Integrand size = 358, antiderivative size = 25 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=4-x+\frac {9}{\left (-3+x^2\right )^2 \left (x+\frac {\log (2)}{\log (x)}\right )^4} \]
Leaf count is larger than twice the leaf count of optimal. \(628\) vs. \(2(25)=50\).
Time = 0.78 (sec) , antiderivative size = 628, normalized size of antiderivative = 25.12 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=\frac {1}{x^4}+\frac {2}{3 x^2}-x+\frac {1}{\left (-3+x^2\right )^2}-\frac {2}{3 \left (-3+x^2\right )}+\frac {9 \log ^4(2)}{x^4 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^4}-\frac {36 \log ^3(2)}{x^4 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^3}-\frac {3 \log ^2(2) \left (180 x^8 \log (2)-1620 x \log ^4(2)+324 \log ^5(2)-216 x^2 \log ^3(2) \left (-15+\log ^2(2)\right )+1080 x^3 \log ^2(2) \left (-3+\log ^2(2)\right )-72 x^7 \left (-3+5 \log ^2(2)\right )+36 x^4 \log (2) \left (45-60 \log ^2(2)+\log ^4(2)\right )-36 x^5 \left (9-60 \log ^2(2)+5 \log ^4(2)\right )+360 x^6 \left (\log ^3(2)-\log (8)\right )+x^9 \left (-36-155 \log ^5(2)+31 \log ^4(2) \log (32)\right )\right )}{2 x^4 \left (-3+x^2\right )^4 (x-\log (2))^5 (\log (2)+x \log (x))^2}-\frac {3 \log (2) \left (-9072 x \log ^6(2)+1296 \log ^7(2)-1296 x^2 \log ^5(2) \left (-21+\log ^2(2)\right )+9072 x^3 \log ^4(2) \left (-5+\log ^2(2)\right )+432 x^4 \log ^3(2) \left (105-63 \log ^2(2)+\log ^4(2)\right )-3024 x^5 \log ^2(2) \left (9-15 \log ^2(2)+\log ^4(2)\right )-48 x^6 \log (2) \left (-189+945 \log ^2(2)-189 \log ^4(2)+\log ^6(2)\right )+48 x^7 \left (-27+567 \log ^2(2)-315 \log ^4(2)+7 \log ^6(2)\right )-4 x^{12} \log (2) \left (84-5310 \log ^3(2)+505 \log ^5(2)+1062 \log ^2(2) \log (32)-101 \log ^4(2) \log (32)\right )+48 x^{10} \log (2) \left (63-35 \log ^2(2)+260 \log ^5(2)-52 \log ^4(2) \log (32)\right )-6 x^9 \left (-216+1512 \log ^2(2)-280 \log ^4(2)+525 \log ^7(2)-105 \log ^6(2) \log (32)\right )+3 x^{11} \left (-144+336 \log ^2(2)-7385 \log ^5(2)+70 \log ^7(2)+1477 \log ^4(2) \log (32)-14 \log ^6(2) \log (32)\right )+x^{13} \left (48-11520 \log ^3(2)+6635 \log ^5(2)-50 \log ^7(2)+2304 \log ^2(2) \log (32)-1327 \log ^4(2) \log (32)+10 \log ^6(2) \log (32)\right )-1008 x^8 \left (-15 \log ^3(2)+\log ^5(2)+\log (512)\right )\right )}{4 x^4 \left (-3+x^2\right )^5 (x-\log (2))^7 (\log (2)+x \log (x))} \]
Integrate[((27*x - 27*x^3 + 9*x^5 - x^7)*Log[2]^5 + (135*x^2 - 135*x^4 + 4 5*x^6 - 5*x^8)*Log[2]^4*Log[x] + (270*x^3 - 270*x^5 + 90*x^7 - 10*x^9)*Log [2]^3*Log[x]^2 + ((-108 + 36*x^2)*Log[2] + (270*x^4 - 270*x^6 + 90*x^8 - 1 0*x^10)*Log[2]^2)*Log[x]^3 + (-36*x^2 + 135*x^5 - 135*x^7 + 45*x^9 - 5*x^1 1)*Log[2]*Log[x]^4 + (108*x - 72*x^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12)*Lo g[x]^5)/((-27*x + 27*x^3 - 9*x^5 + x^7)*Log[2]^5 + (-135*x^2 + 135*x^4 - 4 5*x^6 + 5*x^8)*Log[2]^4*Log[x] + (-270*x^3 + 270*x^5 - 90*x^7 + 10*x^9)*Lo g[2]^3*Log[x]^2 + (-270*x^4 + 270*x^6 - 90*x^8 + 10*x^10)*Log[2]^2*Log[x]^ 3 + (-135*x^5 + 135*x^7 - 45*x^9 + 5*x^11)*Log[2]*Log[x]^4 + (-27*x^6 + 27 *x^8 - 9*x^10 + x^12)*Log[x]^5),x]
x^(-4) + 2/(3*x^2) - x + (-3 + x^2)^(-2) - 2/(3*(-3 + x^2)) + (9*Log[2]^4) /(x^4*(-3 + x^2)^2*(Log[2] + x*Log[x])^4) - (36*Log[2]^3)/(x^4*(-3 + x^2)^ 2*(Log[2] + x*Log[x])^3) - (3*Log[2]^2*(180*x^8*Log[2] - 1620*x*Log[2]^4 + 324*Log[2]^5 - 216*x^2*Log[2]^3*(-15 + Log[2]^2) + 1080*x^3*Log[2]^2*(-3 + Log[2]^2) - 72*x^7*(-3 + 5*Log[2]^2) + 36*x^4*Log[2]*(45 - 60*Log[2]^2 + Log[2]^4) - 36*x^5*(9 - 60*Log[2]^2 + 5*Log[2]^4) + 360*x^6*(Log[2]^3 - L og[8]) + x^9*(-36 - 155*Log[2]^5 + 31*Log[2]^4*Log[32])))/(2*x^4*(-3 + x^2 )^4*(x - Log[2])^5*(Log[2] + x*Log[x])^2) - (3*Log[2]*(-9072*x*Log[2]^6 + 1296*Log[2]^7 - 1296*x^2*Log[2]^5*(-21 + Log[2]^2) + 9072*x^3*Log[2]^4*(-5 + Log[2]^2) + 432*x^4*Log[2]^3*(105 - 63*Log[2]^2 + Log[2]^4) - 3024*x^5* Log[2]^2*(9 - 15*Log[2]^2 + Log[2]^4) - 48*x^6*Log[2]*(-189 + 945*Log[2]^2 - 189*Log[2]^4 + Log[2]^6) + 48*x^7*(-27 + 567*Log[2]^2 - 315*Log[2]^4 + 7*Log[2]^6) - 4*x^12*Log[2]*(84 - 5310*Log[2]^3 + 505*Log[2]^5 + 1062*Log[ 2]^2*Log[32] - 101*Log[2]^4*Log[32]) + 48*x^10*Log[2]*(63 - 35*Log[2]^2 + 260*Log[2]^5 - 52*Log[2]^4*Log[32]) - 6*x^9*(-216 + 1512*Log[2]^2 - 280*Lo g[2]^4 + 525*Log[2]^7 - 105*Log[2]^6*Log[32]) + 3*x^11*(-144 + 336*Log[2]^ 2 - 7385*Log[2]^5 + 70*Log[2]^7 + 1477*Log[2]^4*Log[32] - 14*Log[2]^6*Log[ 32]) + x^13*(48 - 11520*Log[2]^3 + 6635*Log[2]^5 - 50*Log[2]^7 + 2304*Log[ 2]^2*Log[32] - 1327*Log[2]^4*Log[32] + 10*Log[2]^6*Log[32]) - 1008*x^8*(-1 5*Log[2]^3 + Log[2]^5 + Log[512])))/(4*x^4*(-3 + x^2)^5*(x - Log[2])^7*...
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.
| \(\displaystyle \int \frac {\left (-x^7+9 x^5-27 x^3+27 x\right ) \log ^5(2)+\left (-10 x^9+90 x^7-270 x^5+270 x^3\right ) \log ^3(2) \log ^2(x)+\left (-5 x^8+45 x^6-135 x^4+135 x^2\right ) \log ^4(2) \log (x)+\left (-x^{12}+9 x^{10}-27 x^8+27 x^6-72 x^3+108 x\right ) \log ^5(x)+\left (-5 x^{11}+45 x^9-135 x^7+135 x^5-36 x^2\right ) \log (2) \log ^4(x)+\left (\left (36 x^2-108\right ) \log (2)+\left (-10 x^{10}+90 x^8-270 x^6+270 x^4\right ) \log ^2(2)\right ) \log ^3(x)}{\left (x^7-9 x^5+27 x^3-27 x\right ) \log ^5(2)+\left (x^{12}-9 x^{10}+27 x^8-27 x^6\right ) \log ^5(x)+\left (5 x^{11}-45 x^9+135 x^7-135 x^5\right ) \log (2) \log ^4(x)+\left (10 x^{10}-90 x^8+270 x^6-270 x^4\right ) \log ^2(2) \log ^3(x)+\left (10 x^9-90 x^7+270 x^5-270 x^3\right ) \log ^3(2) \log ^2(x)+\left (5 x^8-45 x^6+135 x^4-135 x^2\right ) \log ^4(2) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x \left (x^2-3\right )^3 \log ^5(2)+5 x^2 \left (x^2-3\right )^3 \log ^4(2) \log (x)+10 x^3 \left (x^2-3\right )^3 \log ^3(2) \log ^2(x)+2 \left (x^2-3\right ) \log (2) \left (x^8 \log (32)-30 x^6 \log (2)+45 x^4 \log (2)-18\right ) \log ^3(x)+x \left (x^{11}-9 x^9+27 x^7-27 x^5+72 x^2-108\right ) \log ^5(x)+x^2 \left (5 x^9-45 x^7+135 x^5-135 x^3+36\right ) \log (2) \log ^4(x)}{x \left (3-x^2\right )^3 (x \log (x)+\log (2))^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2 \log ^4(2) (18 x-\log (262144))}{x^5 \left (x^2-3\right )^2 (x \log (x)+\log (2))^5}+\frac {108 \left (3 x^2-5\right ) \log (2)}{x^5 \left (x^2-3\right )^3 (x \log (x)+\log (2))}+\frac {18 \log ^3(2) \left (6 x^3-x^2 \log (4096)-18 x+\log (1073741824)\right )}{x^5 \left (x^2-3\right )^3 (x \log (x)+\log (2))^4}-\frac {36 \log ^2(2) \left (3 x^3-14 x^2 \log (2)-9 x+30 \log (2)\right )}{x^5 \left (x^2-3\right )^3 (x \log (x)+\log (2))^3}+\frac {36 \log (2) \left (x^3-16 x^2 \log (2)-3 x+30 \log (2)\right )}{x^5 \left (x^2-3\right )^3 (x \log (x)+\log (2))^2}+\frac {-x^{11}+9 x^9-27 x^7+27 x^5-72 x^2+108}{x^5 \left (x^2-3\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -x+\frac {1}{27} \log ^4(2) \log (262144) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^5}dx-\frac {4 \log ^4(2) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^5}dx}{3 \sqrt {3}}+\frac {2}{9} \log ^4(2) \log (262144) \int \frac {1}{x^5 (x \log (x)+\log (2))^5}dx-4 \log ^4(2) \int \frac {1}{x^4 (x \log (x)+\log (2))^5}dx+\frac {4}{27} \log ^4(2) \log (262144) \int \frac {1}{x^3 (x \log (x)+\log (2))^5}dx-\frac {8}{3} \log ^4(2) \int \frac {1}{x^2 (x \log (x)+\log (2))^5}dx+\frac {2}{27} \log ^4(2) \log (262144) \int \frac {1}{x (x \log (x)+\log (2))^5}dx-\frac {1}{27} \log ^4(2) \log (262144) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^5}dx-\frac {4 \log ^4(2) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^5}dx}{3 \sqrt {3}}-4 \log ^4(2) \int \frac {1}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^5}dx+\frac {2}{27} \log ^4(2) \log (262144) \int \frac {x}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^5}dx-\frac {1}{9} \log ^3(2) \log (16777216) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^4}dx+\frac {4 \log ^3(2) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^4}dx}{\sqrt {3}}-\frac {2}{3} \log ^3(2) \log (1073741824) \int \frac {1}{x^5 (x \log (x)+\log (2))^4}dx+12 \log ^3(2) \int \frac {1}{x^4 (x \log (x)+\log (2))^4}dx-\frac {2}{3} \log ^3(2) \log (262144) \int \frac {1}{x^3 (x \log (x)+\log (2))^4}dx+8 \log ^3(2) \int \frac {1}{x^2 (x \log (x)+\log (2))^4}dx-\frac {2}{9} \log ^3(2) \log (16777216) \int \frac {1}{x (x \log (x)+\log (2))^4}dx+\frac {1}{9} \log ^3(2) \log (16777216) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^4}dx+\frac {4 \log ^3(2) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^4}dx}{\sqrt {3}}-\frac {2}{3} \log ^3(2) \log (64) \int \frac {x}{\left (x^2-3\right )^3 (x \log (x)+\log (2))^4}dx+12 \log ^3(2) \int \frac {1}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^4}dx-\frac {2}{3} \log ^3(2) \log (64) \int \frac {x}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^4}dx+4 \log ^3(2) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^3}dx-\frac {4 \log ^2(2) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^3}dx}{\sqrt {3}}+40 \log ^3(2) \int \frac {1}{x^5 (x \log (x)+\log (2))^3}dx-12 \log ^2(2) \int \frac {1}{x^4 (x \log (x)+\log (2))^3}dx+\frac {64}{3} \log ^3(2) \int \frac {1}{x^3 (x \log (x)+\log (2))^3}dx-8 \log ^2(2) \int \frac {1}{x^2 (x \log (x)+\log (2))^3}dx+8 \log ^3(2) \int \frac {1}{x (x \log (x)+\log (2))^3}dx-4 \log ^3(2) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^3}dx-\frac {4 \log ^2(2) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^3}dx}{\sqrt {3}}+16 \log ^3(2) \int \frac {x}{\left (x^2-3\right )^3 (x \log (x)+\log (2))^3}dx-12 \log ^2(2) \int \frac {1}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^3}dx+\frac {4}{3} \log ^2(2) \log (4) \int \frac {x}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^3}dx-\frac {4}{3} \log (2) \log (4) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^2}dx+\frac {4 \log (2) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))^2}dx}{3 \sqrt {3}}-40 \log ^2(2) \int \frac {1}{x^5 (x \log (x)+\log (2))^2}dx+4 \log (2) \int \frac {1}{x^4 (x \log (x)+\log (2))^2}dx-\frac {56}{3} \log ^2(2) \int \frac {1}{x^3 (x \log (x)+\log (2))^2}dx+\frac {8}{3} \log (2) \int \frac {1}{x^2 (x \log (x)+\log (2))^2}dx-\frac {16}{3} \log ^2(2) \int \frac {1}{x (x \log (x)+\log (2))^2}dx+\frac {4}{3} \log (2) \log (4) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^2}dx+\frac {4 \log (2) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))^2}dx}{3 \sqrt {3}}-24 \log ^2(2) \int \frac {x}{\left (x^2-3\right )^3 (x \log (x)+\log (2))^2}dx+4 \log (2) \int \frac {1}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^2}dx+\frac {4}{3} \log (2) \log (4) \int \frac {x}{\left (x^2-3\right )^2 (x \log (x)+\log (2))^2}dx+\frac {2}{3} \log (2) \int \frac {1}{\left (\sqrt {3}-x\right ) (x \log (x)+\log (2))}dx+20 \log (2) \int \frac {1}{x^5 (x \log (x)+\log (2))}dx+8 \log (2) \int \frac {1}{x^3 (x \log (x)+\log (2))}dx+\frac {4}{3} \log (2) \int \frac {1}{x (x \log (x)+\log (2))}dx-\frac {2}{3} \log (2) \int \frac {1}{\left (x+\sqrt {3}\right ) (x \log (x)+\log (2))}dx+16 \log (2) \int \frac {x}{\left (x^2-3\right )^3 (x \log (x)+\log (2))}dx-4 \log (2) \int \frac {x}{\left (x^2-3\right )^2 (x \log (x)+\log (2))}dx+\frac {2}{3 \left (3-x^2\right )}+\frac {1}{\left (x^2-3\right )^2}+\frac {2}{3 x^2}+\frac {1}{x^4}\) |
Int[((27*x - 27*x^3 + 9*x^5 - x^7)*Log[2]^5 + (135*x^2 - 135*x^4 + 45*x^6 - 5*x^8)*Log[2]^4*Log[x] + (270*x^3 - 270*x^5 + 90*x^7 - 10*x^9)*Log[2]^3* Log[x]^2 + ((-108 + 36*x^2)*Log[2] + (270*x^4 - 270*x^6 + 90*x^8 - 10*x^10 )*Log[2]^2)*Log[x]^3 + (-36*x^2 + 135*x^5 - 135*x^7 + 45*x^9 - 5*x^11)*Log [2]*Log[x]^4 + (108*x - 72*x^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12)*Log[x]^5 )/((-27*x + 27*x^3 - 9*x^5 + x^7)*Log[2]^5 + (-135*x^2 + 135*x^4 - 45*x^6 + 5*x^8)*Log[2]^4*Log[x] + (-270*x^3 + 270*x^5 - 90*x^7 + 10*x^9)*Log[2]^3 *Log[x]^2 + (-270*x^4 + 270*x^6 - 90*x^8 + 10*x^10)*Log[2]^2*Log[x]^3 + (- 135*x^5 + 135*x^7 - 45*x^9 + 5*x^11)*Log[2]*Log[x]^4 + (-27*x^6 + 27*x^8 - 9*x^10 + x^12)*Log[x]^5),x]
3.8.83.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 6.42 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08
| method | result | size |
| default | \(-x +\frac {9 \ln \left (x \right )^{4}}{\left (x \ln \left (x \right )+\ln \left (2\right )\right )^{4} \left (x^{2}-3\right )^{2}}\) | \(27\) |
| risch | \(-\frac {x^{9}-6 x^{7}+9 x^{5}-9}{x^{4} \left (x^{4}-6 x^{2}+9\right )}-\frac {9 \ln \left (2\right ) \left (4 x^{3} \ln \left (x \right )^{3}+6 x^{2} \ln \left (2\right ) \ln \left (x \right )^{2}+4 \ln \left (x \right ) \ln \left (2\right )^{2} x +\ln \left (2\right )^{3}\right )}{x^{4} \left (x^{4}-6 x^{2}+9\right ) \left (x \ln \left (x \right )+\ln \left (2\right )\right )^{4}}\) | \(96\) |
| parallelrisch | \(\frac {-x^{9} \ln \left (x \right )^{4}+6 x^{7} \ln \left (x \right )^{4}-x^{5} \ln \left (2\right )^{4}+6 x^{3} \ln \left (2\right )^{4}-9 x \ln \left (2\right )^{4}-9 x^{5} \ln \left (x \right )^{4}+9 \ln \left (x \right )^{4}-36 x^{4} \ln \left (2\right ) \ln \left (x \right )^{3}+24 \ln \left (x \right ) \ln \left (2\right )^{3} x^{4}-36 x^{2} \ln \left (2\right )^{3} \ln \left (x \right )-4 \ln \left (x \right )^{3} \ln \left (2\right ) x^{8}-6 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{7}+24 \ln \left (x \right )^{3} \ln \left (2\right ) x^{6}-4 \ln \left (x \right ) \ln \left (2\right )^{3} x^{6}+36 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{5}-54 \ln \left (2\right )^{2} x^{3} \ln \left (x \right )^{2}}{x^{8} \ln \left (x \right )^{4}+4 \ln \left (x \right )^{3} \ln \left (2\right ) x^{7}+6 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{6}-6 x^{6} \ln \left (x \right )^{4}+4 \ln \left (x \right ) \ln \left (2\right )^{3} x^{5}-24 \ln \left (x \right )^{3} \ln \left (2\right ) x^{5}+\ln \left (2\right )^{4} x^{4}-36 x^{4} \ln \left (2\right )^{2} \ln \left (x \right )^{2}+9 x^{4} \ln \left (x \right )^{4}-24 \ln \left (x \right ) \ln \left (2\right )^{3} x^{3}+36 \ln \left (x \right )^{3} \ln \left (2\right ) x^{3}-6 x^{2} \ln \left (2\right )^{4}+54 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{2}+36 x \ln \left (2\right )^{3} \ln \left (x \right )+9 \ln \left (2\right )^{4}}\) | \(321\) |
int(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*ln(x)^5+(-5*x^11+45*x^9-135 *x^7+135*x^5-36*x^2)*ln(2)*ln(x)^4+((-10*x^10+90*x^8-270*x^6+270*x^4)*ln(2 )^2+(36*x^2-108)*ln(2))*ln(x)^3+(-10*x^9+90*x^7-270*x^5+270*x^3)*ln(2)^3*l n(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*ln(2)^4*ln(x)+(-x^7+9*x^5-27*x^3+27 *x)*ln(2)^5)/((x^12-9*x^10+27*x^8-27*x^6)*ln(x)^5+(5*x^11-45*x^9+135*x^7-1 35*x^5)*ln(2)*ln(x)^4+(10*x^10-90*x^8+270*x^6-270*x^4)*ln(2)^2*ln(x)^3+(10 *x^9-90*x^7+270*x^5-270*x^3)*ln(2)^3*ln(x)^2+(5*x^8-45*x^6+135*x^4-135*x^2 )*ln(2)^4*ln(x)+(x^7-9*x^5+27*x^3-27*x)*ln(2)^5),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 211 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 211, normalized size of antiderivative = 8.44 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-\frac {{\left (x^{5} - 6 \, x^{3} + 9 \, x\right )} \log \left (2\right )^{4} + 4 \, {\left (x^{6} - 6 \, x^{4} + 9 \, x^{2}\right )} \log \left (2\right )^{3} \log \left (x\right ) + 6 \, {\left (x^{7} - 6 \, x^{5} + 9 \, x^{3}\right )} \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right )^{3} + {\left (x^{9} - 6 \, x^{7} + 9 \, x^{5} - 9\right )} \log \left (x\right )^{4}}{{\left (x^{4} - 6 \, x^{2} + 9\right )} \log \left (2\right )^{4} + 4 \, {\left (x^{5} - 6 \, x^{3} + 9 \, x\right )} \log \left (2\right )^{3} \log \left (x\right ) + 6 \, {\left (x^{6} - 6 \, x^{4} + 9 \, x^{2}\right )} \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, {\left (x^{7} - 6 \, x^{5} + 9 \, x^{3}\right )} \log \left (2\right ) \log \left (x\right )^{3} + {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \left (x\right )^{4}} \]
integrate(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*log(x)^5+(-5*x^11+45* x^9-135*x^7+135*x^5-36*x^2)*log(2)*log(x)^4+((-10*x^10+90*x^8-270*x^6+270* x^4)*log(2)^2+(36*x^2-108)*log(2))*log(x)^3+(-10*x^9+90*x^7-270*x^5+270*x^ 3)*log(2)^3*log(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*log(2)^4*log(x)+(-x^7 +9*x^5-27*x^3+27*x)*log(2)^5)/((x^12-9*x^10+27*x^8-27*x^6)*log(x)^5+(5*x^1 1-45*x^9+135*x^7-135*x^5)*log(2)*log(x)^4+(10*x^10-90*x^8+270*x^6-270*x^4) *log(2)^2*log(x)^3+(10*x^9-90*x^7+270*x^5-270*x^3)*log(2)^3*log(x)^2+(5*x^ 8-45*x^6+135*x^4-135*x^2)*log(2)^4*log(x)+(x^7-9*x^5+27*x^3-27*x)*log(2)^5 ),x, algorithm=\
-((x^5 - 6*x^3 + 9*x)*log(2)^4 + 4*(x^6 - 6*x^4 + 9*x^2)*log(2)^3*log(x) + 6*(x^7 - 6*x^5 + 9*x^3)*log(2)^2*log(x)^2 + 4*(x^8 - 6*x^6 + 9*x^4)*log(2 )*log(x)^3 + (x^9 - 6*x^7 + 9*x^5 - 9)*log(x)^4)/((x^4 - 6*x^2 + 9)*log(2) ^4 + 4*(x^5 - 6*x^3 + 9*x)*log(2)^3*log(x) + 6*(x^6 - 6*x^4 + 9*x^2)*log(2 )^2*log(x)^2 + 4*(x^7 - 6*x^5 + 9*x^3)*log(2)*log(x)^3 + (x^8 - 6*x^6 + 9* x^4)*log(x)^4)
Leaf count of result is larger than twice the leaf count of optimal. 212 vs. \(2 (20) = 40\).
Time = 0.31 (sec) , antiderivative size = 212, normalized size of antiderivative = 8.48 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=- x + \frac {- 36 x^{3} \log {\left (2 \right )} \log {\left (x \right )}^{3} - 54 x^{2} \log {\left (2 \right )}^{2} \log {\left (x \right )}^{2} - 36 x \log {\left (2 \right )}^{3} \log {\left (x \right )} - 9 \log {\left (2 \right )}^{4}}{x^{8} \log {\left (2 \right )}^{4} - 6 x^{6} \log {\left (2 \right )}^{4} + 9 x^{4} \log {\left (2 \right )}^{4} + \left (x^{12} - 6 x^{10} + 9 x^{8}\right ) \log {\left (x \right )}^{4} + \left (4 x^{9} \log {\left (2 \right )}^{3} - 24 x^{7} \log {\left (2 \right )}^{3} + 36 x^{5} \log {\left (2 \right )}^{3}\right ) \log {\left (x \right )} + \left (6 x^{10} \log {\left (2 \right )}^{2} - 36 x^{8} \log {\left (2 \right )}^{2} + 54 x^{6} \log {\left (2 \right )}^{2}\right ) \log {\left (x \right )}^{2} + \left (4 x^{11} \log {\left (2 \right )} - 24 x^{9} \log {\left (2 \right )} + 36 x^{7} \log {\left (2 \right )}\right ) \log {\left (x \right )}^{3}} + \frac {9}{x^{8} - 6 x^{6} + 9 x^{4}} \]
integrate(((-x**12+9*x**10-27*x**8+27*x**6-72*x**3+108*x)*ln(x)**5+(-5*x** 11+45*x**9-135*x**7+135*x**5-36*x**2)*ln(2)*ln(x)**4+((-10*x**10+90*x**8-2 70*x**6+270*x**4)*ln(2)**2+(36*x**2-108)*ln(2))*ln(x)**3+(-10*x**9+90*x**7 -270*x**5+270*x**3)*ln(2)**3*ln(x)**2+(-5*x**8+45*x**6-135*x**4+135*x**2)* ln(2)**4*ln(x)+(-x**7+9*x**5-27*x**3+27*x)*ln(2)**5)/((x**12-9*x**10+27*x* *8-27*x**6)*ln(x)**5+(5*x**11-45*x**9+135*x**7-135*x**5)*ln(2)*ln(x)**4+(1 0*x**10-90*x**8+270*x**6-270*x**4)*ln(2)**2*ln(x)**3+(10*x**9-90*x**7+270* x**5-270*x**3)*ln(2)**3*ln(x)**2+(5*x**8-45*x**6+135*x**4-135*x**2)*ln(2)* *4*ln(x)+(x**7-9*x**5+27*x**3-27*x)*ln(2)**5),x)
-x + (-36*x**3*log(2)*log(x)**3 - 54*x**2*log(2)**2*log(x)**2 - 36*x*log(2 )**3*log(x) - 9*log(2)**4)/(x**8*log(2)**4 - 6*x**6*log(2)**4 + 9*x**4*log (2)**4 + (x**12 - 6*x**10 + 9*x**8)*log(x)**4 + (4*x**9*log(2)**3 - 24*x** 7*log(2)**3 + 36*x**5*log(2)**3)*log(x) + (6*x**10*log(2)**2 - 36*x**8*log (2)**2 + 54*x**6*log(2)**2)*log(x)**2 + (4*x**11*log(2) - 24*x**9*log(2) + 36*x**7*log(2))*log(x)**3) + 9/(x**8 - 6*x**6 + 9*x**4)
Leaf count of result is larger than twice the leaf count of optimal. 272 vs. \(2 (25) = 50\).
Time = 0.47 (sec) , antiderivative size = 272, normalized size of antiderivative = 10.88 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-\frac {x^{5} \log \left (2\right )^{4} - 6 \, x^{3} \log \left (2\right )^{4} + 9 \, x \log \left (2\right )^{4} + {\left (x^{9} - 6 \, x^{7} + 9 \, x^{5} - 9\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{8} \log \left (2\right ) - 6 \, x^{6} \log \left (2\right ) + 9 \, x^{4} \log \left (2\right )\right )} \log \left (x\right )^{3} + 6 \, {\left (x^{7} \log \left (2\right )^{2} - 6 \, x^{5} \log \left (2\right )^{2} + 9 \, x^{3} \log \left (2\right )^{2}\right )} \log \left (x\right )^{2} + 4 \, {\left (x^{6} \log \left (2\right )^{3} - 6 \, x^{4} \log \left (2\right )^{3} + 9 \, x^{2} \log \left (2\right )^{3}\right )} \log \left (x\right )}{x^{4} \log \left (2\right )^{4} - 6 \, x^{2} \log \left (2\right )^{4} + {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \left (x\right )^{4} + 9 \, \log \left (2\right )^{4} + 4 \, {\left (x^{7} \log \left (2\right ) - 6 \, x^{5} \log \left (2\right ) + 9 \, x^{3} \log \left (2\right )\right )} \log \left (x\right )^{3} + 6 \, {\left (x^{6} \log \left (2\right )^{2} - 6 \, x^{4} \log \left (2\right )^{2} + 9 \, x^{2} \log \left (2\right )^{2}\right )} \log \left (x\right )^{2} + 4 \, {\left (x^{5} \log \left (2\right )^{3} - 6 \, x^{3} \log \left (2\right )^{3} + 9 \, x \log \left (2\right )^{3}\right )} \log \left (x\right )} \]
integrate(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*log(x)^5+(-5*x^11+45* x^9-135*x^7+135*x^5-36*x^2)*log(2)*log(x)^4+((-10*x^10+90*x^8-270*x^6+270* x^4)*log(2)^2+(36*x^2-108)*log(2))*log(x)^3+(-10*x^9+90*x^7-270*x^5+270*x^ 3)*log(2)^3*log(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*log(2)^4*log(x)+(-x^7 +9*x^5-27*x^3+27*x)*log(2)^5)/((x^12-9*x^10+27*x^8-27*x^6)*log(x)^5+(5*x^1 1-45*x^9+135*x^7-135*x^5)*log(2)*log(x)^4+(10*x^10-90*x^8+270*x^6-270*x^4) *log(2)^2*log(x)^3+(10*x^9-90*x^7+270*x^5-270*x^3)*log(2)^3*log(x)^2+(5*x^ 8-45*x^6+135*x^4-135*x^2)*log(2)^4*log(x)+(x^7-9*x^5+27*x^3-27*x)*log(2)^5 ),x, algorithm=\
-(x^5*log(2)^4 - 6*x^3*log(2)^4 + 9*x*log(2)^4 + (x^9 - 6*x^7 + 9*x^5 - 9) *log(x)^4 + 4*(x^8*log(2) - 6*x^6*log(2) + 9*x^4*log(2))*log(x)^3 + 6*(x^7 *log(2)^2 - 6*x^5*log(2)^2 + 9*x^3*log(2)^2)*log(x)^2 + 4*(x^6*log(2)^3 - 6*x^4*log(2)^3 + 9*x^2*log(2)^3)*log(x))/(x^4*log(2)^4 - 6*x^2*log(2)^4 + (x^8 - 6*x^6 + 9*x^4)*log(x)^4 + 9*log(2)^4 + 4*(x^7*log(2) - 6*x^5*log(2) + 9*x^3*log(2))*log(x)^3 + 6*(x^6*log(2)^2 - 6*x^4*log(2)^2 + 9*x^2*log(2 )^2)*log(x)^2 + 4*(x^5*log(2)^3 - 6*x^3*log(2)^3 + 9*x*log(2)^3)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 237 vs. \(2 (25) = 50\).
Time = 0.60 (sec) , antiderivative size = 237, normalized size of antiderivative = 9.48 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-x - \frac {9 \, {\left (4 \, x^{3} \log \left (2\right ) \log \left (x\right )^{3} + 6 \, x^{2} \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, x \log \left (2\right )^{3} \log \left (x\right ) + \log \left (2\right )^{4}\right )}}{x^{12} \log \left (x\right )^{4} + 4 \, x^{11} \log \left (2\right ) \log \left (x\right )^{3} + 6 \, x^{10} \log \left (2\right )^{2} \log \left (x\right )^{2} - 6 \, x^{10} \log \left (x\right )^{4} + 4 \, x^{9} \log \left (2\right )^{3} \log \left (x\right ) - 24 \, x^{9} \log \left (2\right ) \log \left (x\right )^{3} + x^{8} \log \left (2\right )^{4} - 36 \, x^{8} \log \left (2\right )^{2} \log \left (x\right )^{2} + 9 \, x^{8} \log \left (x\right )^{4} - 24 \, x^{7} \log \left (2\right )^{3} \log \left (x\right ) + 36 \, x^{7} \log \left (2\right ) \log \left (x\right )^{3} - 6 \, x^{6} \log \left (2\right )^{4} + 54 \, x^{6} \log \left (2\right )^{2} \log \left (x\right )^{2} + 36 \, x^{5} \log \left (2\right )^{3} \log \left (x\right ) + 9 \, x^{4} \log \left (2\right )^{4}} - \frac {2 \, x^{2} - 9}{3 \, {\left (x^{4} - 6 \, x^{2} + 9\right )}} + \frac {2 \, x^{2} + 3}{3 \, x^{4}} \]
integrate(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*log(x)^5+(-5*x^11+45* x^9-135*x^7+135*x^5-36*x^2)*log(2)*log(x)^4+((-10*x^10+90*x^8-270*x^6+270* x^4)*log(2)^2+(36*x^2-108)*log(2))*log(x)^3+(-10*x^9+90*x^7-270*x^5+270*x^ 3)*log(2)^3*log(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*log(2)^4*log(x)+(-x^7 +9*x^5-27*x^3+27*x)*log(2)^5)/((x^12-9*x^10+27*x^8-27*x^6)*log(x)^5+(5*x^1 1-45*x^9+135*x^7-135*x^5)*log(2)*log(x)^4+(10*x^10-90*x^8+270*x^6-270*x^4) *log(2)^2*log(x)^3+(10*x^9-90*x^7+270*x^5-270*x^3)*log(2)^3*log(x)^2+(5*x^ 8-45*x^6+135*x^4-135*x^2)*log(2)^4*log(x)+(x^7-9*x^5+27*x^3-27*x)*log(2)^5 ),x, algorithm=\
-x - 9*(4*x^3*log(2)*log(x)^3 + 6*x^2*log(2)^2*log(x)^2 + 4*x*log(2)^3*log (x) + log(2)^4)/(x^12*log(x)^4 + 4*x^11*log(2)*log(x)^3 + 6*x^10*log(2)^2* log(x)^2 - 6*x^10*log(x)^4 + 4*x^9*log(2)^3*log(x) - 24*x^9*log(2)*log(x)^ 3 + x^8*log(2)^4 - 36*x^8*log(2)^2*log(x)^2 + 9*x^8*log(x)^4 - 24*x^7*log( 2)^3*log(x) + 36*x^7*log(2)*log(x)^3 - 6*x^6*log(2)^4 + 54*x^6*log(2)^2*lo g(x)^2 + 36*x^5*log(2)^3*log(x) + 9*x^4*log(2)^4) - 1/3*(2*x^2 - 9)/(x^4 - 6*x^2 + 9) + 1/3*(2*x^2 + 3)/x^4
Timed out. \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-\int \frac {\left (-x^{12}+9\,x^{10}-27\,x^8+27\,x^6-72\,x^3+108\,x\right )\,{\ln \left (x\right )}^5-\ln \left (2\right )\,\left (5\,x^{11}-45\,x^9+135\,x^7-135\,x^5+36\,x^2\right )\,{\ln \left (x\right )}^4+\left (\ln \left (2\right )\,\left (36\,x^2-108\right )+{\ln \left (2\right )}^2\,\left (-10\,x^{10}+90\,x^8-270\,x^6+270\,x^4\right )\right )\,{\ln \left (x\right )}^3+{\ln \left (2\right )}^3\,\left (-10\,x^9+90\,x^7-270\,x^5+270\,x^3\right )\,{\ln \left (x\right )}^2+{\ln \left (2\right )}^4\,\left (-5\,x^8+45\,x^6-135\,x^4+135\,x^2\right )\,\ln \left (x\right )+{\ln \left (2\right )}^5\,\left (-x^7+9\,x^5-27\,x^3+27\,x\right )}{\left (-x^{12}+9\,x^{10}-27\,x^8+27\,x^6\right )\,{\ln \left (x\right )}^5+\ln \left (2\right )\,\left (-5\,x^{11}+45\,x^9-135\,x^7+135\,x^5\right )\,{\ln \left (x\right )}^4+{\ln \left (2\right )}^2\,\left (-10\,x^{10}+90\,x^8-270\,x^6+270\,x^4\right )\,{\ln \left (x\right )}^3+{\ln \left (2\right )}^3\,\left (-10\,x^9+90\,x^7-270\,x^5+270\,x^3\right )\,{\ln \left (x\right )}^2+{\ln \left (2\right )}^4\,\left (-5\,x^8+45\,x^6-135\,x^4+135\,x^2\right )\,\ln \left (x\right )+{\ln \left (2\right )}^5\,\left (-x^7+9\,x^5-27\,x^3+27\,x\right )} \,d x \]
int(-(log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^3*(log(2)*(36*x^2 - 108) + log(2)^2*(270*x^4 - 270*x^6 + 90*x^8 - 10*x^10)) + log(x)^5*(108*x - 72*x^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12) + log(2)^4*log(x)*(135*x^2 - 1 35*x^4 + 45*x^6 - 5*x^8) - log(2)*log(x)^4*(36*x^2 - 135*x^5 + 135*x^7 - 4 5*x^9 + 5*x^11) + log(2)^3*log(x)^2*(270*x^3 - 270*x^5 + 90*x^7 - 10*x^9)) /(log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^5*(27*x^6 - 27*x^8 + 9*x ^10 - x^12) + log(2)^4*log(x)*(135*x^2 - 135*x^4 + 45*x^6 - 5*x^8) + log(2 )*log(x)^4*(135*x^5 - 135*x^7 + 45*x^9 - 5*x^11) + log(2)^3*log(x)^2*(270* x^3 - 270*x^5 + 90*x^7 - 10*x^9) + log(2)^2*log(x)^3*(270*x^4 - 270*x^6 + 90*x^8 - 10*x^10)),x)
-int((log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^3*(log(2)*(36*x^2 - 108) + log(2)^2*(270*x^4 - 270*x^6 + 90*x^8 - 10*x^10)) + log(x)^5*(108*x - 72*x^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12) + log(2)^4*log(x)*(135*x^2 - 1 35*x^4 + 45*x^6 - 5*x^8) - log(2)*log(x)^4*(36*x^2 - 135*x^5 + 135*x^7 - 4 5*x^9 + 5*x^11) + log(2)^3*log(x)^2*(270*x^3 - 270*x^5 + 90*x^7 - 10*x^9)) /(log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^5*(27*x^6 - 27*x^8 + 9*x ^10 - x^12) + log(2)^4*log(x)*(135*x^2 - 135*x^4 + 45*x^6 - 5*x^8) + log(2 )*log(x)^4*(135*x^5 - 135*x^7 + 45*x^9 - 5*x^11) + log(2)^3*log(x)^2*(270* x^3 - 270*x^5 + 90*x^7 - 10*x^9) + log(2)^2*log(x)^3*(270*x^4 - 270*x^6 + 90*x^8 - 10*x^10)), x)