Integrand size = 449, antiderivative size = 34 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log (x-\log (3))+\log \left (\left (-3+\frac {3+e^3+\frac {1}{2} \log (2 x)}{x}\right )^2\right )} \]
\[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx \]
Integrate[(-4*x - 2*E^3*x - 6*x^2 + (10 + 4*E^3)*Log[3] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]] + Log[2*x]*(-x + 2*Log [3] + (-x + Log[3])*Log[x - Log[3]]) + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^ 3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x ) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)])/( (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]]^2 + (- x + Log[3])*Log[2*x]*Log[x - Log[3]]^2 + ((-12*x - 4*E^3*x + 12*x^2 + (12 + 4*E^3 - 12*x)*Log[3])*Log[x - Log[3]] + (-2*x + 2*Log[3])*Log[2*x]*Log[x - Log[3]])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^ 3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2 )]^2),x]
Integrate[(-4*x - 2*E^3*x - 6*x^2 + (10 + 4*E^3)*Log[3] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]] + Log[2*x]*(-x + 2*Log [3] + (-x + Log[3])*Log[x - Log[3]]) + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^ 3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x ) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)])/( (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]]^2 + (- x + Log[3])*Log[2*x]*Log[x - Log[3]]^2 + ((-12*x - 4*E^3*x + 12*x^2 + (12 + 4*E^3 - 12*x)*Log[3])*Log[x - Log[3]] + (-2*x + 2*Log[3])*Log[2*x]*Log[x - Log[3]])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^ 3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2 )]^2), 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.
| \(\displaystyle \int \frac {-6 x^2+\left (6 x^2-2 e^3 x-6 x+(\log (3)-x) \log (2 x)+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log \left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )+\left (6 x^2-2 e^3 x-6 x+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log (x-\log (3))-2 e^3 x-4 x+\log (2 x) (-x+(\log (3)-x) \log (x-\log (3))+2 \log (3))+\left (10+4 e^3\right ) \log (3)}{\left (6 x^2-2 e^3 x-6 x+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log ^2(x-\log (3))+\left (6 x^2-2 e^3 x-6 x+(\log (3)-x) \log (2 x)+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log ^2\left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )+\left (\left (12 x^2-4 e^3 x-12 x+\left (-12 x+4 e^3+12\right ) \log (3)\right ) \log (x-\log (3))+(2 \log (3)-2 x) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )+(\log (3)-x) \log (2 x) \log ^2(x-\log (3))} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-6 x^2+\left (6 x^2-2 e^3 x-6 x+(\log (3)-x) \log (2 x)+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log \left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )+\left (6 x^2-2 e^3 x-6 x+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log (x-\log (3))+\left (-4-2 e^3\right ) x+\log (2 x) (-x+(\log (3)-x) \log (x-\log (3))+2 \log (3))+\left (10+4 e^3\right ) \log (3)}{\left (6 x^2-2 e^3 x-6 x+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log ^2(x-\log (3))+\left (6 x^2-2 e^3 x-6 x+(\log (3)-x) \log (2 x)+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log ^2\left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )+\left (\left (12 x^2-4 e^3 x-12 x+\left (-12 x+4 e^3+12\right ) \log (3)\right ) \log (x-\log (3))+(2 \log (3)-2 x) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )+(\log (3)-x) \log (2 x) \log ^2(x-\log (3))}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {6 x^2-\left (6 x^2-2 e^3 x-6 x+(\log (3)-x) \log (2 x)+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log \left (\frac {36 x^2-72 x+e^3 (24-24 x)+\log ^2(2 x)+\left (-12 x+4 e^3+12\right ) \log (2 x)+4 e^6+36}{4 x^2}\right )-\left (6 x^2-2 e^3 x-6 x+\left (-6 x+2 e^3+6\right ) \log (3)\right ) \log (x-\log (3))-\left (-4-2 e^3\right ) x-\log (2 x) (-x+(\log (3)-x) \log (x-\log (3))+2 \log (3))-\left (10+4 e^3\right ) \log (3)}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 x^2}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {2 \left (2+e^3\right ) x}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {\log \left (\frac {\left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right )^2}{4 x^2}\right )}{\left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {2 \left (-3 x+e^3+3\right ) \log (x-\log (3))}{\left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {\log (2 x) (x+x \log (x-\log (3))-\log (3) \log (x-\log (3))-\log (9))}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {2 \left (-5-2 e^3\right ) \log (3)}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {6 x^2}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {2 \left (2+e^3\right ) x}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {\log \left (\frac {\left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right )^2}{4 x^2}\right )}{\left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {2 \left (-3 x+e^3+3\right ) \log (x-\log (3))}{\left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {\log (2 x) (x+x \log (x-\log (3))-\log (3) \log (x-\log (3))-\log (9))}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}+\frac {2 \left (-5-2 e^3\right ) \log (3)}{(x-\log (3)) \left (-6 x+\log (2 x)+6 \left (1+\frac {e^3}{3}\right )\right ) \left (\log \left (\frac {\left (-6 x+\log (2 x)+2 e^3+6\right )^2}{4 x^2}\right )+\log (x-\log (3))\right )^2}\right )dx\) |
Int[(-4*x - 2*E^3*x - 6*x^2 + (10 + 4*E^3)*Log[3] + (-6*x - 2*E^3*x + 6*x^ 2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]] + Log[2*x]*(-x + 2*Log[3] + (-x + Log[3])*Log[x - Log[3]]) + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6* x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72 *x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)])/((-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3])*Log[x - Log[3]]^2 + (-x + Lo g[3])*Log[2*x]*Log[x - Log[3]]^2 + ((-12*x - 4*E^3*x + 12*x^2 + (12 + 4*E^ 3 - 12*x)*Log[3])*Log[x - Log[3]] + (-2*x + 2*Log[3])*Log[2*x]*Log[x - Log [3]])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12 *x)*Log[2*x] + Log[2*x]^2)/(4*x^2)] + (-6*x - 2*E^3*x + 6*x^2 + (6 + 2*E^3 - 6*x)*Log[3] + (-x + Log[3])*Log[2*x])*Log[(36 + 4*E^6 + E^3*(24 - 24*x) - 72*x + 36*x^2 + (12 + 4*E^3 - 12*x)*Log[2*x] + Log[2*x]^2)/(4*x^2)]^2), x]
3.7.33.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Time = 31.29 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.85
| method | result | size |
| parallelrisch | \(\frac {x}{\ln \left (-\ln \left (3\right )+x \right )+\ln \left (\frac {\ln \left (2 x \right )^{2}+\left (4 \,{\mathrm e}^{3}-12 x +12\right ) \ln \left (2 x \right )+4 \,{\mathrm e}^{6}+\left (-24 x +24\right ) {\mathrm e}^{3}+36 x^{2}-72 x +36}{4 x^{2}}\right )}\) | \(63\) |
| default | \(\frac {2 i x}{\pi {\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )\right )}^{2} \operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )\right ) {\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right )}^{2}+\pi {\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right )}^{3}+\pi \,\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right ) \operatorname {csgn}\left (\frac {i}{x^{2}}\right ) \operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )-\pi \,\operatorname {csgn}\left (i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}\right ) {\operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )}^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{x^{2}}\right ) {\operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )}^{2}-\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-\pi \operatorname {csgn}\left (i x^{2}\right )^{3}+\pi {\operatorname {csgn}\left (\frac {i \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )^{2}}{x^{2}}\right )}^{3}-4 i \ln \left (2\right )+2 i \ln \left (-\ln \left (3\right )+x \right )+4 i \ln \left (2 \,{\mathrm e}^{3}+\ln \left (2\right )+\ln \left (x \right )-6 x +6\right )-4 i \ln \left (x \right )}\) | \(351\) |
int((((ln(3)-x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x^2-6*x)*ln(1/ 4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^ 2-72*x+36)/x^2)+((ln(3)-x)*ln(-ln(3)+x)+2*ln(3)-x)*ln(2*x)+((2*exp(3)+6-6* x)*ln(3)-2*x*exp(3)+6*x^2-6*x)*ln(-ln(3)+x)+(4*exp(3)+10)*ln(3)-2*x*exp(3) -6*x^2-4*x)/(((ln(3)-x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x^2-6* x)*ln(1/4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(-24*x+24)*exp( 3)+36*x^2-72*x+36)/x^2)^2+((2*ln(3)-2*x)*ln(-ln(3)+x)*ln(2*x)+((4*exp(3)-1 2*x+12)*ln(3)-4*x*exp(3)+12*x^2-12*x)*ln(-ln(3)+x))*ln(1/4*(ln(2*x)^2+(4*e xp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+( ln(3)-x)*ln(-ln(3)+x)^2*ln(2*x)+((2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x^2-6 *x)*ln(-ln(3)+x)^2),x,method=_RETURNVERBOSE)
x/(ln(-ln(3)+x)+ln(1/4*(ln(2*x)^2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)^2+(- 24*x+24)*exp(3)+36*x^2-72*x+36)/x^2))
Time = 0.37 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.76 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log \left (x - \log \left (3\right )\right ) + \log \left (\frac {36 \, x^{2} - 24 \, {\left (x - 1\right )} e^{3} - 4 \, {\left (3 \, x - e^{3} - 3\right )} \log \left (2 \, x\right ) + \log \left (2 \, x\right )^{2} - 72 \, x + 4 \, e^{6} + 36}{4 \, x^{2}}\right )} \]
integrate((((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6 *x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)^2+(-24*x+24)* exp(3)+36*x^2-72*x+36)/x^2)+((log(3)-x)*log(-log(3)+x)+2*log(3)-x)*log(2*x )+((2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)+(4*exp(3)+ 10)*log(3)-2*x*exp(3)-6*x^2-4*x)/(((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*lo g(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x) +4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)^2+((2*log(3)-2*x)*log(- log(3)+x)*log(2*x)+((4*exp(3)-12*x+12)*log(3)-4*x*exp(3)+12*x^2-12*x)*log( -log(3)+x))*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)^2+(-2 4*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+(log(3)-x)*log(-log(3)+x)^2*log(2*x)+( (2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)^2),x, algorit hm=\
x/(log(x - log(3)) + log(1/4*(36*x^2 - 24*(x - 1)*e^3 - 4*(3*x - e^3 - 3)* log(2*x) + log(2*x)^2 - 72*x + 4*e^6 + 36)/x^2))
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (26) = 52\).
Time = 0.87 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.79 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log {\left (\frac {9 x^{2} - 18 x + \frac {\left (24 - 24 x\right ) e^{3}}{4} + \frac {\left (- 12 x + 12 + 4 e^{3}\right ) \log {\left (2 x \right )}}{4} + \frac {\log {\left (2 x \right )}^{2}}{4} + 9 + e^{6}}{x^{2}} \right )} + \log {\left (x - \log {\left (3 \right )} \right )}} \]
integrate((((ln(3)-x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x**2-6*x )*ln(1/4*(ln(2*x)**2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)**2+(-24*x+24)*exp (3)+36*x**2-72*x+36)/x**2)+((ln(3)-x)*ln(-ln(3)+x)+2*ln(3)-x)*ln(2*x)+((2* exp(3)+6-6*x)*ln(3)-2*x*exp(3)+6*x**2-6*x)*ln(-ln(3)+x)+(4*exp(3)+10)*ln(3 )-2*x*exp(3)-6*x**2-4*x)/(((ln(3)-x)*ln(2*x)+(2*exp(3)+6-6*x)*ln(3)-2*x*ex p(3)+6*x**2-6*x)*ln(1/4*(ln(2*x)**2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)**2 +(-24*x+24)*exp(3)+36*x**2-72*x+36)/x**2)**2+((2*ln(3)-2*x)*ln(-ln(3)+x)*l n(2*x)+((4*exp(3)-12*x+12)*ln(3)-4*x*exp(3)+12*x**2-12*x)*ln(-ln(3)+x))*ln (1/4*(ln(2*x)**2+(4*exp(3)-12*x+12)*ln(2*x)+4*exp(3)**2+(-24*x+24)*exp(3)+ 36*x**2-72*x+36)/x**2)+(ln(3)-x)*ln(-ln(3)+x)**2*ln(2*x)+((2*exp(3)+6-6*x) *ln(3)-2*x*exp(3)+6*x**2-6*x)*ln(-ln(3)+x)**2),x)
x/(log((9*x**2 - 18*x + (24 - 24*x)*exp(3)/4 + (-12*x + 12 + 4*exp(3))*log (2*x)/4 + log(2*x)**2/4 + 9 + exp(6))/x**2) + log(x - log(3)))
Time = 0.46 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.26 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=-\frac {x}{2 \, \log \left (2\right ) - 2 \, \log \left (6 \, x - 2 \, e^{3} - \log \left (2\right ) - \log \left (x\right ) - 6\right ) - \log \left (x - \log \left (3\right )\right ) + 2 \, \log \left (x\right )} \]
integrate((((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6 *x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)^2+(-24*x+24)* exp(3)+36*x^2-72*x+36)/x^2)+((log(3)-x)*log(-log(3)+x)+2*log(3)-x)*log(2*x )+((2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)+(4*exp(3)+ 10)*log(3)-2*x*exp(3)-6*x^2-4*x)/(((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*lo g(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x) +4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)^2+((2*log(3)-2*x)*log(- log(3)+x)*log(2*x)+((4*exp(3)-12*x+12)*log(3)-4*x*exp(3)+12*x^2-12*x)*log( -log(3)+x))*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)^2+(-2 4*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+(log(3)-x)*log(-log(3)+x)^2*log(2*x)+( (2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)^2),x, algorit hm=\
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (33) = 66\).
Time = 16.09 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.35 \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\frac {x}{\log \left (36 \, {\left (x - \log \left (3\right )\right )}^{2} - 24 \, {\left (x - \log \left (3\right )\right )} e^{3} + 72 \, {\left (x - \log \left (3\right )\right )} \log \left (3\right ) - 24 \, e^{3} \log \left (3\right ) + 36 \, \log \left (3\right )^{2} - 12 \, {\left (x - \log \left (3\right )\right )} \log \left (2 \, x\right ) + 4 \, e^{3} \log \left (2 \, x\right ) - 12 \, \log \left (3\right ) \log \left (2 \, x\right ) + \log \left (2 \, x\right )^{2} - 72 \, x + 4 \, e^{6} + 24 \, e^{3} + 12 \, \log \left (2 \, x\right ) + 36\right ) - 2 \, \log \left (2 \, x\right ) + \log \left (x - \log \left (3\right )\right )} \]
integrate((((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6 *x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)^2+(-24*x+24)* exp(3)+36*x^2-72*x+36)/x^2)+((log(3)-x)*log(-log(3)+x)+2*log(3)-x)*log(2*x )+((2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)+(4*exp(3)+ 10)*log(3)-2*x*exp(3)-6*x^2-4*x)/(((log(3)-x)*log(2*x)+(2*exp(3)+6-6*x)*lo g(3)-2*x*exp(3)+6*x^2-6*x)*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x) +4*exp(3)^2+(-24*x+24)*exp(3)+36*x^2-72*x+36)/x^2)^2+((2*log(3)-2*x)*log(- log(3)+x)*log(2*x)+((4*exp(3)-12*x+12)*log(3)-4*x*exp(3)+12*x^2-12*x)*log( -log(3)+x))*log(1/4*(log(2*x)^2+(4*exp(3)-12*x+12)*log(2*x)+4*exp(3)^2+(-2 4*x+24)*exp(3)+36*x^2-72*x+36)/x^2)+(log(3)-x)*log(-log(3)+x)^2*log(2*x)+( (2*exp(3)+6-6*x)*log(3)-2*x*exp(3)+6*x^2-6*x)*log(-log(3)+x)^2),x, algorit hm=\
x/(log(36*(x - log(3))^2 - 24*(x - log(3))*e^3 + 72*(x - log(3))*log(3) - 24*e^3*log(3) + 36*log(3)^2 - 12*(x - log(3))*log(2*x) + 4*e^3*log(2*x) - 12*log(3)*log(2*x) + log(2*x)^2 - 72*x + 4*e^6 + 24*e^3 + 12*log(2*x) + 36 ) - 2*log(2*x) + log(x - log(3)))
Timed out. \[ \int \frac {-4 x-2 e^3 x-6 x^2+\left (10+4 e^3\right ) \log (3)+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log (x-\log (3))+\log (2 x) (-x+2 \log (3)+(-x+\log (3)) \log (x-\log (3)))+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )}{\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)\right ) \log ^2(x-\log (3))+(-x+\log (3)) \log (2 x) \log ^2(x-\log (3))+\left (\left (-12 x-4 e^3 x+12 x^2+\left (12+4 e^3-12 x\right ) \log (3)\right ) \log (x-\log (3))+(-2 x+2 \log (3)) \log (2 x) \log (x-\log (3))\right ) \log \left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )+\left (-6 x-2 e^3 x+6 x^2+\left (6+2 e^3-6 x\right ) \log (3)+(-x+\log (3)) \log (2 x)\right ) \log ^2\left (\frac {36+4 e^6+e^3 (24-24 x)-72 x+36 x^2+\left (12+4 e^3-12 x\right ) \log (2 x)+\log ^2(2 x)}{4 x^2}\right )} \, dx=\int \frac {4\,x+\ln \left (\frac {{\mathrm {e}}^6-18\,x+\frac {\ln \left (2\,x\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )}{4}+\frac {{\ln \left (2\,x\right )}^2}{4}+9\,x^2-\frac {{\mathrm {e}}^3\,\left (24\,x-24\right )}{4}+9}{x^2}\right )\,\left (6\,x+2\,x\,{\mathrm {e}}^3+\ln \left (2\,x\right )\,\left (x-\ln \left (3\right )\right )-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )+2\,x\,{\mathrm {e}}^3+\ln \left (2\,x\right )\,\left (x-2\,\ln \left (3\right )+\ln \left (x-\ln \left (3\right )\right )\,\left (x-\ln \left (3\right )\right )\right )+6\,x^2+\ln \left (x-\ln \left (3\right )\right )\,\left (6\,x+2\,x\,{\mathrm {e}}^3-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )-\ln \left (3\right )\,\left (4\,{\mathrm {e}}^3+10\right )}{{\ln \left (x-\ln \left (3\right )\right )}^2\,\left (6\,x+2\,x\,{\mathrm {e}}^3-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )+\ln \left (\frac {{\mathrm {e}}^6-18\,x+\frac {\ln \left (2\,x\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )}{4}+\frac {{\ln \left (2\,x\right )}^2}{4}+9\,x^2-\frac {{\mathrm {e}}^3\,\left (24\,x-24\right )}{4}+9}{x^2}\right )\,\left (\ln \left (x-\ln \left (3\right )\right )\,\left (12\,x+4\,x\,{\mathrm {e}}^3-\ln \left (3\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )-12\,x^2\right )+\ln \left (x-\ln \left (3\right )\right )\,\ln \left (2\,x\right )\,\left (2\,x-2\,\ln \left (3\right )\right )\right )+{\ln \left (\frac {{\mathrm {e}}^6-18\,x+\frac {\ln \left (2\,x\right )\,\left (4\,{\mathrm {e}}^3-12\,x+12\right )}{4}+\frac {{\ln \left (2\,x\right )}^2}{4}+9\,x^2-\frac {{\mathrm {e}}^3\,\left (24\,x-24\right )}{4}+9}{x^2}\right )}^2\,\left (6\,x+2\,x\,{\mathrm {e}}^3+\ln \left (2\,x\right )\,\left (x-\ln \left (3\right )\right )-\ln \left (3\right )\,\left (2\,{\mathrm {e}}^3-6\,x+6\right )-6\,x^2\right )+{\ln \left (x-\ln \left (3\right )\right )}^2\,\ln \left (2\,x\right )\,\left (x-\ln \left (3\right )\right )} \,d x \]
int((4*x + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log( 2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/x^2)*(6*x + 2*x*exp(3) + lo g(2*x)*(x - log(3)) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + 2*x*exp(3) + log(2*x)*(x - 2*log(3) + log(x - log(3))*(x - log(3))) + 6*x^2 + log(x - l og(3))*(6*x + 2*x*exp(3) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) - log(3)*( 4*exp(3) + 10))/(log(x - log(3))^2*(6*x + 2*x*exp(3) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12)) /4 + log(2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/x^2)*(log(x - log( 3))*(12*x + 4*x*exp(3) - log(3)*(4*exp(3) - 12*x + 12) - 12*x^2) + log(x - log(3))*log(2*x)*(2*x - 2*log(3))) + log((exp(6) - 18*x + (log(2*x)*(4*ex p(3) - 12*x + 12))/4 + log(2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/ x^2)^2*(6*x + 2*x*exp(3) + log(2*x)*(x - log(3)) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + log(x - log(3))^2*log(2*x)*(x - log(3))),x)
int((4*x + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12))/4 + log( 2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/x^2)*(6*x + 2*x*exp(3) + lo g(2*x)*(x - log(3)) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + 2*x*exp(3) + log(2*x)*(x - 2*log(3) + log(x - log(3))*(x - log(3))) + 6*x^2 + log(x - l og(3))*(6*x + 2*x*exp(3) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) - log(3)*( 4*exp(3) + 10))/(log(x - log(3))^2*(6*x + 2*x*exp(3) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + log((exp(6) - 18*x + (log(2*x)*(4*exp(3) - 12*x + 12)) /4 + log(2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/x^2)*(log(x - log( 3))*(12*x + 4*x*exp(3) - log(3)*(4*exp(3) - 12*x + 12) - 12*x^2) + log(x - log(3))*log(2*x)*(2*x - 2*log(3))) + log((exp(6) - 18*x + (log(2*x)*(4*ex p(3) - 12*x + 12))/4 + log(2*x)^2/4 + 9*x^2 - (exp(3)*(24*x - 24))/4 + 9)/ x^2)^2*(6*x + 2*x*exp(3) + log(2*x)*(x - log(3)) - log(3)*(2*exp(3) - 6*x + 6) - 6*x^2) + log(x - log(3))^2*log(2*x)*(x - log(3))), x)