Integrand size = 587, antiderivative size = 22 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\frac {3}{-1+\left (-x+x^2-4 (1+x) \log (2)\right )^4} \] Output:
3/(-1+(x^2-x-(4+4*x)*ln(2))^4)
Leaf count is larger than twice the leaf count of optimal. \(19960\) vs. \(2(22)=44\).
Time = 30.61 (sec) , antiderivative size = 19960, normalized size of antiderivative = 907.27 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\text {Result too large to show} \] Input:
Integrate[(-12*x^3 + 60*x^4 - 108*x^5 + 84*x^6 - 24*x^7 + (-144*x^2 + 384* x^3 - 576*x^5 + 336*x^6)*Log[2] + (-576*x + 2304*x^3 - 1728*x^5)*Log[2]^2 + (-768 - 3072*x + 6144*x^3 + 3840*x^4)*Log[2]^3 + (-3072 - 9216*x - 9216* x^2 - 3072*x^3)*Log[2]^4)/(1 - 2*x^4 + 8*x^5 - 12*x^6 + 8*x^7 - x^8 - 8*x^ 9 + 28*x^10 - 56*x^11 + 70*x^12 - 56*x^13 + 28*x^14 - 8*x^15 + x^16 + (-32 *x^3 + 64*x^4 - 64*x^6 + 64*x^7 - 192*x^8 + 448*x^9 - 448*x^10 + 448*x^12 - 448*x^13 + 192*x^14 - 32*x^15)*Log[2] + (-192*x^2 + 384*x^4 + 256*x^6 - 1792*x^7 + 1792*x^8 + 1792*x^9 - 4480*x^10 + 1792*x^11 + 1792*x^12 - 1792* x^13 + 448*x^14)*Log[2]^2 + (-512*x - 1024*x^2 + 1024*x^4 + 4096*x^5 - 716 8*x^6 - 7168*x^7 + 21504*x^8 - 21504*x^10 + 7168*x^11 + 7168*x^12 - 3584*x ^13)*Log[2]^3 + (-512 - 2048*x - 3072*x^2 - 2048*x^3 + 17408*x^4 - 71680*x ^6 + 107520*x^8 - 71680*x^10 + 17920*x^12)*Log[2]^4 + (57344*x^3 + 114688* x^4 - 114688*x^5 - 344064*x^6 + 344064*x^8 + 114688*x^9 - 114688*x^10 - 57 344*x^11)*Log[2]^5 + (114688*x^2 + 458752*x^3 + 458752*x^4 - 458752*x^5 - 1146880*x^6 - 458752*x^7 + 458752*x^8 + 458752*x^9 + 114688*x^10)*Log[2]^6 + (131072*x + 786432*x^2 + 1835008*x^3 + 1835008*x^4 - 1835008*x^6 - 1835 008*x^7 - 786432*x^8 - 131072*x^9)*Log[2]^7 + (65536 + 524288*x + 1835008* x^2 + 3670016*x^3 + 4587520*x^4 + 3670016*x^5 + 1835008*x^6 + 524288*x^7 + 65536*x^8)*Log[2]^8),x]
Output:
Result too large to show
Leaf count is larger than twice the leaf count of optimal. \(101\) vs. \(2(22)=44\).
Time = 1.41 (sec) , antiderivative size = 101, normalized size of antiderivative = 4.59, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.003, Rules used = {2462, 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.
| \(\displaystyle \int \frac {-24 x^7+84 x^6-108 x^5+60 x^4-12 x^3+\left (-1728 x^5+2304 x^3-576 x\right ) \log ^2(2)+\left (3840 x^4+6144 x^3-3072 x-768\right ) \log ^3(2)+\left (-3072 x^3-9216 x^2-9216 x-3072\right ) \log ^4(2)+\left (336 x^6-576 x^5+384 x^3-144 x^2\right ) \log (2)}{x^{16}-8 x^{15}+28 x^{14}-56 x^{13}+70 x^{12}-56 x^{11}+28 x^{10}-8 x^9-x^8+8 x^7-12 x^6+8 x^5-2 x^4+\left (17920 x^{12}-71680 x^{10}+107520 x^8-71680 x^6+17408 x^4-2048 x^3-3072 x^2-2048 x-512\right ) \log ^4(2)+\left (-131072 x^9-786432 x^8-1835008 x^7-1835008 x^6+1835008 x^4+1835008 x^3+786432 x^2+131072 x\right ) \log ^7(2)+\left (65536 x^8+524288 x^7+1835008 x^6+3670016 x^5+4587520 x^4+3670016 x^3+1835008 x^2+524288 x+65536\right ) \log ^8(2)+\left (-57344 x^{11}-114688 x^{10}+114688 x^9+344064 x^8-344064 x^6-114688 x^5+114688 x^4+57344 x^3\right ) \log ^5(2)+\left (114688 x^{10}+458752 x^9+458752 x^8-458752 x^7-1146880 x^6-458752 x^5+458752 x^4+458752 x^3+114688 x^2\right ) \log ^6(2)+\left (-3584 x^{13}+7168 x^{12}+7168 x^{11}-21504 x^{10}+21504 x^8-7168 x^7-7168 x^6+4096 x^5+1024 x^4-1024 x^2-512 x\right ) \log ^3(2)+\left (-32 x^{15}+192 x^{14}-448 x^{13}+448 x^{12}-448 x^{10}+448 x^9-192 x^8+64 x^7-64 x^6+64 x^4-32 x^3\right ) \log (2)+\left (448 x^{14}-1792 x^{13}+1792 x^{12}+1792 x^{11}-4480 x^{10}+1792 x^9+1792 x^8-1792 x^7+256 x^6+384 x^4-192 x^2\right ) \log ^2(2)+1} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {3 (2 x-1-4 \log (2))}{4 \left (x^2-x (1+\log (16))+1-4 \log (2)\right )^2}+\frac {-6 x+3+\log (4096)}{4 \left (-x^2+x (1+\log (16))+1+\log (16)\right )^2}+\frac {3 \left (2 x^3-3 x^2 (1+\log (16))+x \left (1+16 \log ^2(2)\right )+16 \log ^2(2)+\log (16)\right )}{\left (x^4-2 x^3 (1+\log (16))+x^2 \left (1+16 \log ^2(2)\right )+8 x \log (2) (1+\log (16))+1+16 \log ^2(2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {3+\log (4096)}{4 (1+\log (16)) \left (-x^2+x (1+\log (16))+1+\log (16)\right )}-\frac {3}{4 \left (x^2-x (1+\log (16))+1-4 \log (2)\right )}-\frac {3}{2 \left (x^4-2 x^3 (1+\log (16))+x^2 \left (1+16 \log ^2(2)\right )+8 x \log (2) (1+\log (16))+1+16 \log ^2(2)\right )}\) |
Input:
Int[(-12*x^3 + 60*x^4 - 108*x^5 + 84*x^6 - 24*x^7 + (-144*x^2 + 384*x^3 - 576*x^5 + 336*x^6)*Log[2] + (-576*x + 2304*x^3 - 1728*x^5)*Log[2]^2 + (-76 8 - 3072*x + 6144*x^3 + 3840*x^4)*Log[2]^3 + (-3072 - 9216*x - 9216*x^2 - 3072*x^3)*Log[2]^4)/(1 - 2*x^4 + 8*x^5 - 12*x^6 + 8*x^7 - x^8 - 8*x^9 + 28 *x^10 - 56*x^11 + 70*x^12 - 56*x^13 + 28*x^14 - 8*x^15 + x^16 + (-32*x^3 + 64*x^4 - 64*x^6 + 64*x^7 - 192*x^8 + 448*x^9 - 448*x^10 + 448*x^12 - 448* x^13 + 192*x^14 - 32*x^15)*Log[2] + (-192*x^2 + 384*x^4 + 256*x^6 - 1792*x ^7 + 1792*x^8 + 1792*x^9 - 4480*x^10 + 1792*x^11 + 1792*x^12 - 1792*x^13 + 448*x^14)*Log[2]^2 + (-512*x - 1024*x^2 + 1024*x^4 + 4096*x^5 - 7168*x^6 - 7168*x^7 + 21504*x^8 - 21504*x^10 + 7168*x^11 + 7168*x^12 - 3584*x^13)*L og[2]^3 + (-512 - 2048*x - 3072*x^2 - 2048*x^3 + 17408*x^4 - 71680*x^6 + 1 07520*x^8 - 71680*x^10 + 17920*x^12)*Log[2]^4 + (57344*x^3 + 114688*x^4 - 114688*x^5 - 344064*x^6 + 344064*x^8 + 114688*x^9 - 114688*x^10 - 57344*x^ 11)*Log[2]^5 + (114688*x^2 + 458752*x^3 + 458752*x^4 - 458752*x^5 - 114688 0*x^6 - 458752*x^7 + 458752*x^8 + 458752*x^9 + 114688*x^10)*Log[2]^6 + (13 1072*x + 786432*x^2 + 1835008*x^3 + 1835008*x^4 - 1835008*x^6 - 1835008*x^ 7 - 786432*x^8 - 131072*x^9)*Log[2]^7 + (65536 + 524288*x + 1835008*x^2 + 3670016*x^3 + 4587520*x^4 + 3670016*x^5 + 1835008*x^6 + 524288*x^7 + 65536 *x^8)*Log[2]^8),x]
Output:
-3/(4*(1 + x^2 - 4*Log[2] - x*(1 + Log[16]))) - 3/(2*(1 + x^4 + 16*Log[2]^ 2 + x^2*(1 + 16*Log[2]^2) - 2*x^3*(1 + Log[16]) + 8*x*Log[2]*(1 + Log[16]) )) - (3 + Log[4096])/(4*(1 + Log[16])*(1 - x^2 + Log[16] + x*(1 + Log[16]) ))
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] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Leaf count of result is larger than twice the leaf count of optimal. \(156\) vs. \(2(24)=48\).
Time = 1.72 (sec) , antiderivative size = 157, normalized size of antiderivative = 7.14
| method | result | size |
| gosper | \(\frac {3}{256 \ln \left (2\right )^{4} x^{4}-256 x^{5} \ln \left (2\right )^{3}+96 x^{6} \ln \left (2\right )^{2}-16 \ln \left (2\right ) x^{7}+x^{8}+1024 \ln \left (2\right )^{4} x^{3}-512 \ln \left (2\right )^{3} x^{4}+32 x^{6} \ln \left (2\right )-4 x^{7}+1536 x^{2} \ln \left (2\right )^{4}-192 x^{4} \ln \left (2\right )^{2}+6 x^{6}+1024 \ln \left (2\right )^{4} x +512 \ln \left (2\right )^{3} x^{2}-32 x^{4} \ln \left (2\right )-4 x^{5}+256 \ln \left (2\right )^{4}+256 x \ln \left (2\right )^{3}+96 x^{2} \ln \left (2\right )^{2}+16 x^{3} \ln \left (2\right )+x^{4}-1}\) | \(157\) |
| default | \(-\frac {3}{32 \left (x^{2} \ln \left (2\right )^{2}-\frac {x^{3} \ln \left (2\right )}{2}+\frac {x^{4}}{16}+2 x \ln \left (2\right )^{2}-\frac {x^{3}}{8}+\ln \left (2\right )^{2}+\frac {x \ln \left (2\right )}{2}+\frac {x^{2}}{16}+\frac {1}{16}\right )}+\frac {-3+\frac {3 \left (-4 \ln \left (2\right )-1\right )^{2}}{4}+12 \ln \left (2\right )}{\left (-16 \ln \left (2\right )^{2}-24 \ln \left (2\right )+3\right ) \left (-4 x \ln \left (2\right )+x^{2}-4 \ln \left (2\right )-x +1\right )}+\frac {-3+\frac {3 \left (1+4 \ln \left (2\right )\right ) \left (-4 \ln \left (2\right )-1\right )}{4}-12 \ln \left (2\right )}{\left (-16 \ln \left (2\right )^{2}-24 \ln \left (2\right )-5\right ) \left (-4 x \ln \left (2\right )+x^{2}-4 \ln \left (2\right )-x -1\right )}\) | \(157\) |
| norman | \(\frac {3}{256 \ln \left (2\right )^{4} x^{4}-256 x^{5} \ln \left (2\right )^{3}+96 x^{6} \ln \left (2\right )^{2}-16 \ln \left (2\right ) x^{7}+x^{8}+1024 \ln \left (2\right )^{4} x^{3}-512 \ln \left (2\right )^{3} x^{4}+32 x^{6} \ln \left (2\right )-4 x^{7}+1536 x^{2} \ln \left (2\right )^{4}-192 x^{4} \ln \left (2\right )^{2}+6 x^{6}+1024 \ln \left (2\right )^{4} x +512 \ln \left (2\right )^{3} x^{2}-32 x^{4} \ln \left (2\right )-4 x^{5}+256 \ln \left (2\right )^{4}+256 x \ln \left (2\right )^{3}+96 x^{2} \ln \left (2\right )^{2}+16 x^{3} \ln \left (2\right )+x^{4}-1}\) | \(157\) |
| risch | \(\frac {3}{256 \left (\ln \left (2\right )^{4} x^{4}-x^{5} \ln \left (2\right )^{3}+\frac {3 x^{6} \ln \left (2\right )^{2}}{8}-\frac {\ln \left (2\right ) x^{7}}{16}+\frac {x^{8}}{256}+4 \ln \left (2\right )^{4} x^{3}-2 \ln \left (2\right )^{3} x^{4}+\frac {x^{6} \ln \left (2\right )}{8}-\frac {x^{7}}{64}+6 x^{2} \ln \left (2\right )^{4}-\frac {3 x^{4} \ln \left (2\right )^{2}}{4}+\frac {3 x^{6}}{128}+4 \ln \left (2\right )^{4} x +2 \ln \left (2\right )^{3} x^{2}-\frac {x^{4} \ln \left (2\right )}{8}-\frac {x^{5}}{64}+\ln \left (2\right )^{4}+x \ln \left (2\right )^{3}+\frac {3 x^{2} \ln \left (2\right )^{2}}{8}+\frac {x^{3} \ln \left (2\right )}{16}+\frac {x^{4}}{256}-\frac {1}{256}\right )}\) | \(157\) |
| parallelrisch | \(\frac {3}{256 \ln \left (2\right )^{4} x^{4}-256 x^{5} \ln \left (2\right )^{3}+96 x^{6} \ln \left (2\right )^{2}-16 \ln \left (2\right ) x^{7}+x^{8}+1024 \ln \left (2\right )^{4} x^{3}-512 \ln \left (2\right )^{3} x^{4}+32 x^{6} \ln \left (2\right )-4 x^{7}+1536 x^{2} \ln \left (2\right )^{4}-192 x^{4} \ln \left (2\right )^{2}+6 x^{6}+1024 \ln \left (2\right )^{4} x +512 \ln \left (2\right )^{3} x^{2}-32 x^{4} \ln \left (2\right )-4 x^{5}+256 \ln \left (2\right )^{4}+256 x \ln \left (2\right )^{3}+96 x^{2} \ln \left (2\right )^{2}+16 x^{3} \ln \left (2\right )+x^{4}-1}\) | \(157\) |
Input:
int(((-3072*x^3-9216*x^2-9216*x-3072)*ln(2)^4+(3840*x^4+6144*x^3-3072*x-76 8)*ln(2)^3+(-1728*x^5+2304*x^3-576*x)*ln(2)^2+(336*x^6-576*x^5+384*x^3-144 *x^2)*ln(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524288*x^7+18 35008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+65536)* ln(2)^8+(-131072*x^9-786432*x^8-1835008*x^7-1835008*x^6+1835008*x^4+183500 8*x^3+786432*x^2+131072*x)*ln(2)^7+(114688*x^10+458752*x^9+458752*x^8-4587 52*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*ln(2)^6+(- 57344*x^11-114688*x^10+114688*x^9+344064*x^8-344064*x^6-114688*x^5+114688* x^4+57344*x^3)*ln(2)^5+(17920*x^12-71680*x^10+107520*x^8-71680*x^6+17408*x ^4-2048*x^3-3072*x^2-2048*x-512)*ln(2)^4+(-3584*x^13+7168*x^12+7168*x^11-2 1504*x^10+21504*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-1024*x^2-512*x)*ln (2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+1792*x^9+1792*x^8- 1792*x^7+256*x^6+384*x^4-192*x^2)*ln(2)^2+(-32*x^15+192*x^14-448*x^13+448* x^12-448*x^10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3)*ln(2)+x^16-8*x^ 15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x^7-12*x^6+8*x^5-2* x^4+1),x,method=_RETURNVERBOSE)
Output:
3/(256*ln(2)^4*x^4-256*x^5*ln(2)^3+96*x^6*ln(2)^2-16*ln(2)*x^7+x^8+1024*ln (2)^4*x^3-512*ln(2)^3*x^4+32*x^6*ln(2)-4*x^7+1536*x^2*ln(2)^4-192*x^4*ln(2 )^2+6*x^6+1024*ln(2)^4*x+512*ln(2)^3*x^2-32*x^4*ln(2)-4*x^5+256*ln(2)^4+25 6*x*ln(2)^3+96*x^2*ln(2)^2+16*x^3*ln(2)+x^4-1)
Leaf count of result is larger than twice the leaf count of optimal. 115 vs. \(2 (22) = 44\).
Time = 0.12 (sec) , antiderivative size = 115, normalized size of antiderivative = 5.23 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\frac {3}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + 256 \, {\left (x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x + 1\right )} \log \left (2\right )^{4} + x^{4} - 256 \, {\left (x^{5} + 2 \, x^{4} - 2 \, x^{2} - x\right )} \log \left (2\right )^{3} + 96 \, {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} \log \left (2\right )^{2} - 16 \, {\left (x^{7} - 2 \, x^{6} + 2 \, x^{4} - x^{3}\right )} \log \left (2\right ) - 1} \] Input:
integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-30 72*x-768)*log(2)^3+(-1728*x^5+2304*x^3-576*x)*log(2)^2+(336*x^6-576*x^5+38 4*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524 288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288 *x+65536)*log(2)^8+(-131072*x^9-786432*x^8-1835008*x^7-1835008*x^6+1835008 *x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9+458 752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2 )*log(2)^6+(-57344*x^11-114688*x^10+114688*x^9+344064*x^8-344064*x^6-11468 8*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x^8-716 80*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x ^12+7168*x^11-21504*x^10+21504*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-102 4*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+17 92*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x ^14-448*x^13+448*x^12-448*x^10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3 )*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x ^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="fricas")
Output:
3/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + 256*(x^4 + 4*x^3 + 6*x^2 + 4*x + 1)*log(2 )^4 + x^4 - 256*(x^5 + 2*x^4 - 2*x^2 - x)*log(2)^3 + 96*(x^6 - 2*x^4 + x^2 )*log(2)^2 - 16*(x^7 - 2*x^6 + 2*x^4 - x^3)*log(2) - 1)
Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (17) = 34\).
Time = 11.74 (sec) , antiderivative size = 139, normalized size of antiderivative = 6.32 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\frac {3}{x^{8} + x^{7} \left (- 16 \log {\left (2 \right )} - 4\right ) + x^{6} \cdot \left (6 + 32 \log {\left (2 \right )} + 96 \log {\left (2 \right )}^{2}\right ) + x^{5} \left (- 256 \log {\left (2 \right )}^{3} - 4\right ) + x^{4} \left (- 512 \log {\left (2 \right )}^{3} - 192 \log {\left (2 \right )}^{2} - 32 \log {\left (2 \right )} + 1 + 256 \log {\left (2 \right )}^{4}\right ) + x^{3} \cdot \left (16 \log {\left (2 \right )} + 1024 \log {\left (2 \right )}^{4}\right ) + x^{2} \cdot \left (96 \log {\left (2 \right )}^{2} + 512 \log {\left (2 \right )}^{3} + 1536 \log {\left (2 \right )}^{4}\right ) + x \left (256 \log {\left (2 \right )}^{3} + 1024 \log {\left (2 \right )}^{4}\right ) - 1 + 256 \log {\left (2 \right )}^{4}} \] Input:
integrate(((-3072*x**3-9216*x**2-9216*x-3072)*ln(2)**4+(3840*x**4+6144*x** 3-3072*x-768)*ln(2)**3+(-1728*x**5+2304*x**3-576*x)*ln(2)**2+(336*x**6-576 *x**5+384*x**3-144*x**2)*ln(2)-24*x**7+84*x**6-108*x**5+60*x**4-12*x**3)/( (65536*x**8+524288*x**7+1835008*x**6+3670016*x**5+4587520*x**4+3670016*x** 3+1835008*x**2+524288*x+65536)*ln(2)**8+(-131072*x**9-786432*x**8-1835008* x**7-1835008*x**6+1835008*x**4+1835008*x**3+786432*x**2+131072*x)*ln(2)**7 +(114688*x**10+458752*x**9+458752*x**8-458752*x**7-1146880*x**6-458752*x** 5+458752*x**4+458752*x**3+114688*x**2)*ln(2)**6+(-57344*x**11-114688*x**10 +114688*x**9+344064*x**8-344064*x**6-114688*x**5+114688*x**4+57344*x**3)*l n(2)**5+(17920*x**12-71680*x**10+107520*x**8-71680*x**6+17408*x**4-2048*x* *3-3072*x**2-2048*x-512)*ln(2)**4+(-3584*x**13+7168*x**12+7168*x**11-21504 *x**10+21504*x**8-7168*x**7-7168*x**6+4096*x**5+1024*x**4-1024*x**2-512*x) *ln(2)**3+(448*x**14-1792*x**13+1792*x**12+1792*x**11-4480*x**10+1792*x**9 +1792*x**8-1792*x**7+256*x**6+384*x**4-192*x**2)*ln(2)**2+(-32*x**15+192*x **14-448*x**13+448*x**12-448*x**10+448*x**9-192*x**8+64*x**7-64*x**6+64*x* *4-32*x**3)*ln(2)+x**16-8*x**15+28*x**14-56*x**13+70*x**12-56*x**11+28*x** 10-8*x**9-x**8+8*x**7-12*x**6+8*x**5-2*x**4+1),x)
Output:
3/(x**8 + x**7*(-16*log(2) - 4) + x**6*(6 + 32*log(2) + 96*log(2)**2) + x* *5*(-256*log(2)**3 - 4) + x**4*(-512*log(2)**3 - 192*log(2)**2 - 32*log(2) + 1 + 256*log(2)**4) + x**3*(16*log(2) + 1024*log(2)**4) + x**2*(96*log(2 )**2 + 512*log(2)**3 + 1536*log(2)**4) + x*(256*log(2)**3 + 1024*log(2)**4 ) - 1 + 256*log(2)**4)
Leaf count of result is larger than twice the leaf count of optimal. 136 vs. \(2 (22) = 44\).
Time = 0.05 (sec) , antiderivative size = 136, normalized size of antiderivative = 6.18 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\frac {3}{x^{8} - 4 \, x^{7} {\left (4 \, \log \left (2\right ) + 1\right )} + 2 \, {\left (48 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 3\right )} x^{6} - 4 \, {\left (64 \, \log \left (2\right )^{3} + 1\right )} x^{5} + {\left (256 \, \log \left (2\right )^{4} - 512 \, \log \left (2\right )^{3} - 192 \, \log \left (2\right )^{2} - 32 \, \log \left (2\right ) + 1\right )} x^{4} + 16 \, {\left (64 \, \log \left (2\right )^{4} + \log \left (2\right )\right )} x^{3} + 256 \, \log \left (2\right )^{4} + 32 \, {\left (48 \, \log \left (2\right )^{4} + 16 \, \log \left (2\right )^{3} + 3 \, \log \left (2\right )^{2}\right )} x^{2} + 256 \, {\left (4 \, \log \left (2\right )^{4} + \log \left (2\right )^{3}\right )} x - 1} \] Input:
integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-30 72*x-768)*log(2)^3+(-1728*x^5+2304*x^3-576*x)*log(2)^2+(336*x^6-576*x^5+38 4*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524 288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288 *x+65536)*log(2)^8+(-131072*x^9-786432*x^8-1835008*x^7-1835008*x^6+1835008 *x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9+458 752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2 )*log(2)^6+(-57344*x^11-114688*x^10+114688*x^9+344064*x^8-344064*x^6-11468 8*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x^8-716 80*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x ^12+7168*x^11-21504*x^10+21504*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-102 4*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+17 92*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x ^14-448*x^13+448*x^12-448*x^10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3 )*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x ^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="maxima")
Output:
3/(x^8 - 4*x^7*(4*log(2) + 1) + 2*(48*log(2)^2 + 16*log(2) + 3)*x^6 - 4*(6 4*log(2)^3 + 1)*x^5 + (256*log(2)^4 - 512*log(2)^3 - 192*log(2)^2 - 32*log (2) + 1)*x^4 + 16*(64*log(2)^4 + log(2))*x^3 + 256*log(2)^4 + 32*(48*log(2 )^4 + 16*log(2)^3 + 3*log(2)^2)*x^2 + 256*(4*log(2)^4 + log(2)^3)*x - 1)
Leaf count of result is larger than twice the leaf count of optimal. 120 vs. \(2 (22) = 44\).
Time = 0.29 (sec) , antiderivative size = 120, normalized size of antiderivative = 5.45 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\frac {3}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + 256 \, {\left (x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x\right )} \log \left (2\right )^{4} + x^{4} - 256 \, {\left (x^{5} + 2 \, x^{4} - 2 \, x^{2} - x\right )} \log \left (2\right )^{3} + 256 \, \log \left (2\right )^{4} + 96 \, {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} \log \left (2\right )^{2} - 16 \, {\left (x^{7} - 2 \, x^{6} + 2 \, x^{4} - x^{3}\right )} \log \left (2\right ) - 1} \] Input:
integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-30 72*x-768)*log(2)^3+(-1728*x^5+2304*x^3-576*x)*log(2)^2+(336*x^6-576*x^5+38 4*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524 288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288 *x+65536)*log(2)^8+(-131072*x^9-786432*x^8-1835008*x^7-1835008*x^6+1835008 *x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9+458 752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2 )*log(2)^6+(-57344*x^11-114688*x^10+114688*x^9+344064*x^8-344064*x^6-11468 8*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x^8-716 80*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x ^12+7168*x^11-21504*x^10+21504*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-102 4*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+17 92*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x ^14-448*x^13+448*x^12-448*x^10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3 )*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x ^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="giac")
Output:
3/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + 256*(x^4 + 4*x^3 + 6*x^2 + 4*x)*log(2)^4 + x^4 - 256*(x^5 + 2*x^4 - 2*x^2 - x)*log(2)^3 + 256*log(2)^4 + 96*(x^6 - 2*x^4 + x^2)*log(2)^2 - 16*(x^7 - 2*x^6 + 2*x^4 - x^3)*log(2) - 1)
Timed out. \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\text {Hanged} \] Input:
int(-(log(2)*(144*x^2 - 384*x^3 + 576*x^5 - 336*x^6) + log(2)^2*(576*x - 2 304*x^3 + 1728*x^5) + log(2)^3*(3072*x - 6144*x^3 - 3840*x^4 + 768) + log( 2)^4*(9216*x + 9216*x^2 + 3072*x^3 + 3072) + 12*x^3 - 60*x^4 + 108*x^5 - 8 4*x^6 + 24*x^7)/(log(2)^5*(57344*x^3 + 114688*x^4 - 114688*x^5 - 344064*x^ 6 + 344064*x^8 + 114688*x^9 - 114688*x^10 - 57344*x^11) + log(2)^6*(114688 *x^2 + 458752*x^3 + 458752*x^4 - 458752*x^5 - 1146880*x^6 - 458752*x^7 + 4 58752*x^8 + 458752*x^9 + 114688*x^10) - log(2)*(32*x^3 - 64*x^4 + 64*x^6 - 64*x^7 + 192*x^8 - 448*x^9 + 448*x^10 - 448*x^12 + 448*x^13 - 192*x^14 + 32*x^15) - log(2)^3*(512*x + 1024*x^2 - 1024*x^4 - 4096*x^5 + 7168*x^6 + 7 168*x^7 - 21504*x^8 + 21504*x^10 - 7168*x^11 - 7168*x^12 + 3584*x^13) - 2* x^4 + 8*x^5 - 12*x^6 + 8*x^7 - x^8 - 8*x^9 + 28*x^10 - 56*x^11 + 70*x^12 - 56*x^13 + 28*x^14 - 8*x^15 + x^16 - log(2)^4*(2048*x + 3072*x^2 + 2048*x^ 3 - 17408*x^4 + 71680*x^6 - 107520*x^8 + 71680*x^10 - 17920*x^12 + 512) + log(2)^7*(131072*x + 786432*x^2 + 1835008*x^3 + 1835008*x^4 - 1835008*x^6 - 1835008*x^7 - 786432*x^8 - 131072*x^9) + log(2)^8*(524288*x + 1835008*x^ 2 + 3670016*x^3 + 4587520*x^4 + 3670016*x^5 + 1835008*x^6 + 524288*x^7 + 6 5536*x^8 + 65536) + log(2)^2*(384*x^4 - 192*x^2 + 256*x^6 - 1792*x^7 + 179 2*x^8 + 1792*x^9 - 4480*x^10 + 1792*x^11 + 1792*x^12 - 1792*x^13 + 448*x^1 4) + 1),x)
Output:
\text{Hanged}
Time = 0.18 (sec) , antiderivative size = 156, normalized size of antiderivative = 7.09 \[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx=\frac {3}{256 \mathrm {log}\left (2\right )^{4} x^{4}+1024 \mathrm {log}\left (2\right )^{4} x^{3}+1536 \mathrm {log}\left (2\right )^{4} x^{2}+1024 \mathrm {log}\left (2\right )^{4} x +256 \mathrm {log}\left (2\right )^{4}-256 \mathrm {log}\left (2\right )^{3} x^{5}-512 \mathrm {log}\left (2\right )^{3} x^{4}+512 \mathrm {log}\left (2\right )^{3} x^{2}+256 \mathrm {log}\left (2\right )^{3} x +96 \mathrm {log}\left (2\right )^{2} x^{6}-192 \mathrm {log}\left (2\right )^{2} x^{4}+96 \mathrm {log}\left (2\right )^{2} x^{2}-16 \,\mathrm {log}\left (2\right ) x^{7}+32 \,\mathrm {log}\left (2\right ) x^{6}-32 \,\mathrm {log}\left (2\right ) x^{4}+16 \,\mathrm {log}\left (2\right ) x^{3}+x^{8}-4 x^{7}+6 x^{6}-4 x^{5}+x^{4}-1} \] Input:
int(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-3072*x-7 68)*log(2)^3+(-1728*x^5+2304*x^3-576*x)*log(2)^2+(336*x^6-576*x^5+384*x^3- 144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524288*x^ 7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+655 36)*log(2)^8+(-131072*x^9-786432*x^8-1835008*x^7-1835008*x^6+1835008*x^4+1 835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9+458752*x^ 8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*log( 2)^6+(-57344*x^11-114688*x^10+114688*x^9+344064*x^8-344064*x^6-114688*x^5+ 114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x^8-71680*x^6 +17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x^12+71 68*x^11-21504*x^10+21504*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-1024*x^2- 512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+1792*x^9 +1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x^14-44 8*x^13+448*x^12-448*x^10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3)*log( 2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x^7-12* x^6+8*x^5-2*x^4+1),x)
Output:
3/(256*log(2)**4*x**4 + 1024*log(2)**4*x**3 + 1536*log(2)**4*x**2 + 1024*l og(2)**4*x + 256*log(2)**4 - 256*log(2)**3*x**5 - 512*log(2)**3*x**4 + 512 *log(2)**3*x**2 + 256*log(2)**3*x + 96*log(2)**2*x**6 - 192*log(2)**2*x**4 + 96*log(2)**2*x**2 - 16*log(2)*x**7 + 32*log(2)*x**6 - 32*log(2)*x**4 + 16*log(2)*x**3 + x**8 - 4*x**7 + 6*x**6 - 4*x**5 + x**4 - 1)