Integrand size = 247, antiderivative size = 28 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=1-x \left (3+x+\frac {\left (4+x-x^2\right )^4 (3+\log (x))}{x^4}\right )^2 \] Output:
1-((-x^2+x+4)^4/x^4*(3+ln(x))+3+x)^2*x
Leaf count is larger than twice the leaf count of optimal. \(149\) vs. \(2(28)=56\).
Time = 0.08 (sec) , antiderivative size = 149, normalized size of antiderivative = 5.32 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=-\frac {589824+1179648 x-147456 x^2-1548288 x^3-350208 x^4+941568 x^5+292992 x^6-102972 x^8+87708 x^9+18481 x^{10}-14748 x^{11}-1392 x^{12}+1518 x^{13}-36 x^{14}-72 x^{15}+9 x^{16}+2 \left (4+x-x^2\right )^4 \left (768+768 x-480 x^2-528 x^3+150 x^4+133 x^5-30 x^6-12 x^7+3 x^8\right ) \log (x)+\left (4+x-x^2\right )^8 \log ^2(x)}{x^7} \] Input:
Integrate[(3735552 + 6291456*x - 638976*x^2 - 5160960*x^3 - 815616*x^4 + 1 257472*x^5 + 97216*x^6 + 232352*x^7 + 171568*x^8 - 233522*x^9 - 67735*x^10 + 68780*x^11 + 7886*x^12 - 10118*x^13 + 276*x^14 + 624*x^15 - 87*x^16 + ( 2621440 + 4456448*x - 458752*x^2 - 3784704*x^3 - 626176*x^4 + 1043456*x^5 + 130368*x^6 + 76992*x^7 + 91442*x^8 - 135460*x^9 - 40964*x^10 + 42400*x^1 1 + 4938*x^12 - 6396*x^13 + 176*x^14 + 400*x^15 - 56*x^16)*Log[x] + (45875 2 + 786432*x - 81920*x^2 - 688128*x^3 - 118272*x^4 + 207872*x^5 + 32704*x^ 6 + 11423*x^8 - 19248*x^9 - 6132*x^10 + 6496*x^11 + 770*x^12 - 1008*x^13 + 28*x^14 + 64*x^15 - 9*x^16)*Log[x]^2)/x^8,x]
Output:
-((589824 + 1179648*x - 147456*x^2 - 1548288*x^3 - 350208*x^4 + 941568*x^5 + 292992*x^6 - 102972*x^8 + 87708*x^9 + 18481*x^10 - 14748*x^11 - 1392*x^ 12 + 1518*x^13 - 36*x^14 - 72*x^15 + 9*x^16 + 2*(4 + x - x^2)^4*(768 + 768 *x - 480*x^2 - 528*x^3 + 150*x^4 + 133*x^5 - 30*x^6 - 12*x^7 + 3*x^8)*Log[ x] + (4 + x - x^2)^8*Log[x]^2)/x^7)
Leaf count is larger than twice the leaf count of optimal. \(341\) vs. \(2(28)=56\).
Time = 1.26 (sec) , antiderivative size = 341, normalized size of antiderivative = 12.18, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2010, 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.
| \(\displaystyle \int \frac {-87 x^{16}+624 x^{15}+276 x^{14}-10118 x^{13}+7886 x^{12}+68780 x^{11}-67735 x^{10}-233522 x^9+171568 x^8+232352 x^7+97216 x^6+1257472 x^5-815616 x^4-5160960 x^3-638976 x^2+6291456 x+\left (-9 x^{16}+64 x^{15}+28 x^{14}-1008 x^{13}+770 x^{12}+6496 x^{11}-6132 x^{10}-19248 x^9+11423 x^8+32704 x^6+207872 x^5-118272 x^4-688128 x^3-81920 x^2+786432 x+458752\right ) \log ^2(x)+\left (-56 x^{16}+400 x^{15}+176 x^{14}-6396 x^{13}+4938 x^{12}+42400 x^{11}-40964 x^{10}-135460 x^9+91442 x^8+76992 x^7+130368 x^6+1043456 x^5-626176 x^4-3784704 x^3-458752 x^2+4456448 x+2621440\right ) \log (x)+3735552}{x^8} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (-\frac {\left (9 x^2-x+28\right ) \left (x^2-x-4\right )^7 \log ^2(x)}{x^8}-\frac {2 \left (28 x^{10}-116 x^9-184 x^8+958 x^7+409 x^6-1599 x^5+180 x^4-6272 x^3-6656 x^2+19456 x+20480\right ) \left (x^2-x-4\right )^3 \log (x)}{x^8}+\frac {-87 x^{16}+624 x^{15}+276 x^{14}-10118 x^{13}+7886 x^{12}+68780 x^{11}-67735 x^{10}-233522 x^9+171568 x^8+232352 x^7+97216 x^6+1257472 x^5-815616 x^4-5160960 x^3-638976 x^2+6291456 x+3735552}{x^8}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -9 x^9+x^9 \left (-\log ^2(x)\right )-6 x^9 \log (x)+72 x^8+8 x^8 \log ^2(x)+48 x^8 \log (x)+36 x^7-\frac {589824}{x^7}+4 x^7 \log ^2(x)-\frac {65536 \log ^2(x)}{x^7}+24 x^7 \log (x)-\frac {393216 \log (x)}{x^7}-1518 x^6-\frac {1179648}{x^6}-168 x^6 \log ^2(x)-\frac {131072 \log ^2(x)}{x^6}-1010 x^6 \log (x)-\frac {786432 \log (x)}{x^6}+1392 x^5+\frac {147456}{x^5}+154 x^5 \log ^2(x)+\frac {16384 \log ^2(x)}{x^5}+926 x^5 \log (x)+\frac {98304 \log (x)}{x^5}+14748 x^4+\frac {1548288}{x^4}+1624 x^4 \log ^2(x)+\frac {172032 \log ^2(x)}{x^4}+9788 x^4 \log (x)+\frac {1032192 \log (x)}{x^4}-18481 x^3+\frac {350208}{x^3}-2044 x^3 \log ^2(x)+\frac {39424 \log ^2(x)}{x^3}-12292 x^3 \log (x)+\frac {235008 \log (x)}{x^3}-87708 x^2-\frac {941568}{x^2}-9624 x^2 \log ^2(x)-\frac {103936 \log ^2(x)}{x^2}-58106 x^2 \log (x)-\frac {625664 \log (x)}{x^2}+102972 x-\frac {292992}{x}+11423 x \log ^2(x)+38496 \log ^2(x)-\frac {32704 \log ^2(x)}{x}+68596 x \log (x)+232352 \log (x)-\frac {195776 \log (x)}{x}\) |
Input:
Int[(3735552 + 6291456*x - 638976*x^2 - 5160960*x^3 - 815616*x^4 + 1257472 *x^5 + 97216*x^6 + 232352*x^7 + 171568*x^8 - 233522*x^9 - 67735*x^10 + 687 80*x^11 + 7886*x^12 - 10118*x^13 + 276*x^14 + 624*x^15 - 87*x^16 + (262144 0 + 4456448*x - 458752*x^2 - 3784704*x^3 - 626176*x^4 + 1043456*x^5 + 1303 68*x^6 + 76992*x^7 + 91442*x^8 - 135460*x^9 - 40964*x^10 + 42400*x^11 + 49 38*x^12 - 6396*x^13 + 176*x^14 + 400*x^15 - 56*x^16)*Log[x] + (458752 + 78 6432*x - 81920*x^2 - 688128*x^3 - 118272*x^4 + 207872*x^5 + 32704*x^6 + 11 423*x^8 - 19248*x^9 - 6132*x^10 + 6496*x^11 + 770*x^12 - 1008*x^13 + 28*x^ 14 + 64*x^15 - 9*x^16)*Log[x]^2)/x^8,x]
Output:
-589824/x^7 - 1179648/x^6 + 147456/x^5 + 1548288/x^4 + 350208/x^3 - 941568 /x^2 - 292992/x + 102972*x - 87708*x^2 - 18481*x^3 + 14748*x^4 + 1392*x^5 - 1518*x^6 + 36*x^7 + 72*x^8 - 9*x^9 + 232352*Log[x] - (393216*Log[x])/x^7 - (786432*Log[x])/x^6 + (98304*Log[x])/x^5 + (1032192*Log[x])/x^4 + (2350 08*Log[x])/x^3 - (625664*Log[x])/x^2 - (195776*Log[x])/x + 68596*x*Log[x] - 58106*x^2*Log[x] - 12292*x^3*Log[x] + 9788*x^4*Log[x] + 926*x^5*Log[x] - 1010*x^6*Log[x] + 24*x^7*Log[x] + 48*x^8*Log[x] - 6*x^9*Log[x] + 38496*Lo g[x]^2 - (65536*Log[x]^2)/x^7 - (131072*Log[x]^2)/x^6 + (16384*Log[x]^2)/x ^5 + (172032*Log[x]^2)/x^4 + (39424*Log[x]^2)/x^3 - (103936*Log[x]^2)/x^2 - (32704*Log[x]^2)/x + 11423*x*Log[x]^2 - 9624*x^2*Log[x]^2 - 2044*x^3*Log [x]^2 + 1624*x^4*Log[x]^2 + 154*x^5*Log[x]^2 - 168*x^6*Log[x]^2 + 4*x^7*Lo g[x]^2 + 8*x^8*Log[x]^2 - x^9*Log[x]^2
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Leaf count of result is larger than twice the leaf count of optimal. \(256\) vs. \(2(28)=56\).
Time = 81.05 (sec) , antiderivative size = 257, normalized size of antiderivative = 9.18
| method | result | size |
| risch | \(-\frac {\left (x^{16}-8 x^{15}-4 x^{14}+168 x^{13}-154 x^{12}-1624 x^{11}+2044 x^{10}+9624 x^{9}-11423 x^{8}-38496 x^{7}+32704 x^{6}+103936 x^{5}-39424 x^{4}-172032 x^{3}-16384 x^{2}+131072 x +65536\right ) \ln \left (x \right )^{2}}{x^{7}}-\frac {2 \left (3 x^{16}-24 x^{15}-12 x^{14}+505 x^{13}-463 x^{12}-4894 x^{11}+6146 x^{10}+29053 x^{9}-34298 x^{8}+97888 x^{6}+312832 x^{5}-117504 x^{4}-516096 x^{3}-49152 x^{2}+393216 x +196608\right ) \ln \left (x \right )}{x^{7}}+\frac {-9 x^{16}+72 x^{15}+36 x^{14}-1518 x^{13}+1392 x^{12}+14748 x^{11}-18481 x^{10}-87708 x^{9}+232352 \ln \left (x \right ) x^{7}+102972 x^{8}-292992 x^{6}-941568 x^{5}+350208 x^{4}+1548288 x^{3}+147456 x^{2}-1179648 x -589824}{x^{7}}\) | \(257\) |
| default | \(102972 x +\frac {39424 \ln \left (x \right )^{2}}{x^{3}}+\frac {16384 \ln \left (x \right )^{2}}{x^{5}}-\frac {131072 \ln \left (x \right )^{2}}{x^{6}}+\frac {98304 \ln \left (x \right )}{x^{5}}-\frac {786432 \ln \left (x \right )}{x^{6}}-\frac {625664 \ln \left (x \right )}{x^{2}}-\frac {32704 \ln \left (x \right )^{2}}{x}+926 x^{5} \ln \left (x \right )+1624 x^{4} \ln \left (x \right )^{2}-\frac {1179648}{x^{6}}-\frac {941568}{x^{2}}+9788 x^{4} \ln \left (x \right )+11423 x \ln \left (x \right )^{2}+48 x^{8} \ln \left (x \right )+68596 x \ln \left (x \right )-\frac {292992}{x}-\ln \left (x \right )^{2} x^{9}+8 \ln \left (x \right )^{2} x^{8}-6 \ln \left (x \right ) x^{9}+24 \ln \left (x \right ) x^{7}+4 \ln \left (x \right )^{2} x^{7}-168 \ln \left (x \right )^{2} x^{6}-1010 \ln \left (x \right ) x^{6}+154 x^{5} \ln \left (x \right )^{2}-\frac {103936 \ln \left (x \right )^{2}}{x^{2}}+\frac {350208}{x^{3}}-2044 x^{3} \ln \left (x \right )^{2}+\frac {1548288}{x^{4}}-9624 x^{2} \ln \left (x \right )^{2}+36 x^{7}+72 x^{8}-9 x^{9}-\frac {195776 \ln \left (x \right )}{x}-12292 x^{3} \ln \left (x \right )-58106 x^{2} \ln \left (x \right )+232352 \ln \left (x \right )+38496 \ln \left (x \right )^{2}+14748 x^{4}-18481 x^{3}-87708 x^{2}-1518 x^{6}+1392 x^{5}+\frac {147456}{x^{5}}-\frac {589824}{x^{7}}+\frac {235008 \ln \left (x \right )}{x^{3}}+\frac {1032192 \ln \left (x \right )}{x^{4}}+\frac {172032 \ln \left (x \right )^{2}}{x^{4}}-\frac {65536 \ln \left (x \right )^{2}}{x^{7}}-\frac {393216 \ln \left (x \right )}{x^{7}}\) | \(342\) |
| parallelrisch | \(-\frac {589824+1179648 x -926 x^{12} \ln \left (x \right )-154 \ln \left (x \right )^{2} x^{12}-24 \ln \left (x \right ) x^{14}+1010 \ln \left (x \right ) x^{13}-4 \ln \left (x \right )^{2} x^{14}-48 \ln \left (x \right ) x^{15}+168 \ln \left (x \right )^{2} x^{13}-8 \ln \left (x \right )^{2} x^{15}+6 \ln \left (x \right ) x^{16}+\ln \left (x \right )^{2} x^{16}+625664 x^{5} \ln \left (x \right )-39424 x^{4} \ln \left (x \right )^{2}-235008 x^{4} \ln \left (x \right )+131072 x \ln \left (x \right )^{2}-68596 x^{8} \ln \left (x \right )+786432 x \ln \left (x \right )-9788 \ln \left (x \right ) x^{11}+9624 \ln \left (x \right )^{2} x^{9}-11423 \ln \left (x \right )^{2} x^{8}+58106 \ln \left (x \right ) x^{9}-1624 \ln \left (x \right )^{2} x^{11}+2044 \ln \left (x \right )^{2} x^{10}-232352 \ln \left (x \right ) x^{7}-38496 \ln \left (x \right )^{2} x^{7}+32704 \ln \left (x \right )^{2} x^{6}+195776 \ln \left (x \right ) x^{6}+103936 x^{5} \ln \left (x \right )^{2}-172032 x^{3} \ln \left (x \right )^{2}-14748 x^{11}-1392 x^{12}+1518 x^{13}-36 x^{14}+9 x^{16}-72 x^{15}-16384 x^{2} \ln \left (x \right )^{2}-102972 x^{8}+18481 x^{10}+87708 x^{9}-1032192 x^{3} \ln \left (x \right )-98304 x^{2} \ln \left (x \right )+393216 \ln \left (x \right )+65536 \ln \left (x \right )^{2}-350208 x^{4}-1548288 x^{3}-147456 x^{2}+292992 x^{6}+941568 x^{5}+12292 \ln \left (x \right ) x^{10}}{x^{7}}\) | \(342\) |
| parts | \(102972 x +\frac {39424 \ln \left (x \right )^{2}}{x^{3}}+\frac {16384 \ln \left (x \right )^{2}}{x^{5}}-\frac {131072 \ln \left (x \right )^{2}}{x^{6}}+\frac {98304 \ln \left (x \right )}{x^{5}}-\frac {786432 \ln \left (x \right )}{x^{6}}-\frac {625664 \ln \left (x \right )}{x^{2}}-\frac {32704 \ln \left (x \right )^{2}}{x}+926 x^{5} \ln \left (x \right )+1624 x^{4} \ln \left (x \right )^{2}-\frac {1179648}{x^{6}}-\frac {941568}{x^{2}}+9788 x^{4} \ln \left (x \right )+11423 x \ln \left (x \right )^{2}+48 x^{8} \ln \left (x \right )+68596 x \ln \left (x \right )-\frac {292992}{x}-\ln \left (x \right )^{2} x^{9}+8 \ln \left (x \right )^{2} x^{8}-6 \ln \left (x \right ) x^{9}+24 \ln \left (x \right ) x^{7}+4 \ln \left (x \right )^{2} x^{7}-168 \ln \left (x \right )^{2} x^{6}-1010 \ln \left (x \right ) x^{6}+154 x^{5} \ln \left (x \right )^{2}-\frac {103936 \ln \left (x \right )^{2}}{x^{2}}+\frac {350208}{x^{3}}-2044 x^{3} \ln \left (x \right )^{2}+\frac {1548288}{x^{4}}-9624 x^{2} \ln \left (x \right )^{2}+36 x^{7}+72 x^{8}-9 x^{9}-\frac {195776 \ln \left (x \right )}{x}-12292 x^{3} \ln \left (x \right )-58106 x^{2} \ln \left (x \right )+232352 \ln \left (x \right )+38496 \ln \left (x \right )^{2}+14748 x^{4}-18481 x^{3}-87708 x^{2}-1518 x^{6}+1392 x^{5}+\frac {147456}{x^{5}}-\frac {589824}{x^{7}}+\frac {235008 \ln \left (x \right )}{x^{3}}+\frac {1032192 \ln \left (x \right )}{x^{4}}+\frac {172032 \ln \left (x \right )^{2}}{x^{4}}-\frac {65536 \ln \left (x \right )^{2}}{x^{7}}-\frac {393216 \ln \left (x \right )}{x^{7}}\) | \(342\) |
| orering | \(\text {Expression too large to display}\) | \(3202\) |
Input:
int(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10-19248 *x^9+11423*x^8+32704*x^6+207872*x^5-118272*x^4-688128*x^3-81920*x^2+786432 *x+458752)*ln(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^12+42400*x ^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^5-62617 6*x^4-3784704*x^3-458752*x^2+4456448*x+2621440)*ln(x)-87*x^16+624*x^15+276 *x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+171568*x^8+232 352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+6291456*x+ 3735552)/x^8,x,method=_RETURNVERBOSE)
Output:
-(x^16-8*x^15-4*x^14+168*x^13-154*x^12-1624*x^11+2044*x^10+9624*x^9-11423* x^8-38496*x^7+32704*x^6+103936*x^5-39424*x^4-172032*x^3-16384*x^2+131072*x +65536)/x^7*ln(x)^2-2*(3*x^16-24*x^15-12*x^14+505*x^13-463*x^12-4894*x^11+ 6146*x^10+29053*x^9-34298*x^8+97888*x^6+312832*x^5-117504*x^4-516096*x^3-4 9152*x^2+393216*x+196608)/x^7*ln(x)+(-9*x^16+72*x^15+36*x^14-1518*x^13+139 2*x^12+14748*x^11-18481*x^10-87708*x^9+232352*ln(x)*x^7+102972*x^8-292992* x^6-941568*x^5+350208*x^4+1548288*x^3+147456*x^2-1179648*x-589824)/x^7
Leaf count of result is larger than twice the leaf count of optimal. 247 vs. \(2 (28) = 56\).
Time = 0.07 (sec) , antiderivative size = 247, normalized size of antiderivative = 8.82 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=-\frac {9 \, x^{16} - 72 \, x^{15} - 36 \, x^{14} + 1518 \, x^{13} - 1392 \, x^{12} - 14748 \, x^{11} + 18481 \, x^{10} + 87708 \, x^{9} - 102972 \, x^{8} + 292992 \, x^{6} + 941568 \, x^{5} - 350208 \, x^{4} - 1548288 \, x^{3} + {\left (x^{16} - 8 \, x^{15} - 4 \, x^{14} + 168 \, x^{13} - 154 \, x^{12} - 1624 \, x^{11} + 2044 \, x^{10} + 9624 \, x^{9} - 11423 \, x^{8} - 38496 \, x^{7} + 32704 \, x^{6} + 103936 \, x^{5} - 39424 \, x^{4} - 172032 \, x^{3} - 16384 \, x^{2} + 131072 \, x + 65536\right )} \log \left (x\right )^{2} - 147456 \, x^{2} + 2 \, {\left (3 \, x^{16} - 24 \, x^{15} - 12 \, x^{14} + 505 \, x^{13} - 463 \, x^{12} - 4894 \, x^{11} + 6146 \, x^{10} + 29053 \, x^{9} - 34298 \, x^{8} - 116176 \, x^{7} + 97888 \, x^{6} + 312832 \, x^{5} - 117504 \, x^{4} - 516096 \, x^{3} - 49152 \, x^{2} + 393216 \, x + 196608\right )} \log \left (x\right ) + 1179648 \, x + 589824}{x^{7}} \] Input:
integrate(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10 -19248*x^9+11423*x^8+32704*x^6+207872*x^5-118272*x^4-688128*x^3-81920*x^2+ 786432*x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^12+ 42400*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^ 5-626176*x^4-3784704*x^3-458752*x^2+4456448*x+2621440)*log(x)-87*x^16+624* x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+171568 *x^8+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+62 91456*x+3735552)/x^8,x, algorithm="fricas")
Output:
-(9*x^16 - 72*x^15 - 36*x^14 + 1518*x^13 - 1392*x^12 - 14748*x^11 + 18481* x^10 + 87708*x^9 - 102972*x^8 + 292992*x^6 + 941568*x^5 - 350208*x^4 - 154 8288*x^3 + (x^16 - 8*x^15 - 4*x^14 + 168*x^13 - 154*x^12 - 1624*x^11 + 204 4*x^10 + 9624*x^9 - 11423*x^8 - 38496*x^7 + 32704*x^6 + 103936*x^5 - 39424 *x^4 - 172032*x^3 - 16384*x^2 + 131072*x + 65536)*log(x)^2 - 147456*x^2 + 2*(3*x^16 - 24*x^15 - 12*x^14 + 505*x^13 - 463*x^12 - 4894*x^11 + 6146*x^1 0 + 29053*x^9 - 34298*x^8 - 116176*x^7 + 97888*x^6 + 312832*x^5 - 117504*x ^4 - 516096*x^3 - 49152*x^2 + 393216*x + 196608)*log(x) + 1179648*x + 5898 24)/x^7
Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (24) = 48\).
Time = 0.30 (sec) , antiderivative size = 253, normalized size of antiderivative = 9.04 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=- 9 x^{9} + 72 x^{8} + 36 x^{7} - 1518 x^{6} + 1392 x^{5} + 14748 x^{4} - 18481 x^{3} - 87708 x^{2} + 102972 x + 232352 \log {\left (x \right )} - \frac {292992 x^{6} + 941568 x^{5} - 350208 x^{4} - 1548288 x^{3} - 147456 x^{2} + 1179648 x + 589824}{x^{7}} + \frac {\left (- 6 x^{16} + 48 x^{15} + 24 x^{14} - 1010 x^{13} + 926 x^{12} + 9788 x^{11} - 12292 x^{10} - 58106 x^{9} + 68596 x^{8} - 195776 x^{6} - 625664 x^{5} + 235008 x^{4} + 1032192 x^{3} + 98304 x^{2} - 786432 x - 393216\right ) \log {\left (x \right )}}{x^{7}} + \frac {\left (- x^{16} + 8 x^{15} + 4 x^{14} - 168 x^{13} + 154 x^{12} + 1624 x^{11} - 2044 x^{10} - 9624 x^{9} + 11423 x^{8} + 38496 x^{7} - 32704 x^{6} - 103936 x^{5} + 39424 x^{4} + 172032 x^{3} + 16384 x^{2} - 131072 x - 65536\right ) \log {\left (x \right )}^{2}}{x^{7}} \] Input:
integrate(((-9*x**16+64*x**15+28*x**14-1008*x**13+770*x**12+6496*x**11-613 2*x**10-19248*x**9+11423*x**8+32704*x**6+207872*x**5-118272*x**4-688128*x* *3-81920*x**2+786432*x+458752)*ln(x)**2+(-56*x**16+400*x**15+176*x**14-639 6*x**13+4938*x**12+42400*x**11-40964*x**10-135460*x**9+91442*x**8+76992*x* *7+130368*x**6+1043456*x**5-626176*x**4-3784704*x**3-458752*x**2+4456448*x +2621440)*ln(x)-87*x**16+624*x**15+276*x**14-10118*x**13+7886*x**12+68780* x**11-67735*x**10-233522*x**9+171568*x**8+232352*x**7+97216*x**6+1257472*x **5-815616*x**4-5160960*x**3-638976*x**2+6291456*x+3735552)/x**8,x)
Output:
-9*x**9 + 72*x**8 + 36*x**7 - 1518*x**6 + 1392*x**5 + 14748*x**4 - 18481*x **3 - 87708*x**2 + 102972*x + 232352*log(x) - (292992*x**6 + 941568*x**5 - 350208*x**4 - 1548288*x**3 - 147456*x**2 + 1179648*x + 589824)/x**7 + (-6 *x**16 + 48*x**15 + 24*x**14 - 1010*x**13 + 926*x**12 + 9788*x**11 - 12292 *x**10 - 58106*x**9 + 68596*x**8 - 195776*x**6 - 625664*x**5 + 235008*x**4 + 1032192*x**3 + 98304*x**2 - 786432*x - 393216)*log(x)/x**7 + (-x**16 + 8*x**15 + 4*x**14 - 168*x**13 + 154*x**12 + 1624*x**11 - 2044*x**10 - 9624 *x**9 + 11423*x**8 + 38496*x**7 - 32704*x**6 - 103936*x**5 + 39424*x**4 + 172032*x**3 + 16384*x**2 - 131072*x - 65536)*log(x)**2/x**7
Leaf count of result is larger than twice the leaf count of optimal. 465 vs. \(2 (28) = 56\).
Time = 0.05 (sec) , antiderivative size = 465, normalized size of antiderivative = 16.61 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx =\text {Too large to display} \] Input:
integrate(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10 -19248*x^9+11423*x^8+32704*x^6+207872*x^5-118272*x^4-688128*x^3-81920*x^2+ 786432*x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^12+ 42400*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^ 5-626176*x^4-3784704*x^3-458752*x^2+4456448*x+2621440)*log(x)-87*x^16+624* x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+171568 *x^8+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+62 91456*x+3735552)/x^8,x, algorithm="maxima")
Output:
-1/81*(81*log(x)^2 - 18*log(x) + 2)*x^9 - 56/9*x^9*log(x) + 1/4*(32*log(x) ^2 - 8*log(x) + 1)*x^8 - 727/81*x^9 + 50*x^8*log(x) + 4/49*(49*log(x)^2 - 14*log(x) + 2)*x^7 + 287/4*x^8 + 176/7*x^7*log(x) - 28/3*(18*log(x)^2 - 6* log(x) + 1)*x^6 + 1756/49*x^7 - 1066*x^6*log(x) + 154/25*(25*log(x)^2 - 10 *log(x) + 2)*x^5 - 4526/3*x^6 + 4938/5*x^5*log(x) + 203*(8*log(x)^2 - 4*lo g(x) + 1)*x^4 + 34492/25*x^5 + 10600*x^4*log(x) - 2044/9*(9*log(x)^2 - 6*l og(x) + 2)*x^3 + 14545*x^4 - 40964/3*x^3*log(x) - 4812*(2*log(x)^2 - 2*log (x) + 1)*x^2 - 162241/9*x^3 - 67730*x^2*log(x) + 11423*(log(x)^2 - 2*log(x ) + 2)*x - 82896*x^2 + 91442*x*log(x) + 38496*log(x)^2 + 80126*x - 32704*( log(x)^2 + 2*log(x) + 2)/x - 130368*log(x)/x - 51968*(2*log(x)^2 + 2*log(x ) + 1)/x^2 - 227584/x - 521728*log(x)/x^2 + 39424/9*(9*log(x)^2 + 6*log(x) + 2)/x^3 - 889600/x^2 + 626176/3*log(x)/x^3 + 21504*(8*log(x)^2 + 4*log(x ) + 1)/x^4 + 3073024/9/x^3 + 946176*log(x)/x^4 + 16384/25*(25*log(x)^2 + 1 0*log(x) + 2)/x^5 + 1526784/x^4 + 458752/5*log(x)/x^5 - 65536/9*(18*log(x) ^2 + 6*log(x) + 1)/x^6 + 3653632/25/x^5 - 2228224/3*log(x)/x^6 - 65536/49* (49*log(x)^2 + 14*log(x) + 2)/x^7 - 10551296/9/x^6 - 2621440/7*log(x)/x^7 - 28770304/49/x^7 + 232352*log(x)
\[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=\int { -\frac {87 \, x^{16} - 624 \, x^{15} - 276 \, x^{14} + 10118 \, x^{13} - 7886 \, x^{12} - 68780 \, x^{11} + 67735 \, x^{10} + 233522 \, x^{9} - 171568 \, x^{8} - 232352 \, x^{7} - 97216 \, x^{6} - 1257472 \, x^{5} + 815616 \, x^{4} + 5160960 \, x^{3} + {\left (9 \, x^{16} - 64 \, x^{15} - 28 \, x^{14} + 1008 \, x^{13} - 770 \, x^{12} - 6496 \, x^{11} + 6132 \, x^{10} + 19248 \, x^{9} - 11423 \, x^{8} - 32704 \, x^{6} - 207872 \, x^{5} + 118272 \, x^{4} + 688128 \, x^{3} + 81920 \, x^{2} - 786432 \, x - 458752\right )} \log \left (x\right )^{2} + 638976 \, x^{2} + 2 \, {\left (28 \, x^{16} - 200 \, x^{15} - 88 \, x^{14} + 3198 \, x^{13} - 2469 \, x^{12} - 21200 \, x^{11} + 20482 \, x^{10} + 67730 \, x^{9} - 45721 \, x^{8} - 38496 \, x^{7} - 65184 \, x^{6} - 521728 \, x^{5} + 313088 \, x^{4} + 1892352 \, x^{3} + 229376 \, x^{2} - 2228224 \, x - 1310720\right )} \log \left (x\right ) - 6291456 \, x - 3735552}{x^{8}} \,d x } \] Input:
integrate(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10 -19248*x^9+11423*x^8+32704*x^6+207872*x^5-118272*x^4-688128*x^3-81920*x^2+ 786432*x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^12+ 42400*x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^ 5-626176*x^4-3784704*x^3-458752*x^2+4456448*x+2621440)*log(x)-87*x^16+624* x^15+276*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+171568 *x^8+232352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+62 91456*x+3735552)/x^8,x, algorithm="giac")
Output:
integrate(-(87*x^16 - 624*x^15 - 276*x^14 + 10118*x^13 - 7886*x^12 - 68780 *x^11 + 67735*x^10 + 233522*x^9 - 171568*x^8 - 232352*x^7 - 97216*x^6 - 12 57472*x^5 + 815616*x^4 + 5160960*x^3 + (9*x^16 - 64*x^15 - 28*x^14 + 1008* x^13 - 770*x^12 - 6496*x^11 + 6132*x^10 + 19248*x^9 - 11423*x^8 - 32704*x^ 6 - 207872*x^5 + 118272*x^4 + 688128*x^3 + 81920*x^2 - 786432*x - 458752)* log(x)^2 + 638976*x^2 + 2*(28*x^16 - 200*x^15 - 88*x^14 + 3198*x^13 - 2469 *x^12 - 21200*x^11 + 20482*x^10 + 67730*x^9 - 45721*x^8 - 38496*x^7 - 6518 4*x^6 - 521728*x^5 + 313088*x^4 + 1892352*x^3 + 229376*x^2 - 2228224*x - 1 310720)*log(x) - 6291456*x - 3735552)/x^8, x)
Time = 2.08 (sec) , antiderivative size = 255, normalized size of antiderivative = 9.11 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=102972\,x+\frac {15119344\,\ln \left (x\right )}{35}-{\ln \left (x\right )}^2\,\left (\frac {x^{16}-8\,x^{15}-4\,x^{14}+168\,x^{13}-154\,x^{12}-1624\,x^{11}+2044\,x^{10}+9624\,x^9-11423\,x^8+32704\,x^6+103936\,x^5-39424\,x^4-172032\,x^3-16384\,x^2+131072\,x+65536}{x^7}-38496\right )-\frac {292992\,x^6+941568\,x^5-350208\,x^4-1548288\,x^3-147456\,x^2+1179648\,x+589824}{x^7}-87708\,x^2-18481\,x^3+14748\,x^4+1392\,x^5-1518\,x^6+36\,x^7+72\,x^8-9\,x^9-\frac {\ln \left (x\right )\,\left (6\,x^{16}-48\,x^{15}-24\,x^{14}+1010\,x^{13}-926\,x^{12}-9788\,x^{11}+12292\,x^{10}+58106\,x^9-68596\,x^8+\frac {6987024\,x^7}{35}+195776\,x^6+625664\,x^5-235008\,x^4-1032192\,x^3-98304\,x^2+786432\,x+393216\right )}{x^7} \] Input:
int((6291456*x + log(x)*(4456448*x - 458752*x^2 - 3784704*x^3 - 626176*x^4 + 1043456*x^5 + 130368*x^6 + 76992*x^7 + 91442*x^8 - 135460*x^9 - 40964*x ^10 + 42400*x^11 + 4938*x^12 - 6396*x^13 + 176*x^14 + 400*x^15 - 56*x^16 + 2621440) - 638976*x^2 - 5160960*x^3 - 815616*x^4 + 1257472*x^5 + 97216*x^ 6 + 232352*x^7 + 171568*x^8 - 233522*x^9 - 67735*x^10 + 68780*x^11 + 7886* x^12 - 10118*x^13 + 276*x^14 + 624*x^15 - 87*x^16 + log(x)^2*(786432*x - 8 1920*x^2 - 688128*x^3 - 118272*x^4 + 207872*x^5 + 32704*x^6 + 11423*x^8 - 19248*x^9 - 6132*x^10 + 6496*x^11 + 770*x^12 - 1008*x^13 + 28*x^14 + 64*x^ 15 - 9*x^16 + 458752) + 3735552)/x^8,x)
Output:
102972*x + (15119344*log(x))/35 - log(x)^2*((131072*x - 16384*x^2 - 172032 *x^3 - 39424*x^4 + 103936*x^5 + 32704*x^6 - 11423*x^8 + 9624*x^9 + 2044*x^ 10 - 1624*x^11 - 154*x^12 + 168*x^13 - 4*x^14 - 8*x^15 + x^16 + 65536)/x^7 - 38496) - (1179648*x - 147456*x^2 - 1548288*x^3 - 350208*x^4 + 941568*x^ 5 + 292992*x^6 + 589824)/x^7 - 87708*x^2 - 18481*x^3 + 14748*x^4 + 1392*x^ 5 - 1518*x^6 + 36*x^7 + 72*x^8 - 9*x^9 - (log(x)*(786432*x - 98304*x^2 - 1 032192*x^3 - 235008*x^4 + 625664*x^5 + 195776*x^6 + (6987024*x^7)/35 - 685 96*x^8 + 58106*x^9 + 12292*x^10 - 9788*x^11 - 926*x^12 + 1010*x^13 - 24*x^ 14 - 48*x^15 + 6*x^16 + 393216))/x^7
Time = 0.22 (sec) , antiderivative size = 341, normalized size of antiderivative = 12.18 \[ \int \frac {3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+\left (2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}\right ) \log (x)+\left (458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}\right ) \log ^2(x)}{x^8} \, dx=\frac {-589824-1179648 x +39424 \mathrm {log}\left (x \right )^{2} x^{4}+172032 \mathrm {log}\left (x \right )^{2} x^{3}-103936 \mathrm {log}\left (x \right )^{2} x^{5}-18481 x^{10}-87708 x^{9}+16384 \mathrm {log}\left (x \right )^{2} x^{2}+235008 \,\mathrm {log}\left (x \right ) x^{4}+147456 x^{2}-941568 x^{5}+72 x^{15}-9 x^{16}+36 x^{14}-1518 x^{13}+14748 x^{11}+1548288 x^{3}-32704 \mathrm {log}\left (x \right )^{2} x^{6}+232352 \,\mathrm {log}\left (x \right ) x^{7}-195776 \,\mathrm {log}\left (x \right ) x^{6}+102972 x^{8}-292992 x^{6}-393216 \,\mathrm {log}\left (x \right )+98304 \,\mathrm {log}\left (x \right ) x^{2}+1392 x^{12}-\mathrm {log}\left (x \right )^{2} x^{16}+8 \mathrm {log}\left (x \right )^{2} x^{15}+4 \mathrm {log}\left (x \right )^{2} x^{14}-168 \mathrm {log}\left (x \right )^{2} x^{13}+154 \mathrm {log}\left (x \right )^{2} x^{12}+1624 \mathrm {log}\left (x \right )^{2} x^{11}-2044 \mathrm {log}\left (x \right )^{2} x^{10}-9624 \mathrm {log}\left (x \right )^{2} x^{9}+11423 \mathrm {log}\left (x \right )^{2} x^{8}+38496 \mathrm {log}\left (x \right )^{2} x^{7}-6 \,\mathrm {log}\left (x \right ) x^{16}+48 \,\mathrm {log}\left (x \right ) x^{15}+24 \,\mathrm {log}\left (x \right ) x^{14}-1010 \,\mathrm {log}\left (x \right ) x^{13}+926 \,\mathrm {log}\left (x \right ) x^{12}+9788 \,\mathrm {log}\left (x \right ) x^{11}-12292 \,\mathrm {log}\left (x \right ) x^{10}-58106 \,\mathrm {log}\left (x \right ) x^{9}+68596 \,\mathrm {log}\left (x \right ) x^{8}-625664 \,\mathrm {log}\left (x \right ) x^{5}+1032192 \,\mathrm {log}\left (x \right ) x^{3}+350208 x^{4}-65536 \mathrm {log}\left (x \right )^{2}-786432 \,\mathrm {log}\left (x \right ) x -131072 \mathrm {log}\left (x \right )^{2} x}{x^{7}} \] Input:
int(((-9*x^16+64*x^15+28*x^14-1008*x^13+770*x^12+6496*x^11-6132*x^10-19248 *x^9+11423*x^8+32704*x^6+207872*x^5-118272*x^4-688128*x^3-81920*x^2+786432 *x+458752)*log(x)^2+(-56*x^16+400*x^15+176*x^14-6396*x^13+4938*x^12+42400* x^11-40964*x^10-135460*x^9+91442*x^8+76992*x^7+130368*x^6+1043456*x^5-6261 76*x^4-3784704*x^3-458752*x^2+4456448*x+2621440)*log(x)-87*x^16+624*x^15+2 76*x^14-10118*x^13+7886*x^12+68780*x^11-67735*x^10-233522*x^9+171568*x^8+2 32352*x^7+97216*x^6+1257472*x^5-815616*x^4-5160960*x^3-638976*x^2+6291456* x+3735552)/x^8,x)
Output:
( - log(x)**2*x**16 + 8*log(x)**2*x**15 + 4*log(x)**2*x**14 - 168*log(x)** 2*x**13 + 154*log(x)**2*x**12 + 1624*log(x)**2*x**11 - 2044*log(x)**2*x**1 0 - 9624*log(x)**2*x**9 + 11423*log(x)**2*x**8 + 38496*log(x)**2*x**7 - 32 704*log(x)**2*x**6 - 103936*log(x)**2*x**5 + 39424*log(x)**2*x**4 + 172032 *log(x)**2*x**3 + 16384*log(x)**2*x**2 - 131072*log(x)**2*x - 65536*log(x) **2 - 6*log(x)*x**16 + 48*log(x)*x**15 + 24*log(x)*x**14 - 1010*log(x)*x** 13 + 926*log(x)*x**12 + 9788*log(x)*x**11 - 12292*log(x)*x**10 - 58106*log (x)*x**9 + 68596*log(x)*x**8 + 232352*log(x)*x**7 - 195776*log(x)*x**6 - 6 25664*log(x)*x**5 + 235008*log(x)*x**4 + 1032192*log(x)*x**3 + 98304*log(x )*x**2 - 786432*log(x)*x - 393216*log(x) - 9*x**16 + 72*x**15 + 36*x**14 - 1518*x**13 + 1392*x**12 + 14748*x**11 - 18481*x**10 - 87708*x**9 + 102972 *x**8 - 292992*x**6 - 941568*x**5 + 350208*x**4 + 1548288*x**3 + 147456*x* *2 - 1179648*x - 589824)/x**7