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

Optimal result

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

[Out]

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

Rubi [F]

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

[In]

Int[(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[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]]*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]

[Out]

3/x + E^x/(5*x) - ExpIntegralEi[x]/5 + (2*Defer[Int][E^x/(x^2*Log[x]*Log[Log[x]]*Log[144*Log[Log[x]]^2]*(3 + L
og[Log[144*Log[Log[x]]^2]])), x])/5 - Defer[Int][(E^x*Log[3/x + Log[Log[144*Log[Log[x]]^2]]/x])/x^2, x]/5 + De
fer[Int][(E^x*Log[3/x + Log[Log[144*Log[Log[x]]^2]]/x])/x, x]/5

Rubi steps \begin{align*} \text {integral}& = \int \frac {-15-e^x+\frac {2 e^x}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}+e^x (-1+x) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{5 x^2} \, dx \\ & = \frac {1}{5} \int \frac {-15-e^x+\frac {2 e^x}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}+e^x (-1+x) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2} \, dx \\ & = \frac {1}{5} \int \left (-\frac {15}{x^2}+\frac {e^x \left (2-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (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 )-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )+3 x \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{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 ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )+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 ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )\right )}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}\right ) \, dx \\ & = \frac {3}{x}+\frac {1}{5} \int \frac {e^x \left (2-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (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 )-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )+3 x \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{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 ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )+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 ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )\right )}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )} \, dx \\ & = \frac {3}{x}+\frac {1}{5} \int \frac {e^x \left (-1+\frac {2}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}+(-1+x) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )\right )}{x^2} \, dx \\ & = \frac {3}{x}+\frac {1}{5} \int \left (\frac {e^x \left (2-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (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 )\right )}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}+\frac {e^x (-1+x) \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2}\right ) \, dx \\ & = \frac {3}{x}+\frac {1}{5} \int \frac {e^x \left (2-3 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (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 )\right )}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )} \, dx+\frac {1}{5} \int \frac {e^x (-1+x) \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2} \, dx \\ & = \frac {3}{x}+\frac {1}{5} \int \frac {e^x \left (-1+\frac {2}{\log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}\right )}{x^2} \, dx+\frac {1}{5} \int \left (-\frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2}+\frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x}\right ) \, dx \\ & = \frac {3}{x}+\frac {1}{5} \int \left (-\frac {e^x}{x^2}+\frac {2 e^x}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )}\right ) \, dx-\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2} \, dx+\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x} \, dx \\ & = \frac {3}{x}-\frac {1}{5} \int \frac {e^x}{x^2} \, dx-\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2} \, dx+\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x} \, dx+\frac {2}{5} \int \frac {e^x}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )} \, dx \\ & = \frac {3}{x}+\frac {e^x}{5 x}-\frac {1}{5} \int \frac {e^x}{x} \, dx-\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2} \, dx+\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x} \, dx+\frac {2}{5} \int \frac {e^x}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )} \, dx \\ & = \frac {3}{x}+\frac {e^x}{5 x}-\frac {\operatorname {ExpIntegralEi}(x)}{5}-\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x^2} \, dx+\frac {1}{5} \int \frac {e^x \log \left (\frac {3}{x}+\frac {\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{x} \, dx+\frac {2}{5} \int \frac {e^x}{x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \left (3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 5.21 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {15+e^x \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{5 x} \]

[In]

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]]*Lo
g[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]]*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]

[Out]

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

Maple [C] (warning: unable to verify)

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}\]

[In]

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*ln(ln(x))^2))+3)/x)+(-exp(x)-15)*ln(x)*ln(ln(x))*ln(144*ln(ln(x))^2)*ln(l
n(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)

[Out]

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*l
n(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*l
n(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*exp(x)+I*Pi*c
sgn(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)+2*exp(x)*ln(x)-30)/x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=\frac {e^{x} \log \left (\frac {\log \left (\log \left (144 \, \log \left (\log \left (x\right )\right )^{2}\right )\right ) + 3}{x}\right ) + 15}{5 \, x} \]

[In]

integrate((((-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(lo
g(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(l
og(x))*log(144*log(log(x))^2)),x, algorithm="fricas")

[Out]

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

Sympy [F(-1)]

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

[In]

integrate((((-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*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*ln(ln(x))**2))+15*x**2*ln(x)*ln(ln(x))*ln(144*ln(ln(x))**2)),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.39 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=-\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (\log \left (2\right ) + \log \left (\log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (\log \left (\log \left (x\right )\right )\right )\right ) + 3\right ) - 15}{5 \, x} \]

[In]

integrate((((-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(lo
g(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(l
og(x))*log(144*log(log(x))^2)),x, algorithm="maxima")

[Out]

-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)

none

Time = 2.07 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int \frac {2 e^x+\left (-45-3 e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+\left (-15-e^x\right ) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )+\left (e^x (-3+3 x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+e^x (-1+x) \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )\right ) \log \left (\frac {3+\log \left (\log \left (144 \log ^2(\log (x))\right )\right )}{x}\right )}{15 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right )+5 x^2 \log (x) \log (\log (x)) \log \left (144 \log ^2(\log (x))\right ) \log \left (\log \left (144 \log ^2(\log (x))\right )\right )} \, dx=-\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (\log \left (\log \left (144 \, \log \left (\log \left (x\right )\right )^{2}\right )\right ) + 3\right ) - 15}{5 \, x} \]

[In]

integrate((((-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(lo
g(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(l
og(x))*log(144*log(log(x))^2)),x, algorithm="giac")

[Out]

-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 \]

[In]

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*log(log(x))^2)*log(x)*log(log(144*log(log(x))^2))*(x - 1)) - log(log(x))*l
og(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)

[Out]

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*log(log(x))^2)*log(x)*log(log(144*log(log(x))^2))*(x - 1)) - log(log(x))*l
og(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)