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(148\) vs. \(2(23)=46\).
Time = 2.31 (sec) , antiderivative size = 149, normalized size of antiderivative = 6.21
| method | result | size |
| risch | \(18225 \ln \left (x \right )^{2} {\mathrm e}^{16} x^{6}-72900 \ln \left (x \right )^{2} {\mathrm e}^{12} x^{7}+109350 \ln \left (x \right )^{2} {\mathrm e}^{8} x^{8}-72900 \ln \left (x \right )^{2} {\mathrm e}^{4} x^{9}+18225 x^{10} \ln \left (x \right )^{2}-7290 \ln \left (x \right ) {\mathrm e}^{16} x^{7}+29160 \ln \left (x \right ) {\mathrm e}^{12} x^{8}-43740 \ln \left (x \right ) {\mathrm e}^{8} x^{9}+29160 \ln \left (x \right ) {\mathrm e}^{4} x^{10}-7290 x^{11} \ln \left (x \right )+729 x^{8} {\mathrm e}^{16}-2916 \,{\mathrm e}^{12} x^{9}+4374 \,{\mathrm e}^{8} x^{10}-2916 \,{\mathrm e}^{4} x^{11}+729 x^{12}\) | \(149\) |
| parallelrisch | \(18225 \ln \left (x \right )^{2} {\mathrm e}^{16} x^{6}-72900 \ln \left (x \right )^{2} {\mathrm e}^{12} x^{7}+109350 \ln \left (x \right )^{2} {\mathrm e}^{8} x^{8}-72900 \ln \left (x \right )^{2} {\mathrm e}^{4} x^{9}+18225 x^{10} \ln \left (x \right )^{2}-7290 \ln \left (x \right ) {\mathrm e}^{16} x^{7}+29160 \ln \left (x \right ) {\mathrm e}^{12} x^{8}-43740 \ln \left (x \right ) {\mathrm e}^{8} x^{9}+29160 \ln \left (x \right ) {\mathrm e}^{4} x^{10}-7290 x^{11} \ln \left (x \right )+729 x^{8} {\mathrm e}^{16}-2916 \,{\mathrm e}^{12} x^{9}+4374 \,{\mathrm e}^{8} x^{10}-2916 \,{\mathrm e}^{4} x^{11}+729 x^{12}\) | \(149\) |
| default | \(109350 \,{\mathrm e}^{16} \left (\frac {x^{6} \ln \left (x \right )^{2}}{6}-\frac {x^{6} \ln \left (x \right )}{18}+\frac {x^{6}}{108}\right )-510300 \,{\mathrm e}^{12} \left (\frac {x^{7} \ln \left (x \right )^{2}}{7}-\frac {2 x^{7} \ln \left (x \right )}{49}+\frac {2 x^{7}}{343}\right )+874800 \,{\mathrm e}^{8} \left (\frac {x^{8} \ln \left (x \right )^{2}}{8}-\frac {x^{8} \ln \left (x \right )}{32}+\frac {x^{8}}{256}\right )-656100 \,{\mathrm e}^{4} \left (\frac {x^{9} \ln \left (x \right )^{2}}{9}-\frac {2 x^{9} \ln \left (x \right )}{81}+\frac {2 x^{9}}{729}\right )+18225 x^{10} \ln \left (x \right )^{2}-51030 \,{\mathrm e}^{16} \left (\frac {x^{7} \ln \left (x \right )}{7}-\frac {x^{7}}{49}\right )+233280 \,{\mathrm e}^{12} \left (\frac {x^{8} \ln \left (x \right )}{8}-\frac {x^{8}}{64}\right )-393660 \,{\mathrm e}^{8} \left (\frac {x^{9} \ln \left (x \right )}{9}-\frac {x^{9}}{81}\right )+291600 \,{\mathrm e}^{4} \left (\frac {x^{10} \ln \left (x \right )}{10}-\frac {x^{10}}{100}\right )-7290 x^{11} \ln \left (x \right )+36450 \,{\mathrm e}^{16} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )-145800 \,{\mathrm e}^{12} \left (\frac {x^{7} \ln \left (x \right )}{7}-\frac {x^{7}}{49}\right )+218700 \,{\mathrm e}^{8} \left (\frac {x^{8} \ln \left (x \right )}{8}-\frac {x^{8}}{64}\right )-145800 \,{\mathrm e}^{4} \left (\frac {x^{9} \ln \left (x \right )}{9}-\frac {x^{9}}{81}\right )+1458 \,{\mathrm e}^{16} \left (\frac {1}{2} x^{8}-\frac {5}{7} x^{7}\right )+2916 \,{\mathrm e}^{12} \left (-x^{9}+\frac {5}{4} x^{8}\right )+43740 \,{\mathrm e}^{8} \left (\frac {1}{10} x^{10}-\frac {1}{9} x^{9}\right )+2916 \,{\mathrm e}^{4} \left (-x^{11}+x^{10}\right )+729 x^{12}\) | \(345\) |
| parts | \(109350 \,{\mathrm e}^{16} \left (\frac {x^{6} \ln \left (x \right )^{2}}{6}-\frac {x^{6} \ln \left (x \right )}{18}+\frac {x^{6}}{108}\right )-510300 \,{\mathrm e}^{12} \left (\frac {x^{7} \ln \left (x \right )^{2}}{7}-\frac {2 x^{7} \ln \left (x \right )}{49}+\frac {2 x^{7}}{343}\right )+874800 \,{\mathrm e}^{8} \left (\frac {x^{8} \ln \left (x \right )^{2}}{8}-\frac {x^{8} \ln \left (x \right )}{32}+\frac {x^{8}}{256}\right )-656100 \,{\mathrm e}^{4} \left (\frac {x^{9} \ln \left (x \right )^{2}}{9}-\frac {2 x^{9} \ln \left (x \right )}{81}+\frac {2 x^{9}}{729}\right )+18225 x^{10} \ln \left (x \right )^{2}-51030 \,{\mathrm e}^{16} \left (\frac {x^{7} \ln \left (x \right )}{7}-\frac {x^{7}}{49}\right )+233280 \,{\mathrm e}^{12} \left (\frac {x^{8} \ln \left (x \right )}{8}-\frac {x^{8}}{64}\right )-393660 \,{\mathrm e}^{8} \left (\frac {x^{9} \ln \left (x \right )}{9}-\frac {x^{9}}{81}\right )+291600 \,{\mathrm e}^{4} \left (\frac {x^{10} \ln \left (x \right )}{10}-\frac {x^{10}}{100}\right )-7290 x^{11} \ln \left (x \right )+36450 \,{\mathrm e}^{16} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )-145800 \,{\mathrm e}^{12} \left (\frac {x^{7} \ln \left (x \right )}{7}-\frac {x^{7}}{49}\right )+218700 \,{\mathrm e}^{8} \left (\frac {x^{8} \ln \left (x \right )}{8}-\frac {x^{8}}{64}\right )-145800 \,{\mathrm e}^{4} \left (\frac {x^{9} \ln \left (x \right )}{9}-\frac {x^{9}}{81}\right )+729 x^{12}-4860 \,{\mathrm e}^{8} x^{9}+2916 \,{\mathrm e}^{4} x^{10}-2916 \,{\mathrm e}^{4} x^{11}+4374 \,{\mathrm e}^{8} x^{10}+3645 \,{\mathrm e}^{12} x^{8}-2916 \,{\mathrm e}^{12} x^{9}-\frac {7290 \,{\mathrm e}^{16} x^{7}}{7}+729 x^{8} {\mathrm e}^{16}\) | \(349\) |
int((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656100*x^ 8*exp(4)+182250*x^9)*ln(x)^2+((-51030*x^6+36450*x^5)*exp(4)^4+(233280*x^7- 145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^9-145800* x^8)*exp(4)-80190*x^10+36450*x^9)*ln(x)+(5832*x^7-7290*x^6)*exp(4)^4+(-262 44*x^8+29160*x^7)*exp(4)^3+(43740*x^9-43740*x^8)*exp(4)^2+(-32076*x^10+291 60*x^9)*exp(4)+8748*x^11-7290*x^10,x,method=_RETURNVERBOSE)
18225*ln(x)^2*exp(4)^4*x^6-72900*ln(x)^2*exp(4)^3*x^7+109350*ln(x)^2*exp(4 )^2*x^8-72900*ln(x)^2*exp(4)*x^9+18225*x^10*ln(x)^2-7290*ln(x)*exp(4)^4*x^ 7+29160*ln(x)*exp(4)^3*x^8-43740*ln(x)*exp(4)^2*x^9+29160*ln(x)*exp(4)*x^1 0-7290*x^11*ln(x)+729*x^8*exp(4)^4-2916*exp(4)^3*x^9+4374*exp(4)^2*x^10-29 16*exp(4)*x^11+729*x^12
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (23) = 46\).
Time = 0.25 (sec) , antiderivative size = 106, normalized size of antiderivative = 4.42 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=729 \, x^{12} - 2916 \, x^{11} e^{4} + 4374 \, x^{10} e^{8} - 2916 \, x^{9} e^{12} + 729 \, x^{8} e^{16} + 18225 \, {\left (x^{10} - 4 \, x^{9} e^{4} + 6 \, x^{8} e^{8} - 4 \, x^{7} e^{12} + x^{6} e^{16}\right )} \log \left (x\right )^{2} - 7290 \, {\left (x^{11} - 4 \, x^{10} e^{4} + 6 \, x^{9} e^{8} - 4 \, x^{8} e^{12} + x^{7} e^{16}\right )} \log \left (x\right ) \]
integrate((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656 100*x^8*exp(4)+182250*x^9)*log(x)^2+((-51030*x^6+36450*x^5)*exp(4)^4+(2332 80*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^9- 145800*x^8)*exp(4)-80190*x^10+36450*x^9)*log(x)+(5832*x^7-7290*x^6)*exp(4) ^4+(-26244*x^8+29160*x^7)*exp(4)^3+(43740*x^9-43740*x^8)*exp(4)^2+(-32076* x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x, algorithm=\
729*x^12 - 2916*x^11*e^4 + 4374*x^10*e^8 - 2916*x^9*e^12 + 729*x^8*e^16 + 18225*(x^10 - 4*x^9*e^4 + 6*x^8*e^8 - 4*x^7*e^12 + x^6*e^16)*log(x)^2 - 72 90*(x^11 - 4*x^10*e^4 + 6*x^9*e^8 - 4*x^8*e^12 + x^7*e^16)*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (20) = 40\).
Time = 0.15 (sec) , antiderivative size = 124, normalized size of antiderivative = 5.17 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=729 x^{12} - 2916 x^{11} e^{4} + 4374 x^{10} e^{8} - 2916 x^{9} e^{12} + 729 x^{8} e^{16} + \left (18225 x^{10} - 72900 x^{9} e^{4} + 109350 x^{8} e^{8} - 72900 x^{7} e^{12} + 18225 x^{6} e^{16}\right ) \log {\left (x \right )}^{2} + \left (- 7290 x^{11} + 29160 x^{10} e^{4} - 43740 x^{9} e^{8} + 29160 x^{8} e^{12} - 7290 x^{7} e^{16}\right ) \log {\left (x \right )} \]
integrate((109350*x**5*exp(4)**4-510300*x**6*exp(4)**3+874800*x**7*exp(4)* *2-656100*x**8*exp(4)+182250*x**9)*ln(x)**2+((-51030*x**6+36450*x**5)*exp( 4)**4+(233280*x**7-145800*x**6)*exp(4)**3+(-393660*x**8+218700*x**7)*exp(4 )**2+(291600*x**9-145800*x**8)*exp(4)-80190*x**10+36450*x**9)*ln(x)+(5832* x**7-7290*x**6)*exp(4)**4+(-26244*x**8+29160*x**7)*exp(4)**3+(43740*x**9-4 3740*x**8)*exp(4)**2+(-32076*x**10+29160*x**9)*exp(4)+8748*x**11-7290*x**1 0,x)
729*x**12 - 2916*x**11*exp(4) + 4374*x**10*exp(8) - 2916*x**9*exp(12) + 72 9*x**8*exp(16) + (18225*x**10 - 72900*x**9*exp(4) + 109350*x**8*exp(8) - 7 2900*x**7*exp(12) + 18225*x**6*exp(16))*log(x)**2 + (-7290*x**11 + 29160*x **10*exp(4) - 43740*x**9*exp(8) + 29160*x**8*exp(12) - 7290*x**7*exp(16))* log(x)
Leaf count of result is larger than twice the leaf count of optimal. 308 vs. \(2 (23) = 46\).
Time = 0.20 (sec) , antiderivative size = 308, normalized size of antiderivative = 12.83 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=729 \, x^{12} + \frac {729}{2} \, {\left (50 \, \log \left (x\right )^{2} - 10 \, \log \left (x\right ) + 1\right )} x^{10} - \frac {729}{2} \, x^{10} {\left (8 \, e^{4} + 1\right )} - 900 \, {\left (81 \, e^{4} \log \left (x\right )^{2} - 18 \, e^{4} \log \left (x\right ) + 2 \, e^{4}\right )} x^{9} + 180 \, x^{9} {\left (27 \, e^{8} + 10 \, e^{4}\right )} + \frac {54675}{16} \, {\left (32 \, e^{8} \log \left (x\right )^{2} - 8 \, e^{8} \log \left (x\right ) + e^{8}\right )} x^{8} - \frac {3645}{16} \, x^{8} {\left (16 \, e^{12} + 15 \, e^{8}\right )} - \frac {72900}{49} \, {\left (49 \, e^{12} \log \left (x\right )^{2} - 14 \, e^{12} \log \left (x\right ) + 2 \, e^{12}\right )} x^{7} + \frac {7290}{49} \, x^{7} {\left (7 \, e^{16} + 20 \, e^{12}\right )} + \frac {2025}{2} \, {\left (18 \, e^{16} \log \left (x\right )^{2} - 6 \, e^{16} \log \left (x\right ) + e^{16}\right )} x^{6} - \frac {2025}{2} \, x^{6} e^{16} + \frac {729}{7} \, {\left (7 \, x^{8} - 10 \, x^{7}\right )} e^{16} - 729 \, {\left (4 \, x^{9} - 5 \, x^{8}\right )} e^{12} + 486 \, {\left (9 \, x^{10} - 10 \, x^{9}\right )} e^{8} - 2916 \, {\left (x^{11} - x^{10}\right )} e^{4} - \frac {405}{14} \, {\left (252 \, x^{11} - 126 \, x^{10} + 42 \, {\left (6 \, x^{7} - 5 \, x^{6}\right )} e^{16} - 144 \, {\left (7 \, x^{8} - 5 \, x^{7}\right )} e^{12} + 189 \, {\left (8 \, x^{9} - 5 \, x^{8}\right )} e^{8} - 112 \, {\left (9 \, x^{10} - 5 \, x^{9}\right )} e^{4}\right )} \log \left (x\right ) \]
integrate((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656 100*x^8*exp(4)+182250*x^9)*log(x)^2+((-51030*x^6+36450*x^5)*exp(4)^4+(2332 80*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^9- 145800*x^8)*exp(4)-80190*x^10+36450*x^9)*log(x)+(5832*x^7-7290*x^6)*exp(4) ^4+(-26244*x^8+29160*x^7)*exp(4)^3+(43740*x^9-43740*x^8)*exp(4)^2+(-32076* x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x, algorithm=\
729*x^12 + 729/2*(50*log(x)^2 - 10*log(x) + 1)*x^10 - 729/2*x^10*(8*e^4 + 1) - 900*(81*e^4*log(x)^2 - 18*e^4*log(x) + 2*e^4)*x^9 + 180*x^9*(27*e^8 + 10*e^4) + 54675/16*(32*e^8*log(x)^2 - 8*e^8*log(x) + e^8)*x^8 - 3645/16*x ^8*(16*e^12 + 15*e^8) - 72900/49*(49*e^12*log(x)^2 - 14*e^12*log(x) + 2*e^ 12)*x^7 + 7290/49*x^7*(7*e^16 + 20*e^12) + 2025/2*(18*e^16*log(x)^2 - 6*e^ 16*log(x) + e^16)*x^6 - 2025/2*x^6*e^16 + 729/7*(7*x^8 - 10*x^7)*e^16 - 72 9*(4*x^9 - 5*x^8)*e^12 + 486*(9*x^10 - 10*x^9)*e^8 - 2916*(x^11 - x^10)*e^ 4 - 405/14*(252*x^11 - 126*x^10 + 42*(6*x^7 - 5*x^6)*e^16 - 144*(7*x^8 - 5 *x^7)*e^12 + 189*(8*x^9 - 5*x^8)*e^8 - 112*(9*x^10 - 5*x^9)*e^4)*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 188 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 188, normalized size of antiderivative = 7.83 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=729 \, x^{12} - 7290 \, x^{11} \log \left (x\right ) + 29160 \, x^{10} e^{4} \log \left (x\right ) + 18225 \, x^{10} \log \left (x\right )^{2} - 72900 \, x^{9} e^{4} \log \left (x\right )^{2} - 2916 \, x^{10} e^{4} - 43740 \, x^{9} e^{8} \log \left (x\right ) + 109350 \, x^{8} e^{8} \log \left (x\right )^{2} + 4860 \, x^{9} e^{8} + 29160 \, x^{8} e^{12} \log \left (x\right ) - 72900 \, x^{7} e^{12} \log \left (x\right )^{2} - 3645 \, x^{8} e^{12} - 7290 \, x^{7} e^{16} \log \left (x\right ) + 18225 \, x^{6} e^{16} \log \left (x\right )^{2} + \frac {7290}{7} \, x^{7} e^{16} + \frac {729}{7} \, {\left (7 \, x^{8} - 10 \, x^{7}\right )} e^{16} - 729 \, {\left (4 \, x^{9} - 5 \, x^{8}\right )} e^{12} + 486 \, {\left (9 \, x^{10} - 10 \, x^{9}\right )} e^{8} - 2916 \, {\left (x^{11} - x^{10}\right )} e^{4} \]
integrate((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656 100*x^8*exp(4)+182250*x^9)*log(x)^2+((-51030*x^6+36450*x^5)*exp(4)^4+(2332 80*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^9- 145800*x^8)*exp(4)-80190*x^10+36450*x^9)*log(x)+(5832*x^7-7290*x^6)*exp(4) ^4+(-26244*x^8+29160*x^7)*exp(4)^3+(43740*x^9-43740*x^8)*exp(4)^2+(-32076* x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x, algorithm=\
729*x^12 - 7290*x^11*log(x) + 29160*x^10*e^4*log(x) + 18225*x^10*log(x)^2 - 72900*x^9*e^4*log(x)^2 - 2916*x^10*e^4 - 43740*x^9*e^8*log(x) + 109350*x ^8*e^8*log(x)^2 + 4860*x^9*e^8 + 29160*x^8*e^12*log(x) - 72900*x^7*e^12*lo g(x)^2 - 3645*x^8*e^12 - 7290*x^7*e^16*log(x) + 18225*x^6*e^16*log(x)^2 + 7290/7*x^7*e^16 + 729/7*(7*x^8 - 10*x^7)*e^16 - 729*(4*x^9 - 5*x^8)*e^12 + 486*(9*x^10 - 10*x^9)*e^8 - 2916*(x^11 - x^10)*e^4
Time = 9.16 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int \left (-7290 x^{10}+8748 x^{11}+e^{16} \left (-7290 x^6+5832 x^7\right )+e^{12} \left (29160 x^7-26244 x^8\right )+e^8 \left (-43740 x^8+43740 x^9\right )+e^4 \left (29160 x^9-32076 x^{10}\right )+\left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x)+\left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x)\right ) \, dx=729\,x^6\,{\left (x-5\,\ln \left (x\right )\right )}^2\,{\left (x-{\mathrm {e}}^4\right )}^4 \]
int(log(x)*(exp(16)*(36450*x^5 - 51030*x^6) - exp(12)*(145800*x^6 - 233280 *x^7) - exp(4)*(145800*x^8 - 291600*x^9) + exp(8)*(218700*x^7 - 393660*x^8 ) + 36450*x^9 - 80190*x^10) - exp(16)*(7290*x^6 - 5832*x^7) + exp(12)*(291 60*x^7 - 26244*x^8) + exp(4)*(29160*x^9 - 32076*x^10) - exp(8)*(43740*x^8 - 43740*x^9) + log(x)^2*(874800*x^7*exp(8) - 656100*x^8*exp(4) - 510300*x^ 6*exp(12) + 109350*x^5*exp(16) + 182250*x^9) - 7290*x^10 + 8748*x^11,x)