Integrand size = 312, antiderivative size = 21 \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{(-4+(-8+x) (-x+\log (2)))^2+\log (x)} \end {dmath*}
Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(21)=42\).
Time = 5.48 (sec) , antiderivative size = 113, normalized size of antiderivative = 5.38 \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=-\frac {5 \left (-1-4 x^4+6 x^3 (8+\log (2))-2 x^2 \left (72+32 \log (2)+\log ^2(2)\right )+8 x \left (8+17 \log (2)+2 \log ^2(2)\right )\right )}{\left (1+4 x^4-6 x^3 (8+\log (2))-2 x (8+\log (2)) (4+\log (256))+2 x^2 \left (72+\log ^2(2)+2 \log (65536)\right )\right ) \left (\left (4+x^2-x (8+\log (2))+\log (256)\right )^2+\log (x)\right )} \end {dmath*}
Integrate[(-5 + 320*x - 720*x^2 + 240*x^3 - 20*x^4 + (680*x - 320*x^2 + 30 *x^3)*Log[2] + (80*x - 10*x^2)*Log[2]^2)/(256*x - 2048*x^2 + 6400*x^3 - 97 28*x^4 + 7264*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + (2048*x - 12544*x^ 2 + 27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8)*Log[2] + (6144*x - 26112*x^2 + 33888*x^3 - 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7 )*Log[2]^2 + (8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6)* Log[2]^3 + (4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)*Log[2]^4 + (32*x - 128*x^2 + 144*x^3 - 32*x^4 + 2*x^5 + (128*x - 272*x^2 + 64*x^3 - 4*x^4)*L og[2] + (128*x - 32*x^2 + 2*x^3)*Log[2]^2)*Log[x] + x*Log[x]^2),x]
(-5*(-1 - 4*x^4 + 6*x^3*(8 + Log[2]) - 2*x^2*(72 + 32*Log[2] + Log[2]^2) + 8*x*(8 + 17*Log[2] + 2*Log[2]^2)))/((1 + 4*x^4 - 6*x^3*(8 + Log[2]) - 2*x *(8 + Log[2])*(4 + Log[256]) + 2*x^2*(72 + Log[2]^2 + 2*Log[65536]))*((4 + x^2 - x*(8 + Log[2]) + Log[256])^2 + Log[x]))
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.
| \(\displaystyle \int \frac {-20 x^4+240 x^3-720 x^2+\left (80 x-10 x^2\right ) \log ^2(2)+\left (30 x^3-320 x^2+680 x\right ) \log (2)+320 x-5}{x^9-32 x^8+400 x^7-2432 x^6+7264 x^5-9728 x^4+6400 x^3-2048 x^2+\left (x^5-32 x^4+384 x^3-2048 x^2+4096 x\right ) \log ^4(2)+\left (2 x^5-32 x^4+144 x^3-128 x^2+\left (2 x^3-32 x^2+128 x\right ) \log ^2(2)+\left (-4 x^4+64 x^3-272 x^2+128 x\right ) \log (2)+32 x\right ) \log (x)+\left (-4 x^6+128 x^5-1552 x^4+8576 x^3-19456 x^2+8192 x\right ) \log ^3(2)+\left (6 x^7-192 x^6+2352 x^5-13440 x^4+33888 x^3-26112 x^2+6144 x\right ) \log ^2(2)+\left (-4 x^8+128 x^7-1584 x^6+9344 x^5-25792 x^4+27648 x^3-12544 x^2+2048 x\right ) \log (2)+256 x+x \log ^2(x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {5 \left (-4 x^4+6 x^3 (8+\log (2))-2 x^2 \left (72+\log ^2(2)+32 \log (2)\right )+8 x (8+\log (2)) (1+2 \log (2))-1\right )}{x \left (\left (x^2-x (8+\log (2))+4+\log (256)\right )^2+\log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 5 \int -\frac {4 x^4-6 (8+\log (2)) x^3+2 \left (72+32 \log (2)+\log ^2(2)\right ) x^2-8 (8+\log (2)) (1+\log (4)) x+1}{x \left (\left (x^2-(8+\log (2)) x+\log (256)+4\right )^2+\log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -5 \int \frac {4 x^4-6 (8+\log (2)) x^3+2 \left (72+32 \log (2)+\log ^2(2)\right ) x^2-8 (8+\log (2)) (1+\log (4)) x+1}{x \left (\left (x^2-(8+\log (2)) x+\log (256)+4\right )^2+\log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {4 x^3}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}+\frac {6 (-8-\log (2)) x^2}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}+\frac {2 \left (72+32 \log (2)+\log ^2(2)\right ) x}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}+\frac {8 (8+\log (2)) (-1-\log (4))}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}+\frac {1}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2 x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -5 \left (2 \left (72+\log ^2(2)+32 \log (2)\right ) \int \frac {x}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}dx-8 (8+\log (2)) (1+\log (4)) \int \frac {1}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}dx+\int \frac {1}{x \left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}dx-6 (8+\log (2)) \int \frac {x^2}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}dx+4 \int \frac {x^3}{\left (x^4-16 \left (1+\frac {\log (2)}{8}\right ) x^3+72 \left (1+\frac {1}{72} \log (2) (32+\log (2))\right ) x^2-64 \left (1+\frac {1}{8} \log (2) \left (1+\frac {(8+\log (2)) \log (256)}{\log (16)}\right )\right ) x+\log (x)+16 (1+(1+\log (2)) \log (16))\right )^2}dx\right )\) |
Int[(-5 + 320*x - 720*x^2 + 240*x^3 - 20*x^4 + (680*x - 320*x^2 + 30*x^3)* Log[2] + (80*x - 10*x^2)*Log[2]^2)/(256*x - 2048*x^2 + 6400*x^3 - 9728*x^4 + 7264*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + (2048*x - 12544*x^2 + 27 648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8)*Log[2] + (614 4*x - 26112*x^2 + 33888*x^3 - 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7)*Log[ 2]^2 + (8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6)*Log[2] ^3 + (4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)*Log[2]^4 + (32*x - 128*x ^2 + 144*x^3 - 32*x^4 + 2*x^5 + (128*x - 272*x^2 + 64*x^3 - 4*x^4)*Log[2] + (128*x - 32*x^2 + 2*x^3)*Log[2]^2)*Log[x] + x*Log[x]^2),x]
3.5.8.3.1 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[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. \(68\) vs. \(2(21)=42\).
Time = 3.84 (sec) , antiderivative size = 69, normalized size of antiderivative = 3.29
| method | result | size |
| default | \(\frac {5}{x^{2} \ln \left (2\right )^{2}-2 x^{3} \ln \left (2\right )+x^{4}-16 x \ln \left (2\right )^{2}+32 x^{2} \ln \left (2\right )-16 x^{3}+64 \ln \left (2\right )^{2}-136 x \ln \left (2\right )+72 x^{2}+\ln \left (x \right )+64 \ln \left (2\right )-64 x +16}\) | \(69\) |
| risch | \(\frac {5}{x^{2} \ln \left (2\right )^{2}-2 x^{3} \ln \left (2\right )+x^{4}-16 x \ln \left (2\right )^{2}+32 x^{2} \ln \left (2\right )-16 x^{3}+64 \ln \left (2\right )^{2}-136 x \ln \left (2\right )+72 x^{2}+\ln \left (x \right )+64 \ln \left (2\right )-64 x +16}\) | \(69\) |
| parallelrisch | \(\frac {5}{x^{2} \ln \left (2\right )^{2}-2 x^{3} \ln \left (2\right )+x^{4}-16 x \ln \left (2\right )^{2}+32 x^{2} \ln \left (2\right )-16 x^{3}+64 \ln \left (2\right )^{2}-136 x \ln \left (2\right )+72 x^{2}+\ln \left (x \right )+64 \ln \left (2\right )-64 x +16}\) | \(69\) |
int(((-10*x^2+80*x)*ln(2)^2+(30*x^3-320*x^2+680*x)*ln(2)-20*x^4+240*x^3-72 0*x^2+320*x-5)/(x*ln(x)^2+((2*x^3-32*x^2+128*x)*ln(2)^2+(-4*x^4+64*x^3-272 *x^2+128*x)*ln(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*ln(x)+(x^5-32*x^4+384 *x^3-2048*x^2+4096*x)*ln(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x^3-19456*x^2+ 8192*x)*ln(2)^3+(6*x^7-192*x^6+2352*x^5-13440*x^4+33888*x^3-26112*x^2+6144 *x)*ln(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4+27648*x^3-12544*x^ 2+2048*x)*ln(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728*x^4+6400*x^3-204 8*x^2+256*x),x,method=_RETURNVERBOSE)
5/(x^2*ln(2)^2-2*x^3*ln(2)+x^4-16*x*ln(2)^2+32*x^2*ln(2)-16*x^3+64*ln(2)^2 -136*x*ln(2)+72*x^2+ln(x)+64*ln(2)-64*x+16)
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (21) = 42\).
Time = 0.27 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.57 \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 16 \, x^{3} + {\left (x^{2} - 16 \, x + 64\right )} \log \left (2\right )^{2} + 72 \, x^{2} - 2 \, {\left (x^{3} - 16 \, x^{2} + 68 \, x - 32\right )} \log \left (2\right ) - 64 \, x + \log \left (x\right ) + 16} \end {dmath*}
integrate(((-10*x^2+80*x)*log(2)^2+(30*x^3-320*x^2+680*x)*log(2)-20*x^4+24 0*x^3-720*x^2+320*x-5)/(x*log(x)^2+((2*x^3-32*x^2+128*x)*log(2)^2+(-4*x^4+ 64*x^3-272*x^2+128*x)*log(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*log(x)+(x^ 5-32*x^4+384*x^3-2048*x^2+4096*x)*log(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x ^3-19456*x^2+8192*x)*log(2)^3+(6*x^7-192*x^6+2352*x^5-13440*x^4+33888*x^3- 26112*x^2+6144*x)*log(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4+276 48*x^3-12544*x^2+2048*x)*log(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728* x^4+6400*x^3-2048*x^2+256*x),x, algorithm=\
5/(x^4 - 16*x^3 + (x^2 - 16*x + 64)*log(2)^2 + 72*x^2 - 2*(x^3 - 16*x^2 + 68*x - 32)*log(2) - 64*x + log(x) + 16)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (15) = 30\).
Time = 0.15 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.57 \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 16 x^{3} - 2 x^{3} \log {\left (2 \right )} + x^{2} \log {\left (2 \right )}^{2} + 32 x^{2} \log {\left (2 \right )} + 72 x^{2} - 136 x \log {\left (2 \right )} - 64 x - 16 x \log {\left (2 \right )}^{2} + \log {\left (x \right )} + 16 + 64 \log {\left (2 \right )}^{2} + 64 \log {\left (2 \right )}} \end {dmath*}
integrate(((-10*x**2+80*x)*ln(2)**2+(30*x**3-320*x**2+680*x)*ln(2)-20*x**4 +240*x**3-720*x**2+320*x-5)/(x*ln(x)**2+((2*x**3-32*x**2+128*x)*ln(2)**2+( -4*x**4+64*x**3-272*x**2+128*x)*ln(2)+2*x**5-32*x**4+144*x**3-128*x**2+32* x)*ln(x)+(x**5-32*x**4+384*x**3-2048*x**2+4096*x)*ln(2)**4+(-4*x**6+128*x* *5-1552*x**4+8576*x**3-19456*x**2+8192*x)*ln(2)**3+(6*x**7-192*x**6+2352*x **5-13440*x**4+33888*x**3-26112*x**2+6144*x)*ln(2)**2+(-4*x**8+128*x**7-15 84*x**6+9344*x**5-25792*x**4+27648*x**3-12544*x**2+2048*x)*ln(2)+x**9-32*x **8+400*x**7-2432*x**6+7264*x**5-9728*x**4+6400*x**3-2048*x**2+256*x),x)
5/(x**4 - 16*x**3 - 2*x**3*log(2) + x**2*log(2)**2 + 32*x**2*log(2) + 72*x **2 - 136*x*log(2) - 64*x - 16*x*log(2)**2 + log(x) + 16 + 64*log(2)**2 + 64*log(2))
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (21) = 42\).
Time = 0.33 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.81 \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 2 \, x^{3} {\left (\log \left (2\right ) + 8\right )} + {\left (\log \left (2\right )^{2} + 32 \, \log \left (2\right ) + 72\right )} x^{2} - 8 \, {\left (2 \, \log \left (2\right )^{2} + 17 \, \log \left (2\right ) + 8\right )} x + 64 \, \log \left (2\right )^{2} + 64 \, \log \left (2\right ) + \log \left (x\right ) + 16} \end {dmath*}
integrate(((-10*x^2+80*x)*log(2)^2+(30*x^3-320*x^2+680*x)*log(2)-20*x^4+24 0*x^3-720*x^2+320*x-5)/(x*log(x)^2+((2*x^3-32*x^2+128*x)*log(2)^2+(-4*x^4+ 64*x^3-272*x^2+128*x)*log(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*log(x)+(x^ 5-32*x^4+384*x^3-2048*x^2+4096*x)*log(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x ^3-19456*x^2+8192*x)*log(2)^3+(6*x^7-192*x^6+2352*x^5-13440*x^4+33888*x^3- 26112*x^2+6144*x)*log(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4+276 48*x^3-12544*x^2+2048*x)*log(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728* x^4+6400*x^3-2048*x^2+256*x),x, algorithm=\
5/(x^4 - 2*x^3*(log(2) + 8) + (log(2)^2 + 32*log(2) + 72)*x^2 - 8*(2*log(2 )^2 + 17*log(2) + 8)*x + 64*log(2)^2 + 64*log(2) + log(x) + 16)
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (21) = 42\).
Time = 0.30 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.24 \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\frac {5}{x^{4} - 2 \, x^{3} \log \left (2\right ) + x^{2} \log \left (2\right )^{2} - 16 \, x^{3} + 32 \, x^{2} \log \left (2\right ) - 16 \, x \log \left (2\right )^{2} + 72 \, x^{2} - 136 \, x \log \left (2\right ) + 64 \, \log \left (2\right )^{2} - 64 \, x + 64 \, \log \left (2\right ) + \log \left (x\right ) + 16} \end {dmath*}
integrate(((-10*x^2+80*x)*log(2)^2+(30*x^3-320*x^2+680*x)*log(2)-20*x^4+24 0*x^3-720*x^2+320*x-5)/(x*log(x)^2+((2*x^3-32*x^2+128*x)*log(2)^2+(-4*x^4+ 64*x^3-272*x^2+128*x)*log(2)+2*x^5-32*x^4+144*x^3-128*x^2+32*x)*log(x)+(x^ 5-32*x^4+384*x^3-2048*x^2+4096*x)*log(2)^4+(-4*x^6+128*x^5-1552*x^4+8576*x ^3-19456*x^2+8192*x)*log(2)^3+(6*x^7-192*x^6+2352*x^5-13440*x^4+33888*x^3- 26112*x^2+6144*x)*log(2)^2+(-4*x^8+128*x^7-1584*x^6+9344*x^5-25792*x^4+276 48*x^3-12544*x^2+2048*x)*log(2)+x^9-32*x^8+400*x^7-2432*x^6+7264*x^5-9728* x^4+6400*x^3-2048*x^2+256*x),x, algorithm=\
5/(x^4 - 2*x^3*log(2) + x^2*log(2)^2 - 16*x^3 + 32*x^2*log(2) - 16*x*log(2 )^2 + 72*x^2 - 136*x*log(2) + 64*log(2)^2 - 64*x + 64*log(2) + log(x) + 16 )
Timed out. \begin {dmath*} \int \frac {-5+320 x-720 x^2+240 x^3-20 x^4+\left (680 x-320 x^2+30 x^3\right ) \log (2)+\left (80 x-10 x^2\right ) \log ^2(2)}{256 x-2048 x^2+6400 x^3-9728 x^4+7264 x^5-2432 x^6+400 x^7-32 x^8+x^9+\left (2048 x-12544 x^2+27648 x^3-25792 x^4+9344 x^5-1584 x^6+128 x^7-4 x^8\right ) \log (2)+\left (6144 x-26112 x^2+33888 x^3-13440 x^4+2352 x^5-192 x^6+6 x^7\right ) \log ^2(2)+\left (8192 x-19456 x^2+8576 x^3-1552 x^4+128 x^5-4 x^6\right ) \log ^3(2)+\left (4096 x-2048 x^2+384 x^3-32 x^4+x^5\right ) \log ^4(2)+\left (32 x-128 x^2+144 x^3-32 x^4+2 x^5+\left (128 x-272 x^2+64 x^3-4 x^4\right ) \log (2)+\left (128 x-32 x^2+2 x^3\right ) \log ^2(2)\right ) \log (x)+x \log ^2(x)} \, dx=\int \frac {320\,x+\ln \left (2\right )\,\left (30\,x^3-320\,x^2+680\,x\right )+{\ln \left (2\right )}^2\,\left (80\,x-10\,x^2\right )-720\,x^2+240\,x^3-20\,x^4-5}{256\,x+x\,{\ln \left (x\right )}^2+{\ln \left (2\right )}^3\,\left (-4\,x^6+128\,x^5-1552\,x^4+8576\,x^3-19456\,x^2+8192\,x\right )+\ln \left (2\right )\,\left (-4\,x^8+128\,x^7-1584\,x^6+9344\,x^5-25792\,x^4+27648\,x^3-12544\,x^2+2048\,x\right )+{\ln \left (2\right )}^2\,\left (6\,x^7-192\,x^6+2352\,x^5-13440\,x^4+33888\,x^3-26112\,x^2+6144\,x\right )+\ln \left (x\right )\,\left (32\,x+\ln \left (2\right )\,\left (-4\,x^4+64\,x^3-272\,x^2+128\,x\right )+{\ln \left (2\right )}^2\,\left (2\,x^3-32\,x^2+128\,x\right )-128\,x^2+144\,x^3-32\,x^4+2\,x^5\right )-2048\,x^2+6400\,x^3-9728\,x^4+7264\,x^5-2432\,x^6+400\,x^7-32\,x^8+x^9+{\ln \left (2\right )}^4\,\left (x^5-32\,x^4+384\,x^3-2048\,x^2+4096\,x\right )} \,d x \end {dmath*}
int((320*x + log(2)*(680*x - 320*x^2 + 30*x^3) + log(2)^2*(80*x - 10*x^2) - 720*x^2 + 240*x^3 - 20*x^4 - 5)/(256*x + x*log(x)^2 + log(2)^3*(8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6) + log(2)*(2048*x - 125 44*x^2 + 27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8) + log(2)^2*(6144*x - 26112*x^2 + 33888*x^3 - 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7) + log(x)*(32*x + log(2)*(128*x - 272*x^2 + 64*x^3 - 4*x^4) + log( 2)^2*(128*x - 32*x^2 + 2*x^3) - 128*x^2 + 144*x^3 - 32*x^4 + 2*x^5) - 2048 *x^2 + 6400*x^3 - 9728*x^4 + 7264*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + log(2)^4*(4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)),x)
int((320*x + log(2)*(680*x - 320*x^2 + 30*x^3) + log(2)^2*(80*x - 10*x^2) - 720*x^2 + 240*x^3 - 20*x^4 - 5)/(256*x + x*log(x)^2 + log(2)^3*(8192*x - 19456*x^2 + 8576*x^3 - 1552*x^4 + 128*x^5 - 4*x^6) + log(2)*(2048*x - 125 44*x^2 + 27648*x^3 - 25792*x^4 + 9344*x^5 - 1584*x^6 + 128*x^7 - 4*x^8) + log(2)^2*(6144*x - 26112*x^2 + 33888*x^3 - 13440*x^4 + 2352*x^5 - 192*x^6 + 6*x^7) + log(x)*(32*x + log(2)*(128*x - 272*x^2 + 64*x^3 - 4*x^4) + log( 2)^2*(128*x - 32*x^2 + 2*x^3) - 128*x^2 + 144*x^3 - 32*x^4 + 2*x^5) - 2048 *x^2 + 6400*x^3 - 9728*x^4 + 7264*x^5 - 2432*x^6 + 400*x^7 - 32*x^8 + x^9 + log(2)^4*(4096*x - 2048*x^2 + 384*x^3 - 32*x^4 + x^5)), x)