Integrand size = 175, antiderivative size = 29 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {3+\frac {1}{5} e^x \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x} \]
Time = 5.21 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {15+e^x \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{5 x} \]
Integrate[(2*E^x + (-45 - 3*E^x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2] + (-15 - E^x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2]*Log[Log[144*Log[L og[x]]^2]] + (E^x*(-3 + 3*x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2] + E ^x*(-1 + x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2]*Log[Log[144*Log[Log[ x]]^2]])*Log[(3 + Log[Log[144*Log[Log[x]]^2]])/x])/(15*x^2*Log[x]*Log[Log[ x]]*Log[144*Log[Log[x]]^2] + 5*x^2*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^ 2]*Log[Log[144*Log[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.
| \(\displaystyle \int \frac {2 e^x+\left (-3 e^x-45\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-e^x-15\right ) \log (x) \log (\log (x)) \log \left (\log \left (144 \log ^2(\log (x))\right )\right ) \log \left (144 \log ^2(\log (x))\right )+\left (e^x (3 x-3) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (x-1) \log (x) \log (\log (x)) \log \left (\log \left (144 \log ^2(\log (x))\right )\right ) \log \left (144 \log ^2(\log (x))\right )\right ) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-e^x+e^x (x-1) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right )+\frac {2 e^x}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3\right )}-15}{5 x^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{5} \int -\frac {e^x (1-x) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right )+e^x-\frac {2 e^x}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3\right )}+15}{x^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{5} \int \frac {e^x (1-x) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right )+e^x-\frac {2 e^x}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3\right )}+15}{x^2}dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle -\frac {1}{5} \int \left (\frac {15}{x^2}-\frac {e^x \left (-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )-\log (x) \log (\log (x)) \log \left (\log \left (144 \log ^2(\log (x))\right )\right ) \log \left (144 \log ^2(\log (x))\right )+3 x \log (x) \log (\log (x)) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right ) \log \left (144 \log ^2(\log (x))\right )-3 \log (x) \log (\log (x)) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right ) \log \left (144 \log ^2(\log (x))\right )+x \log (x) \log (\log (x)) \log \left (\log \left (144 \log ^2(\log (x))\right )\right ) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right ) \log \left (144 \log ^2(\log (x))\right )-\log (x) \log (\log (x)) \log \left (\log \left (144 \log ^2(\log (x))\right )\right ) \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3}{x}\right ) \log \left (144 \log ^2(\log (x))\right )+2\right )}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{5} \left (2 \int \frac {e^x}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3\right )}dx-\int \frac {e^x \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}+\frac {3}{x}\right )}{x^2}dx+\int \frac {e^x \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}+\frac {3}{x}\right )}{x}dx-\operatorname {ExpIntegralEi}(x)+\frac {e^x}{x}+\frac {15}{x}\right )\) |
Int[(2*E^x + (-45 - 3*E^x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2] + (-1 5 - E^x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2]*Log[Log[144*Log[Log[x]] ^2]] + (E^x*(-3 + 3*x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2] + E^x*(-1 + x)*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2]*Log[Log[144*Log[Log[x]]^2] ])*Log[(3 + Log[Log[144*Log[Log[x]]^2]])/x])/(15*x^2*Log[x]*Log[Log[x]]*Lo g[144*Log[Log[x]]^2] + 5*x^2*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2]*Log [Log[144*Log[Log[x]]^2]]),x]
3.22.2.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.82 (sec) , antiderivative size = 443, normalized size of antiderivative = 15.28
\[\frac {{\mathrm e}^{x} \ln \left (\ln \left (2 \ln \left (3\right )+4 \ln \left (2\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )}{5 x}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i}{x}\right ) \operatorname {csgn}\left (i \left (\ln \left (2 \ln \left (12\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )\right ) \operatorname {csgn}\left (\frac {i \left (\ln \left (2 \ln \left (12\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )}{x}\right ) {\mathrm e}^{x}-i \pi \,\operatorname {csgn}\left (\frac {i}{x}\right ) {\operatorname {csgn}\left (\frac {i \left (\ln \left (2 \ln \left (12\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )}{x}\right )}^{2} {\mathrm e}^{x}-i \pi \,\operatorname {csgn}\left (i \left (\ln \left (2 \ln \left (12\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )\right ) {\operatorname {csgn}\left (\frac {i \left (\ln \left (2 \ln \left (12\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )}{x}\right )}^{2} {\mathrm e}^{x}+i \pi {\operatorname {csgn}\left (\frac {i \left (\ln \left (2 \ln \left (12\right )+2 \ln \left (\ln \left (\ln \left (x \right )\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )+\operatorname {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )\right )}^{2}}{2}\right )+3\right )}{x}\right )}^{3} {\mathrm e}^{x}+2 \,{\mathrm e}^{x} \ln \left (x \right )-30}{10 x}\]
int((((-1+x)*exp(x)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2)*ln(ln(144*ln(ln(x) )^2))+(-3+3*x)*exp(x)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2))*ln((ln(ln(144*l n(ln(x))^2))+3)/x)+(-exp(x)-15)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2)*ln(ln( 144*ln(ln(x))^2))+(-3*exp(x)-45)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2)+2*exp (x))/(5*x^2*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2)*ln(ln(144*ln(ln(x))^2))+15 *x^2*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2)),x)
1/5/x*exp(x)*ln(ln(2*ln(3)+4*ln(2)+2*ln(ln(ln(x)))-1/2*I*Pi*csgn(I*ln(ln(x ))^2)*(-csgn(I*ln(ln(x))^2)+csgn(I*ln(ln(x))))^2)+3)-1/10*(I*Pi*csgn(I/x)* csgn(I*(ln(2*ln(12)+2*ln(ln(ln(x)))-1/2*I*Pi*csgn(I*ln(ln(x))^2)*(-csgn(I* ln(ln(x))^2)+csgn(I*ln(ln(x))))^2)+3))*csgn(I/x*(ln(2*ln(12)+2*ln(ln(ln(x) ))-1/2*I*Pi*csgn(I*ln(ln(x))^2)*(-csgn(I*ln(ln(x))^2)+csgn(I*ln(ln(x))))^2 )+3))*exp(x)-I*Pi*csgn(I/x)*csgn(I/x*(ln(2*ln(12)+2*ln(ln(ln(x)))-1/2*I*Pi *csgn(I*ln(ln(x))^2)*(-csgn(I*ln(ln(x))^2)+csgn(I*ln(ln(x))))^2)+3))^2*exp (x)-I*Pi*csgn(I*(ln(2*ln(12)+2*ln(ln(ln(x)))-1/2*I*Pi*csgn(I*ln(ln(x))^2)* (-csgn(I*ln(ln(x))^2)+csgn(I*ln(ln(x))))^2)+3))*csgn(I/x*(ln(2*ln(12)+2*ln (ln(ln(x)))-1/2*I*Pi*csgn(I*ln(ln(x))^2)*(-csgn(I*ln(ln(x))^2)+csgn(I*ln(l n(x))))^2)+3))^2*exp(x)+I*Pi*csgn(I/x*(ln(2*ln(12)+2*ln(ln(ln(x)))-1/2*I*P i*csgn(I*ln(ln(x))^2)*(-csgn(I*ln(ln(x))^2)+csgn(I*ln(ln(x))))^2)+3))^3*ex p(x)+2*exp(x)*ln(x)-30)/x
Time = 0.24 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {e^{x} \log \left (\frac {\log \left (\log \left (144 \, \log \left (\log \left (x\right )\right )^{2}\right )\right ) + 3}{x}\right ) + 15}{5 \, x} \]
integrate((((-1+x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x))^2)*log(lo g(144*log(log(x))^2))+(-3+3*x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x ))^2))*log((log(log(144*log(log(x))^2))+3)/x)+(-exp(x)-15)*log(x)*log(log( x))*log(144*log(log(x))^2)*log(log(144*log(log(x))^2))+(-3*exp(x)-45)*log( x)*log(log(x))*log(144*log(log(x))^2)+2*exp(x))/(5*x^2*log(x)*log(log(x))* log(144*log(log(x))^2)*log(log(144*log(log(x))^2))+15*x^2*log(x)*log(log(x ))*log(144*log(log(x))^2)),x, algorithm=\
Timed out. \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\text {Timed out} \]
integrate((((-1+x)*exp(x)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))**2)*ln(ln(144*l n(ln(x))**2))+(-3+3*x)*exp(x)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))**2))*ln((ln (ln(144*ln(ln(x))**2))+3)/x)+(-exp(x)-15)*ln(x)*ln(ln(x))*ln(144*ln(ln(x)) **2)*ln(ln(144*ln(ln(x))**2))+(-3*exp(x)-45)*ln(x)*ln(ln(x))*ln(144*ln(ln( x))**2)+2*exp(x))/(5*x**2*ln(x)*ln(ln(x))*ln(144*ln(ln(x))**2)*ln(ln(144*l n(ln(x))**2))+15*x**2*ln(x)*ln(ln(x))*ln(144*ln(ln(x))**2)),x)
Time = 0.39 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=-\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (\log \left (2\right ) + \log \left (\log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (\log \left (\log \left (x\right )\right )\right )\right ) + 3\right ) - 15}{5 \, x} \]
integrate((((-1+x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x))^2)*log(lo g(144*log(log(x))^2))+(-3+3*x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x ))^2))*log((log(log(144*log(log(x))^2))+3)/x)+(-exp(x)-15)*log(x)*log(log( x))*log(144*log(log(x))^2)*log(log(144*log(log(x))^2))+(-3*exp(x)-45)*log( x)*log(log(x))*log(144*log(log(x))^2)+2*exp(x))/(5*x^2*log(x)*log(log(x))* log(144*log(log(x))^2)*log(log(144*log(log(x))^2))+15*x^2*log(x)*log(log(x ))*log(144*log(log(x))^2)),x, algorithm=\
Time = 2.07 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=-\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (\log \left (\log \left (144 \, \log \left (\log \left (x\right )\right )^{2}\right )\right ) + 3\right ) - 15}{5 \, x} \]
integrate((((-1+x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x))^2)*log(lo g(144*log(log(x))^2))+(-3+3*x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x ))^2))*log((log(log(144*log(log(x))^2))+3)/x)+(-exp(x)-15)*log(x)*log(log( x))*log(144*log(log(x))^2)*log(log(144*log(log(x))^2))+(-3*exp(x)-45)*log( x)*log(log(x))*log(144*log(log(x))^2)+2*exp(x))/(5*x^2*log(x)*log(log(x))* log(144*log(log(x))^2)*log(log(144*log(log(x))^2))+15*x^2*log(x)*log(log(x ))*log(144*log(log(x))^2)),x, algorithm=\
Timed out. \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\int \frac {2\,{\mathrm {e}}^x+\ln \left (\frac {\ln \left (\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\right )+3}{x}\right )\,\left (\ln \left (\ln \left (x\right )\right )\,{\mathrm {e}}^x\,\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\,\ln \left (x\right )\,\left (3\,x-3\right )+\ln \left (\ln \left (x\right )\right )\,{\mathrm {e}}^x\,\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\,\ln \left (x\right )\,\ln \left (\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\right )\,\left (x-1\right )\right )-\ln \left (\ln \left (x\right )\right )\,\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\,\ln \left (x\right )\,\left (3\,{\mathrm {e}}^x+45\right )-\ln \left (\ln \left (x\right )\right )\,\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\,\ln \left (x\right )\,\ln \left (\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\right )\,\left ({\mathrm {e}}^x+15\right )}{15\,x^2\,\ln \left (\ln \left (x\right )\right )\,\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\,\ln \left (x\right )+5\,x^2\,\ln \left (\ln \left (x\right )\right )\,\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\,\ln \left (x\right )\,\ln \left (\ln \left (144\,{\ln \left (\ln \left (x\right )\right )}^2\right )\right )} \,d x \]
int((2*exp(x) + log((log(log(144*log(log(x))^2)) + 3)/x)*(log(log(x))*exp( x)*log(144*log(log(x))^2)*log(x)*(3*x - 3) + log(log(x))*exp(x)*log(144*lo g(log(x))^2)*log(x)*log(log(144*log(log(x))^2))*(x - 1)) - log(log(x))*log (144*log(log(x))^2)*log(x)*(3*exp(x) + 45) - log(log(x))*log(144*log(log(x ))^2)*log(x)*log(log(144*log(log(x))^2))*(exp(x) + 15))/(15*x^2*log(log(x) )*log(144*log(log(x))^2)*log(x) + 5*x^2*log(log(x))*log(144*log(log(x))^2) *log(x)*log(log(144*log(log(x))^2))),x)
int((2*exp(x) + log((log(log(144*log(log(x))^2)) + 3)/x)*(log(log(x))*exp( x)*log(144*log(log(x))^2)*log(x)*(3*x - 3) + log(log(x))*exp(x)*log(144*lo g(log(x))^2)*log(x)*log(log(144*log(log(x))^2))*(x - 1)) - log(log(x))*log (144*log(log(x))^2)*log(x)*(3*exp(x) + 45) - log(log(x))*log(144*log(log(x ))^2)*log(x)*log(log(144*log(log(x))^2))*(exp(x) + 15))/(15*x^2*log(log(x) )*log(144*log(log(x))^2)*log(x) + 5*x^2*log(log(x))*log(144*log(log(x))^2) *log(x)*log(log(144*log(log(x))^2))), x)