Integrand size = 146, antiderivative size = 28 \[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=4 \log \left (2 e^{-\frac {x}{\log (8)}}-4 x+\frac {4}{3 (4+\log (x))}\right ) \]
\[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=\int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx \]
Integrate[(192*x + E^(x/Log[8])*(8 + 384*x)*Log[8] + (96*x + 192*E^(x/Log[ 8])*x*Log[8])*Log[x] + (12*x + 24*E^(x/Log[8])*x*Log[8])*Log[x]^2)/(-48*x* Log[8] + E^(x/Log[8])*(-8*x + 96*x^2)*Log[8] + (-24*x*Log[8] + E^(x/Log[8] )*(-2*x + 48*x^2)*Log[8])*Log[x] + (-3*x*Log[8] + 6*E^(x/Log[8])*x^2*Log[8 ])*Log[x]^2),x]
Integrate[(192*x + E^(x/Log[8])*(8 + 384*x)*Log[8] + (96*x + 192*E^(x/Log[ 8])*x*Log[8])*Log[x] + (12*x + 24*E^(x/Log[8])*x*Log[8])*Log[x]^2)/(-48*x* Log[8] + E^(x/Log[8])*(-8*x + 96*x^2)*Log[8] + (-24*x*Log[8] + E^(x/Log[8] )*(-2*x + 48*x^2)*Log[8])*Log[x] + (-3*x*Log[8] + 6*E^(x/Log[8])*x^2*Log[8 ])*Log[x]^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.
| \(\displaystyle \int \frac {192 x+\left (12 x+24 x \log (8) e^{\frac {x}{\log (8)}}\right ) \log ^2(x)+\left (96 x+192 x \log (8) e^{\frac {x}{\log (8)}}\right ) \log (x)+(384 x+8) \log (8) e^{\frac {x}{\log (8)}}}{\left (6 x^2 \log (8) e^{\frac {x}{\log (8)}}-3 x \log (8)\right ) \log ^2(x)+\left (\left (48 x^2-2 x\right ) \log (8) e^{\frac {x}{\log (8)}}-24 x \log (8)\right ) \log (x)+\left (96 x^2-8 x\right ) \log (8) e^{\frac {x}{\log (8)}}-48 x \log (8)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-192 x-\left (\left (12 x+24 x \log (8) e^{\frac {x}{\log (8)}}\right ) \log ^2(x)\right )-\left (96 x+192 x \log (8) e^{\frac {x}{\log (8)}}\right ) \log (x)-(384 x+8) \log (8) e^{\frac {x}{\log (8)}}}{x \log (8) (\log (x)+4) \left (-24 x e^{\frac {x}{\log (8)}}-6 x e^{\frac {x}{\log (8)}} \log (x)+2 e^{\frac {x}{\log (8)}}+3 \log (x)+12\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {4 \left (3 \left (2 e^{\frac {x}{\log (8)}} \log (8) x+x\right ) \log ^2(x)+24 \left (2 e^{\frac {x}{\log (8)}} \log (8) x+x\right ) \log (x)+48 x+2 e^{\frac {x}{\log (8)}} (48 x+1) \log (8)\right )}{x (\log (x)+4) \left (-24 e^{\frac {x}{\log (8)}} x-6 e^{\frac {x}{\log (8)}} \log (x) x+2 e^{\frac {x}{\log (8)}}+3 \log (x)+12\right )}dx}{\log (8)}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {4 \int \frac {3 \left (2 e^{\frac {x}{\log (8)}} \log (8) x+x\right ) \log ^2(x)+24 \left (2 e^{\frac {x}{\log (8)}} \log (8) x+x\right ) \log (x)+48 x+2 e^{\frac {x}{\log (8)}} (48 x+1) \log (8)}{x (\log (x)+4) \left (-24 e^{\frac {x}{\log (8)}} x-6 e^{\frac {x}{\log (8)}} \log (x) x+2 e^{\frac {x}{\log (8)}}+3 \log (x)+12\right )}dx}{\log (8)}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {4 \int \left (\frac {3 \left (-3 \log ^2(x) x^2-24 \log (x) x^2-48 x^2-3 \log (8) \log ^2(x) x+(1-24 \log (8)) \log (x) x+4 (1-12 \log (8)) x-\log (8)\right )}{x (-3 \log (x) x-12 x+1) \left (-24 e^{\frac {x}{\log (8)}} x-6 e^{\frac {x}{\log (8)}} \log (x) x+2 e^{\frac {x}{\log (8)}}+3 \log (x)+12\right )}-\frac {\log (8) \left (3 x \log ^2(x)+24 x \log (x)+48 x+1\right )}{x (\log (x)+4) (3 \log (x) x+12 x-1)}\right )dx}{\log (8)}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {4 \left (-9 \log (8) \int \frac {\log ^2(x)}{(3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx-9 \int \frac {x \log ^2(x)}{(3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx-3 \log (8) \int \frac {1}{3 \log (x) x+12 x-1}dx-\log (8) \int \frac {1}{x (3 \log (x) x+12 x-1)}dx+12 (1-12 \log (8)) \int \frac {1}{(3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx-3 \log (8) \int \frac {1}{x (3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx-144 \int \frac {x}{(3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx+3 (1-24 \log (8)) \int \frac {\log (x)}{(3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx-72 \int \frac {x \log (x)}{(3 \log (x) x+12 x-1) \left (24 e^{\frac {x}{\log (8)}} x+6 e^{\frac {x}{\log (8)}} \log (x) x-2 e^{\frac {x}{\log (8)}}-3 \log (x)-12\right )}dx-\log (8) \log (x)+\log (8) \log (\log (x)+4)\right )}{\log (8)}\) |
Int[(192*x + E^(x/Log[8])*(8 + 384*x)*Log[8] + (96*x + 192*E^(x/Log[8])*x* Log[8])*Log[x] + (12*x + 24*E^(x/Log[8])*x*Log[8])*Log[x]^2)/(-48*x*Log[8] + E^(x/Log[8])*(-8*x + 96*x^2)*Log[8] + (-24*x*Log[8] + E^(x/Log[8])*(-2* x + 48*x^2)*Log[8])*Log[x] + (-3*x*Log[8] + 6*E^(x/Log[8])*x^2*Log[8])*Log [x]^2),x]
3.5.85.3.1 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]]
Time = 3.05 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11
| method | result | size |
| norman | \(-\frac {4 x}{3 \ln \left (2\right )}-4 \ln \left (\ln \left (x \right )+4\right )+4 \ln \left (6 \ln \left (x \right ) {\mathrm e}^{\frac {x}{3 \ln \left (2\right )}} x +24 x \,{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}-2 \,{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}-3 \ln \left (x \right )-12\right )\) | \(59\) |
| parallelrisch | \(\frac {-12 \ln \left (\ln \left (x \right )+4\right ) \ln \left (2\right )+12 \ln \left (\ln \left (x \right ) {\mathrm e}^{\frac {x}{3 \ln \left (2\right )}} x +4 x \,{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}-\frac {\ln \left (x \right )}{2}-\frac {{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}}{3}-2\right ) \ln \left (2\right )-4 x}{3 \ln \left (2\right )}\) | \(64\) |
| risch | \(4 \ln \left (x \right )+4 \ln \left ({\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}-\frac {1}{2 x}\right )-\frac {4 x}{3 \ln \left (2\right )}+4 \ln \left (\ln \left (x \right )+\frac {8 x \,{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}-\frac {2 \,{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}}{3}-4}{2 x \,{\mathrm e}^{\frac {x}{3 \ln \left (2\right )}}-1}\right )-4 \ln \left (\ln \left (x \right )+4\right )\) | \(83\) |
int(((72*x*ln(2)*exp(1/3*x/ln(2))+12*x)*ln(x)^2+(576*x*ln(2)*exp(1/3*x/ln( 2))+96*x)*ln(x)+3*(384*x+8)*ln(2)*exp(1/3*x/ln(2))+192*x)/((18*x^2*ln(2)*e xp(1/3*x/ln(2))-9*x*ln(2))*ln(x)^2+(3*(48*x^2-2*x)*ln(2)*exp(1/3*x/ln(2))- 72*x*ln(2))*ln(x)+3*(96*x^2-8*x)*ln(2)*exp(1/3*x/ln(2))-144*x*ln(2)),x,met hod=_RETURNVERBOSE)
-4/3*x/ln(2)-4*ln(ln(x)+4)+4*ln(6*ln(x)*exp(1/3*x/ln(2))*x+24*x*exp(1/3*x/ ln(2))-2*exp(1/3*x/ln(2))-3*ln(x)-12)
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.64 \[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=\frac {4 \, {\left (3 \, \log \left (2\right ) \log \left (x\right ) + 3 \, \log \left (2\right ) \log \left (\frac {2 \, {\left (12 \, x - 1\right )} e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} + 3 \, {\left (2 \, x e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} - 1\right )} \log \left (x\right ) - 12}{2 \, x e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} - 1}\right ) + 3 \, \log \left (2\right ) \log \left (\frac {2 \, x e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} - 1}{x}\right ) - 3 \, \log \left (2\right ) \log \left (\log \left (x\right ) + 4\right ) - x\right )}}{3 \, \log \left (2\right )} \]
integrate(((72*x*log(2)*exp(1/3*x/log(2))+12*x)*log(x)^2+(576*x*log(2)*exp (1/3*x/log(2))+96*x)*log(x)+3*(384*x+8)*log(2)*exp(1/3*x/log(2))+192*x)/(( 18*x^2*log(2)*exp(1/3*x/log(2))-9*x*log(2))*log(x)^2+(3*(48*x^2-2*x)*log(2 )*exp(1/3*x/log(2))-72*x*log(2))*log(x)+3*(96*x^2-8*x)*log(2)*exp(1/3*x/lo g(2))-144*x*log(2)),x, algorithm=\
4/3*(3*log(2)*log(x) + 3*log(2)*log((2*(12*x - 1)*e^(1/3*x/log(2)) + 3*(2* x*e^(1/3*x/log(2)) - 1)*log(x) - 12)/(2*x*e^(1/3*x/log(2)) - 1)) + 3*log(2 )*log((2*x*e^(1/3*x/log(2)) - 1)/x) - 3*log(2)*log(log(x) + 4) - x)/log(2)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (24) = 48\).
Time = 2.05 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=\frac {- 4 x + 12 \log {\left (2 \right )} \log {\left (x \right )}}{3 \log {\left (2 \right )}} + 4 \log {\left (\frac {- 3 \log {\left (x \right )} - 12}{6 x \log {\left (x \right )} + 24 x - 2} + e^{\frac {x}{3 \log {\left (2 \right )}}} \right )} - 4 \log {\left (\log {\left (x \right )} + 4 \right )} + 4 \log {\left (\log {\left (x \right )} + \frac {96 x - 8}{24 x} \right )} \]
integrate(((72*x*ln(2)*exp(1/3*x/ln(2))+12*x)*ln(x)**2+(576*x*ln(2)*exp(1/ 3*x/ln(2))+96*x)*ln(x)+3*(384*x+8)*ln(2)*exp(1/3*x/ln(2))+192*x)/((18*x**2 *ln(2)*exp(1/3*x/ln(2))-9*x*ln(2))*ln(x)**2+(3*(48*x**2-2*x)*ln(2)*exp(1/3 *x/ln(2))-72*x*ln(2))*ln(x)+3*(96*x**2-8*x)*ln(2)*exp(1/3*x/ln(2))-144*x*l n(2)),x)
(-4*x + 12*log(2)*log(x))/(3*log(2)) + 4*log((-3*log(x) - 12)/(6*x*log(x) + 24*x - 2) + exp(x/(3*log(2)))) - 4*log(log(x) + 4) + 4*log(log(x) + (96* x - 8)/(24*x))
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (25) = 50\).
Time = 0.34 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.86 \[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=-\frac {4 \, x}{3 \, \log \left (2\right )} + 4 \, \log \left (x\right ) + 4 \, \log \left (\frac {2 \, {\left (3 \, x \log \left (x\right ) + 12 \, x - 1\right )} e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} - 3 \, \log \left (x\right ) - 12}{2 \, {\left (3 \, x \log \left (x\right ) + 12 \, x - 1\right )}}\right ) + 4 \, \log \left (\frac {3 \, x \log \left (x\right ) + 12 \, x - 1}{3 \, x}\right ) - 4 \, \log \left (\log \left (x\right ) + 4\right ) \]
integrate(((72*x*log(2)*exp(1/3*x/log(2))+12*x)*log(x)^2+(576*x*log(2)*exp (1/3*x/log(2))+96*x)*log(x)+3*(384*x+8)*log(2)*exp(1/3*x/log(2))+192*x)/(( 18*x^2*log(2)*exp(1/3*x/log(2))-9*x*log(2))*log(x)^2+(3*(48*x^2-2*x)*log(2 )*exp(1/3*x/log(2))-72*x*log(2))*log(x)+3*(96*x^2-8*x)*log(2)*exp(1/3*x/lo g(2))-144*x*log(2)),x, algorithm=\
-4/3*x/log(2) + 4*log(x) + 4*log(1/2*(2*(3*x*log(x) + 12*x - 1)*e^(1/3*x/l og(2)) - 3*log(x) - 12)/(3*x*log(x) + 12*x - 1)) + 4*log(1/3*(3*x*log(x) + 12*x - 1)/x) - 4*log(log(x) + 4)
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (25) = 50\).
Time = 0.32 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.36 \[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=\frac {4 \, {\left (3 \, \log \left (2\right ) \log \left (6 \, x e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} \log \left (x\right ) + 24 \, x e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} - 2 \, e^{\left (\frac {x}{3 \, \log \left (2\right )}\right )} - 3 \, \log \left (x\right ) - 12\right ) + 3 \, \log \left (2\right ) \log \left (3 \, x \log \left (x\right ) + 12 \, x - 1\right ) - 3 \, \log \left (2\right ) \log \left (-3 \, x \log \left (x\right ) - 12 \, x + 1\right ) - 3 \, \log \left (2\right ) \log \left (\log \left (x\right ) + 4\right ) - x\right )}}{3 \, \log \left (2\right )} \]
integrate(((72*x*log(2)*exp(1/3*x/log(2))+12*x)*log(x)^2+(576*x*log(2)*exp (1/3*x/log(2))+96*x)*log(x)+3*(384*x+8)*log(2)*exp(1/3*x/log(2))+192*x)/(( 18*x^2*log(2)*exp(1/3*x/log(2))-9*x*log(2))*log(x)^2+(3*(48*x^2-2*x)*log(2 )*exp(1/3*x/log(2))-72*x*log(2))*log(x)+3*(96*x^2-8*x)*log(2)*exp(1/3*x/lo g(2))-144*x*log(2)),x, algorithm=\
4/3*(3*log(2)*log(6*x*e^(1/3*x/log(2))*log(x) + 24*x*e^(1/3*x/log(2)) - 2* e^(1/3*x/log(2)) - 3*log(x) - 12) + 3*log(2)*log(3*x*log(x) + 12*x - 1) - 3*log(2)*log(-3*x*log(x) - 12*x + 1) - 3*log(2)*log(log(x) + 4) - x)/log(2 )
Timed out. \[ \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx=\int -\frac {\left (12\,x+72\,x\,{\mathrm {e}}^{\frac {x}{3\,\ln \left (2\right )}}\,\ln \left (2\right )\right )\,{\ln \left (x\right )}^2+\left (96\,x+576\,x\,{\mathrm {e}}^{\frac {x}{3\,\ln \left (2\right )}}\,\ln \left (2\right )\right )\,\ln \left (x\right )+192\,x+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \left (2\right )}}\,\ln \left (2\right )\,\left (384\,x+8\right )}{\left (9\,x\,\ln \left (2\right )-18\,x^2\,{\mathrm {e}}^{\frac {x}{3\,\ln \left (2\right )}}\,\ln \left (2\right )\right )\,{\ln \left (x\right )}^2+\left (72\,x\,\ln \left (2\right )+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \left (2\right )}}\,\ln \left (2\right )\,\left (2\,x-48\,x^2\right )\right )\,\ln \left (x\right )+144\,x\,\ln \left (2\right )+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \left (2\right )}}\,\ln \left (2\right )\,\left (8\,x-96\,x^2\right )} \,d x \]
int(-(192*x + log(x)^2*(12*x + 72*x*exp(x/(3*log(2)))*log(2)) + log(x)*(96 *x + 576*x*exp(x/(3*log(2)))*log(2)) + 3*exp(x/(3*log(2)))*log(2)*(384*x + 8))/(log(x)*(72*x*log(2) + 3*exp(x/(3*log(2)))*log(2)*(2*x - 48*x^2)) + 1 44*x*log(2) + log(x)^2*(9*x*log(2) - 18*x^2*exp(x/(3*log(2)))*log(2)) + 3* exp(x/(3*log(2)))*log(2)*(8*x - 96*x^2)),x)
int(-(192*x + log(x)^2*(12*x + 72*x*exp(x/(3*log(2)))*log(2)) + log(x)*(96 *x + 576*x*exp(x/(3*log(2)))*log(2)) + 3*exp(x/(3*log(2)))*log(2)*(384*x + 8))/(log(x)*(72*x*log(2) + 3*exp(x/(3*log(2)))*log(2)*(2*x - 48*x^2)) + 1 44*x*log(2) + log(x)^2*(9*x*log(2) - 18*x^2*exp(x/(3*log(2)))*log(2)) + 3* exp(x/(3*log(2)))*log(2)*(8*x - 96*x^2)), x)