\(\int \frac {2 e^x+(-45-3 e^x) \log (x) \log (\log (x)) \log (144 \log ^2(\log (x)))+(-15-e^x) \log (x) \log (\log (x)) \log (144 \log ^2(\log (x))) \log (\log (144 \log ^2(\log (x))))+(e^x (-3+3 x) \log (x) \log (\log (x)) \log (144 \log ^2(\log (x)))+e^x (-1+x) \log (x) \log (\log (x)) \log (144 \log ^2(\log (x))) \log (\log (144 \log ^2(\log (x))))) \log (\frac {3+\log (\log (144 \log ^2(\log (x))))}{x})}{15 x^2 \log (x) \log (\log (x)) \log (144 \log ^2(\log (x)))+5 x^2 \log (x) \log (\log (x)) \log (144 \log ^2(\log (x))) \log (\log (144 \log ^2(\log (x))))} \, dx\) [2102]

Optimal result

Integrand size = 175, antiderivative size = 29 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {3+\frac {1}{5} e^x \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x} \] Output:

(3+1/5*exp(x)*ln((ln(ln(144*ln(ln(x))^2))+3)/x))/x
 

Mathematica [A] (verified)

Time = 4.49 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {15+e^x \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{5 x} \] Input:

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]
 

Output:

(15 + E^x*Log[(3 + Log[Log[144*Log[Log[x]]^2]])/x])/(5*x)
 

Rubi [F]

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

\(\displaystyle \frac {1}{5} \left (2 \int \frac {e^x}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (\log \left (\log \left (144 \log ^2(\log (x))\right )\right )+3\right )}dx-\int \frac {e^x \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}+\frac {3}{x}\right )}{x^2}dx+\int \frac {e^x \log \left (\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}+\frac {3}{x}\right )}{x}dx-\operatorname {ExpIntegralEi}(x)+\frac {e^x}{x}+\frac {15}{x}\right )\)

Input:

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]
 

Output:

$Aborted
 

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.41 (sec) , antiderivative size = 443, normalized size of antiderivative = 15.28

\[\frac {{\mathrm e}^{x} \ln \left (\ln \left (4 \ln \left (2\right )+2 \ln \left (3\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 (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 (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 ) \operatorname {csgn}\left (\frac {i}{x}\right ) {\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}-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 )}^{2} \operatorname {csgn}\left (\frac {i}{x}\right ) {\mathrm e}^{x}+2 \,{\mathrm e}^{x} \ln \left (x \right )-30}{10 x}\]

Input:

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)
 

Output:

1/5/x*exp(x)*ln(ln(4*ln(2)+2*ln(3)+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*(l 
n(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))^2*e 
xp(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 
(ln(x))))^2)+3))*csgn(I/x)*exp(x)+I*Pi*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))^3*exp(x)-I*Pi*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*csgn(I/x)*e 
xp(x)+2*exp(x)*ln(x)-30)/x
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {e^{x} \log \left (\frac {\log \left (\log \left (144 \, \log \left (\log \left (x\right )\right )^{2}\right )\right ) + 3}{x}\right ) + 15}{5 \, x} \] Input:

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="fricas")
 

Output:

1/5*(e^x*log((log(log(144*log(log(x))^2)) + 3)/x) + 15)/x
 

Sympy [F(-1)]

Timed out. \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\text {Timed out} \] Input:

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)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=-\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (\log \left (2\right ) + \log \left (\log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (\log \left (\log \left (x\right )\right )\right )\right ) + 3\right ) - 15}{5 \, x} \] Input:

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="maxima")
 

Output:

-1/5*(e^x*log(x) - e^x*log(log(2) + log(log(3) + 2*log(2) + log(log(log(x) 
))) + 3) - 15)/x
 

Giac [A] (verification not implemented)

Time = 2.03 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=-\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (\log \left (\log \left (144 \, \log \left (\log \left (x\right )\right )^{2}\right )\right ) + 3\right ) - 15}{5 \, x} \] Input:

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="giac")
 

Output:

-1/5*(e^x*log(x) - e^x*log(log(log(144*log(log(x))^2)) + 3) - 15)/x
 

Mupad [F(-1)]

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 \] Input:

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)
 

Output:

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)
 

Reduce [B] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {e^{x} \mathrm {log}\left (\frac {\mathrm {log}\left (\mathrm {log}\left (144 \mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2}\right )\right )+3}{x}\right )+15}{5 x} \] Input:

int((((-1+x)*exp(x)*log(x)*log(log(x))*log(144*log(log(x))^2)*log(log(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))*lo 
g(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(14 
4*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)
 

Output:

(e**x*log((log(log(144*log(log(x))**2)) + 3)/x) + 15)/(5*x)