Integrand size = 148, antiderivative size = 25 \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=\frac {x^2 \left (-13+x-\frac {x}{-1+x}\right )^2}{\left (x^2+\log (2)\right )^2} \]
Leaf count is larger than twice the leaf count of optimal. \(406\) vs. \(2(25)=50\).
Time = 0.28 (sec) , antiderivative size = 406, normalized size of antiderivative = 16.24 \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=-\frac {-2 x^4 \left (500+\log ^2(2) (5630-395 \log (4))+\log (2) (2422-325 \log (4))-2 \log ^5(2) (-238+\log (4))+37 \log (4)+2 \log ^4(2) (1067+\log (4))+\log ^3(2) (5750+163 \log (4))\right )+x^3 \left (24 \log ^6(2)+\log ^3(2) (18168-2210 \log (4))+\log ^5(2) (1246-20 \log (4))-65 (-24+\log (4))+9 \log ^4(2) (1340+13 \log (4))+6 \log (2) (1319+25 \log (4))-4 \log ^2(2) (-3805+341 \log (4))\right )+2 \log ^2(2) \left (2-102 \log (4)+\log ^4(2) (736+\log (4))+72 \log ^2(2) (-13+8 \log (4))-\log ^3(2) (1132+363 \log (4))+\log (2) (214+478 \log (4))\right )-x \log (2) \left (39 \log (4)+4 \log ^5(2) (46+\log (4))-7 \log (2) (10+21 \log (4))-2 \log ^4(2) (1295+36 \log (4))+15 \log ^3(2) (-94+89 \log (4))+\log ^2(2) (334+745 \log (4))\right )+2 x^2 \left (-338-7 \log ^5(2) (-128+\log (4))+\log ^6(2) (28+\log (4))-3 \log (2) (562+55 \log (4))-3 \log ^4(2) (1212+199 \log (4))+\log ^2(2) (-3028+827 \log (4))+\log ^3(2) (-4984+1003 \log (4))\right )+x^5 \left (112+88 \log ^5(2)+\log (2) (482-315 \log (4))+39 \log (4)+2 \log ^4(2) (97+6 \log (4))+\log ^3(2) (1870+183 \log (4))-125 \log ^2(2) (-14+\log (64))\right )}{4 (-1+x)^2 (1+\log (2))^5 \left (x^2+\log (2)\right )^2} \]
Integrate[(338*x^3 - 1066*x^4 + 1170*x^5 - 472*x^6 + 28*x^7 + (-338*x + 11 70*x^2 - 1394*x^3 + 652*x^4 - 96*x^5 + 4*x^6)*Log[2])/(-x^6 + 3*x^7 - 3*x^ 8 + x^9 + (-3*x^4 + 9*x^5 - 9*x^6 + 3*x^7)*Log[2] + (-3*x^2 + 9*x^3 - 9*x^ 4 + 3*x^5)*Log[2]^2 + (-1 + 3*x - 3*x^2 + x^3)*Log[2]^3),x]
-1/4*(-2*x^4*(500 + Log[2]^2*(5630 - 395*Log[4]) + Log[2]*(2422 - 325*Log[ 4]) - 2*Log[2]^5*(-238 + Log[4]) + 37*Log[4] + 2*Log[2]^4*(1067 + Log[4]) + Log[2]^3*(5750 + 163*Log[4])) + x^3*(24*Log[2]^6 + Log[2]^3*(18168 - 221 0*Log[4]) + Log[2]^5*(1246 - 20*Log[4]) - 65*(-24 + Log[4]) + 9*Log[2]^4*( 1340 + 13*Log[4]) + 6*Log[2]*(1319 + 25*Log[4]) - 4*Log[2]^2*(-3805 + 341* Log[4])) + 2*Log[2]^2*(2 - 102*Log[4] + Log[2]^4*(736 + Log[4]) + 72*Log[2 ]^2*(-13 + 8*Log[4]) - Log[2]^3*(1132 + 363*Log[4]) + Log[2]*(214 + 478*Lo g[4])) - x*Log[2]*(39*Log[4] + 4*Log[2]^5*(46 + Log[4]) - 7*Log[2]*(10 + 2 1*Log[4]) - 2*Log[2]^4*(1295 + 36*Log[4]) + 15*Log[2]^3*(-94 + 89*Log[4]) + Log[2]^2*(334 + 745*Log[4])) + 2*x^2*(-338 - 7*Log[2]^5*(-128 + Log[4]) + Log[2]^6*(28 + Log[4]) - 3*Log[2]*(562 + 55*Log[4]) - 3*Log[2]^4*(1212 + 199*Log[4]) + Log[2]^2*(-3028 + 827*Log[4]) + Log[2]^3*(-4984 + 1003*Log[ 4])) + x^5*(112 + 88*Log[2]^5 + Log[2]*(482 - 315*Log[4]) + 39*Log[4] + 2* Log[2]^4*(97 + 6*Log[4]) + Log[2]^3*(1870 + 183*Log[4]) - 125*Log[2]^2*(-1 4 + Log[64])))/((-1 + x)^2*(1 + Log[2])^5*(x^2 + Log[2])^2)
Leaf count is larger than twice the leaf count of optimal. \(285\) vs. \(2(25)=50\).
Time = 0.59 (sec) , antiderivative size = 285, normalized size of antiderivative = 11.40, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, 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.
| \(\displaystyle \int \frac {28 x^7-472 x^6+1170 x^5-1066 x^4+338 x^3+\left (4 x^6-96 x^5+652 x^4-1394 x^3+1170 x^2-338 x\right ) \log (2)}{x^9-3 x^8+3 x^7-x^6+\left (x^3-3 x^2+3 x-1\right ) \log ^3(2)+\left (3 x^7-9 x^6+9 x^5-3 x^4\right ) \log (2)+\left (3 x^5-9 x^4+9 x^3-3 x^2\right ) \log ^2(2)} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {4 \log (2) \left (x \left (169-\log ^3(2)+192 \log ^2(2)+360 \log (2)\right )+2 \log (2) (2+\log (2)) (13+14 \log (2))\right )}{(1+\log (2))^2 \left (x^2+\log (2)\right )^3}+\frac {4 \left (13+7 \log ^3(2)+21 \log ^2(2)+28 \log (2)\right )}{(1+\log (2))^3 \left (x^2+\log (2)\right )}+\frac {2 \left (-\left (x \left (169-2 \log ^4(2)+188 \log ^3(2)+576 \log ^2(2)+551 \log (2)\right )\right )-\log (2) \left (130+70 \log ^3(2)+249 \log ^2(2)+313 \log (2)\right )\right )}{(1+\log (2))^3 \left (x^2+\log (2)\right )^2}-\frac {4 (6+\log (128))}{(x-1)^2 (1+\log (2))^3}-\frac {2}{(x-1)^3 (1+\log (2))^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {\left (130+70 \log ^3(2)+249 \log ^2(2)+313 \log (2)\right ) \arctan \left (\frac {x}{\sqrt {\log (2)}}\right )}{\sqrt {\log (2)} (1+\log (2))^3}+\frac {4 \left (13+7 \log ^3(2)+21 \log ^2(2)+28 \log (2)\right ) \arctan \left (\frac {x}{\sqrt {\log (2)}}\right )}{\sqrt {\log (2)} (1+\log (2))^3}+\frac {3 (2+\log (2)) (13+14 \log (2)) \arctan \left (\frac {x}{\sqrt {\log (2)}}\right )}{\sqrt {\log (2)} (1+\log (2))^2}-\frac {\log (2) \left (-2 x (2+\log (2)) (13+14 \log (2))+169-\log ^3(2)+192 \log ^2(2)+360 \log (2)\right )}{(1+\log (2))^2 \left (x^2+\log (2)\right )^2}+\frac {-\left (x \left (130+70 \log ^3(2)+249 \log ^2(2)+313 \log (2)\right )\right )+169-2 \log ^4(2)+188 \log ^3(2)+576 \log ^2(2)+551 \log (2)}{(1+\log (2))^3 \left (x^2+\log (2)\right )}+\frac {3 x (2+\log (2)) (13+14 \log (2))}{(1+\log (2))^2 \left (x^2+\log (2)\right )}-\frac {4 (6+\log (128))}{(1-x) (1+\log (2))^3}+\frac {1}{(1-x)^2 (1+\log (2))^2}\) |
Int[(338*x^3 - 1066*x^4 + 1170*x^5 - 472*x^6 + 28*x^7 + (-338*x + 1170*x^2 - 1394*x^3 + 652*x^4 - 96*x^5 + 4*x^6)*Log[2])/(-x^6 + 3*x^7 - 3*x^8 + x^ 9 + (-3*x^4 + 9*x^5 - 9*x^6 + 3*x^7)*Log[2] + (-3*x^2 + 9*x^3 - 9*x^4 + 3* x^5)*Log[2]^2 + (-1 + 3*x - 3*x^2 + x^3)*Log[2]^3),x]
1/((1 - x)^2*(1 + Log[2])^2) + (3*ArcTan[x/Sqrt[Log[2]]]*(2 + Log[2])*(13 + 14*Log[2]))/(Sqrt[Log[2]]*(1 + Log[2])^2) + (3*x*(2 + Log[2])*(13 + 14*L og[2]))/((1 + Log[2])^2*(x^2 + Log[2])) + (4*ArcTan[x/Sqrt[Log[2]]]*(13 + 28*Log[2] + 21*Log[2]^2 + 7*Log[2]^3))/(Sqrt[Log[2]]*(1 + Log[2])^3) - (Ar cTan[x/Sqrt[Log[2]]]*(130 + 313*Log[2] + 249*Log[2]^2 + 70*Log[2]^3))/(Sqr t[Log[2]]*(1 + Log[2])^3) - (Log[2]*(169 + 360*Log[2] + 192*Log[2]^2 - Log [2]^3 - 2*x*(2 + Log[2])*(13 + 14*Log[2])))/((1 + Log[2])^2*(x^2 + Log[2]) ^2) + (169 + 551*Log[2] + 576*Log[2]^2 + 188*Log[2]^3 - 2*Log[2]^4 - x*(13 0 + 313*Log[2] + 249*Log[2]^2 + 70*Log[2]^3))/((1 + Log[2])^3*(x^2 + Log[2 ])) - (4*(6 + Log[128]))/((1 - x)*(1 + Log[2])^3)
3.25.12.3.1 Defintions of rubi rules used
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. \(69\) vs. \(2(25)=50\).
Time = 0.22 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.80
| method | result | size |
| norman | \(\frac {-28 x^{5}+2 x \ln \left (2\right )^{2}+\left (4 \ln \left (2\right )-390\right ) x^{3}+\left (-2 \ln \left (2\right )+250\right ) x^{4}+\left (-\ln \left (2\right )^{2}-2 \ln \left (2\right )+169\right ) x^{2}-\ln \left (2\right )^{2}}{\left (-1+x \right )^{2} \left (\ln \left (2\right )+x^{2}\right )^{2}}\) | \(70\) |
| risch | \(\frac {-28 x^{5}+2 x \ln \left (2\right )^{2}+\left (4 \ln \left (2\right )-390\right ) x^{3}+\left (-2 \ln \left (2\right )+250\right ) x^{4}+\left (-\ln \left (2\right )^{2}-2 \ln \left (2\right )+169\right ) x^{2}-\ln \left (2\right )^{2}}{x^{6}+2 x^{4} \ln \left (2\right )-2 x^{5}+x^{2} \ln \left (2\right )^{2}-4 x^{3} \ln \left (2\right )+x^{4}-2 x \ln \left (2\right )^{2}+2 x^{2} \ln \left (2\right )+\ln \left (2\right )^{2}}\) | \(111\) |
| gosper | \(-\frac {2 x^{4} \ln \left (2\right )+28 x^{5}+x^{2} \ln \left (2\right )^{2}-4 x^{3} \ln \left (2\right )-250 x^{4}-2 x \ln \left (2\right )^{2}+2 x^{2} \ln \left (2\right )+390 x^{3}+\ln \left (2\right )^{2}-169 x^{2}}{x^{6}+2 x^{4} \ln \left (2\right )-2 x^{5}+x^{2} \ln \left (2\right )^{2}-4 x^{3} \ln \left (2\right )+x^{4}-2 x \ln \left (2\right )^{2}+2 x^{2} \ln \left (2\right )+\ln \left (2\right )^{2}}\) | \(118\) |
| parallelrisch | \(\frac {-2 x^{4} \ln \left (2\right )-28 x^{5}-x^{2} \ln \left (2\right )^{2}+4 x^{3} \ln \left (2\right )+250 x^{4}+2 x \ln \left (2\right )^{2}-2 x^{2} \ln \left (2\right )-390 x^{3}-\ln \left (2\right )^{2}+169 x^{2}}{x^{6}+2 x^{4} \ln \left (2\right )-2 x^{5}+x^{2} \ln \left (2\right )^{2}-4 x^{3} \ln \left (2\right )+x^{4}-2 x \ln \left (2\right )^{2}+2 x^{2} \ln \left (2\right )+\ln \left (2\right )^{2}}\) | \(120\) |
| default | \(\frac {2 \left (-14 \ln \left (2\right )^{3}-42 \ln \left (2\right )^{2}-56 \ln \left (2\right )-26\right ) x^{3}+2 \left (-\ln \left (2\right )^{4}+94 \ln \left (2\right )^{3}+288 \ln \left (2\right )^{2}+\frac {551 \ln \left (2\right )}{2}+\frac {169}{2}\right ) x^{2}+2 \left (13 \ln \left (2\right )^{3}+11 \ln \left (2\right )^{2}\right ) x -\ln \left (2\right )^{5}-3 \ln \left (2\right )^{4}+24 \ln \left (2\right )^{3}+22 \ln \left (2\right )^{2}}{\left (\ln \left (2\right )+x^{2}\right )^{2} \left (1+\ln \left (2\right )\right )^{3}}-\frac {2 \left (-14 \ln \left (2\right )-12\right )}{\left (1+\ln \left (2\right )\right )^{3} \left (-1+x \right )}+\frac {1}{\left (1+\ln \left (2\right )\right )^{2} \left (-1+x \right )^{2}}\) | \(139\) |
int(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*ln(2)+28*x^7-472*x^6+1 170*x^5-1066*x^4+338*x^3)/((x^3-3*x^2+3*x-1)*ln(2)^3+(3*x^5-9*x^4+9*x^3-3* x^2)*ln(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*ln(2)+x^9-3*x^8+3*x^7-x^6),x,method =_RETURNVERBOSE)
(-28*x^5+2*x*ln(2)^2+(4*ln(2)-390)*x^3+(-2*ln(2)+250)*x^4+(-ln(2)^2-2*ln(2 )+169)*x^2-ln(2)^2)/(-1+x)^2/(ln(2)+x^2)^2
Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (25) = 50\).
Time = 0.24 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.80 \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=-\frac {28 \, x^{5} - 250 \, x^{4} + 390 \, x^{3} + {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - 169 \, x^{2} + 2 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \left (2\right )}{x^{6} - 2 \, x^{5} + x^{4} + {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} + 2 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \left (2\right )} \]
integrate(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*log(2)+28*x^7-47 2*x^6+1170*x^5-1066*x^4+338*x^3)/((x^3-3*x^2+3*x-1)*log(2)^3+(3*x^5-9*x^4+ 9*x^3-3*x^2)*log(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*log(2)+x^9-3*x^8+3*x^7-x^6 ),x, algorithm=\
-(28*x^5 - 250*x^4 + 390*x^3 + (x^2 - 2*x + 1)*log(2)^2 - 169*x^2 + 2*(x^4 - 2*x^3 + x^2)*log(2))/(x^6 - 2*x^5 + x^4 + (x^2 - 2*x + 1)*log(2)^2 + 2* (x^4 - 2*x^3 + x^2)*log(2))
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (20) = 40\).
Time = 4.53 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.28 \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=\frac {- 28 x^{5} + x^{4} \cdot \left (250 - 2 \log {\left (2 \right )}\right ) + x^{3} \left (-390 + 4 \log {\left (2 \right )}\right ) + x^{2} \left (- 2 \log {\left (2 \right )} - \log {\left (2 \right )}^{2} + 169\right ) + 2 x \log {\left (2 \right )}^{2} - \log {\left (2 \right )}^{2}}{x^{6} - 2 x^{5} + x^{4} \cdot \left (1 + 2 \log {\left (2 \right )}\right ) - 4 x^{3} \log {\left (2 \right )} + x^{2} \left (\log {\left (2 \right )}^{2} + 2 \log {\left (2 \right )}\right ) - 2 x \log {\left (2 \right )}^{2} + \log {\left (2 \right )}^{2}} \]
integrate(((4*x**6-96*x**5+652*x**4-1394*x**3+1170*x**2-338*x)*ln(2)+28*x* *7-472*x**6+1170*x**5-1066*x**4+338*x**3)/((x**3-3*x**2+3*x-1)*ln(2)**3+(3 *x**5-9*x**4+9*x**3-3*x**2)*ln(2)**2+(3*x**7-9*x**6+9*x**5-3*x**4)*ln(2)+x **9-3*x**8+3*x**7-x**6),x)
(-28*x**5 + x**4*(250 - 2*log(2)) + x**3*(-390 + 4*log(2)) + x**2*(-2*log( 2) - log(2)**2 + 169) + 2*x*log(2)**2 - log(2)**2)/(x**6 - 2*x**5 + x**4*( 1 + 2*log(2)) - 4*x**3*log(2) + x**2*(log(2)**2 + 2*log(2)) - 2*x*log(2)** 2 + log(2)**2)
Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (25) = 50\).
Time = 0.24 (sec) , antiderivative size = 105, normalized size of antiderivative = 4.20 \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=-\frac {28 \, x^{5} + 2 \, x^{4} {\left (\log \left (2\right ) - 125\right )} - 2 \, x^{3} {\left (2 \, \log \left (2\right ) - 195\right )} + {\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) - 169\right )} x^{2} - 2 \, x \log \left (2\right )^{2} + \log \left (2\right )^{2}}{x^{6} - 2 \, x^{5} + x^{4} {\left (2 \, \log \left (2\right ) + 1\right )} - 4 \, x^{3} \log \left (2\right ) + {\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right )\right )} x^{2} - 2 \, x \log \left (2\right )^{2} + \log \left (2\right )^{2}} \]
integrate(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*log(2)+28*x^7-47 2*x^6+1170*x^5-1066*x^4+338*x^3)/((x^3-3*x^2+3*x-1)*log(2)^3+(3*x^5-9*x^4+ 9*x^3-3*x^2)*log(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*log(2)+x^9-3*x^8+3*x^7-x^6 ),x, algorithm=\
-(28*x^5 + 2*x^4*(log(2) - 125) - 2*x^3*(2*log(2) - 195) + (log(2)^2 + 2*l og(2) - 169)*x^2 - 2*x*log(2)^2 + log(2)^2)/(x^6 - 2*x^5 + x^4*(2*log(2) + 1) - 4*x^3*log(2) + (log(2)^2 + 2*log(2))*x^2 - 2*x*log(2)^2 + log(2)^2)
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (25) = 50\).
Time = 0.29 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.28 \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=-\frac {28 \, x^{5} + 2 \, x^{4} \log \left (2\right ) - 250 \, x^{4} - 4 \, x^{3} \log \left (2\right ) + x^{2} \log \left (2\right )^{2} + 390 \, x^{3} + 2 \, x^{2} \log \left (2\right ) - 2 \, x \log \left (2\right )^{2} - 169 \, x^{2} + \log \left (2\right )^{2}}{{\left (x^{3} - x^{2} + x \log \left (2\right ) - \log \left (2\right )\right )}^{2}} \]
integrate(((4*x^6-96*x^5+652*x^4-1394*x^3+1170*x^2-338*x)*log(2)+28*x^7-47 2*x^6+1170*x^5-1066*x^4+338*x^3)/((x^3-3*x^2+3*x-1)*log(2)^3+(3*x^5-9*x^4+ 9*x^3-3*x^2)*log(2)^2+(3*x^7-9*x^6+9*x^5-3*x^4)*log(2)+x^9-3*x^8+3*x^7-x^6 ),x, algorithm=\
-(28*x^5 + 2*x^4*log(2) - 250*x^4 - 4*x^3*log(2) + x^2*log(2)^2 + 390*x^3 + 2*x^2*log(2) - 2*x*log(2)^2 - 169*x^2 + log(2)^2)/(x^3 - x^2 + x*log(2) - log(2))^2
Timed out. \[ \int \frac {338 x^3-1066 x^4+1170 x^5-472 x^6+28 x^7+\left (-338 x+1170 x^2-1394 x^3+652 x^4-96 x^5+4 x^6\right ) \log (2)}{-x^6+3 x^7-3 x^8+x^9+\left (-3 x^4+9 x^5-9 x^6+3 x^7\right ) \log (2)+\left (-3 x^2+9 x^3-9 x^4+3 x^5\right ) \log ^2(2)+\left (-1+3 x-3 x^2+x^3\right ) \log ^3(2)} \, dx=\text {Hanged} \]