Integrand size = 152, antiderivative size = 27 \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}} \] Output:
exp(exp(exp(x^3/ln(-ln(23/3)-I*Pi+3+x))))
Time = 0.07 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}} \] Input:
Integrate[(E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*P i + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x - Log[23/3]])*(x^3 + (-9*x^2 - 3*x^3 + 3*x^2*(I*Pi + Log[23/3]))*Log[3 - I*Pi + x - Log[23/3]]))/((-3 + I *Pi - x + Log[23/3])*Log[3 - I*Pi + x - Log[23/3]]^2),x]
Output:
E^E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]])
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.
| \(\displaystyle \int \frac {\left (x^3+\left (-3 x^3-9 x^2+3 x^2 \left (\log \left (\frac {23}{3}\right )+i \pi \right )\right ) \log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )\right ) \exp \left (\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}+e^{e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}\right )}{\left (-x+i \pi -3+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 x^2 \exp \left (\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}+e^{e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}\right )}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}-\frac {x^3 \exp \left (\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}+e^{e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}\right )}{\left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right ) \log ^2\left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {3 x^2 \exp \left (\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}+e^{e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}\right )}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}-\frac {x^3 \exp \left (\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}+e^{e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}}\right )}{\left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right ) \log ^2\left (x-i \pi +3-\log \left (\frac {23}{3}\right )\right )}\right )dx\) |
Input:
Int[(E^(E^E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + E^(x^3/Log[3 - I*Pi + x - Log[23/3]]) + x^3/Log[3 - I*Pi + x - Log[23/3]])*(x^3 + (-9*x^2 - 3*x^3 + 3*x^2*(I*Pi + Log[23/3]))*Log[3 - I*Pi + x - Log[23/3]]))/((-3 + I*Pi - x + Log[23/3])*Log[3 - I*Pi + x - Log[23/3]]^2),x]
Output:
$Aborted
Time = 1.69 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89
| method | result | size |
| risch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{3}}{\ln \left (-\ln \left (23\right )+\ln \left (3\right )-i \pi +3+x \right )}}}}\) | \(24\) |
Input:
int(((3*x^2*(ln(23/3)+I*Pi)-3*x^3-9*x^2)*ln(-ln(23/3)-I*Pi+3+x)+x^3)*exp(x ^3/ln(-ln(23/3)-I*Pi+3+x))*exp(exp(x^3/ln(-ln(23/3)-I*Pi+3+x)))*exp(exp(ex p(x^3/ln(-ln(23/3)-I*Pi+3+x))))/(ln(23/3)+I*Pi-3-x)/ln(-ln(23/3)-I*Pi+3+x) ^2,x,method=_RETURNVERBOSE)
Output:
exp(exp(exp(x^3/ln(-ln(23)+ln(3)-I*Pi+3+x))))
Time = 0.13 (sec) , antiderivative size = 179, normalized size of antiderivative = 6.63 \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=\cosh \left (-\cosh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right ) + \sinh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right )\right ) - \sinh \left (-\cosh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right ) + \sinh \left (-\cosh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right ) + \sinh \left (-\frac {x^{3}}{\log \left (-i \, \pi + x - \log \left (\frac {23}{3}\right ) + 3\right )}\right )\right )\right ) \] Input:
integrate(((3*x^2*(log(23/3)+I*pi)-3*x^3-9*x^2)*log(-log(23/3)-I*pi+3+x)+x ^3)*exp(x^3/log(-log(23/3)-I*pi+3+x))*exp(exp(x^3/log(-log(23/3)-I*pi+3+x) ))*exp(exp(exp(x^3/log(-log(23/3)-I*pi+3+x))))/(log(23/3)+I*pi-3-x)/log(-l og(23/3)-I*pi+3+x)^2,x, algorithm="fricas")
Output:
cosh(-cosh(-cosh(-x^3/log(-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*p i + x - log(23/3) + 3))) + sinh(-cosh(-x^3/log(-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3)))) - sinh(-cosh(-cosh(-x^3/log (-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3))) + sinh(-cosh(-x^3/log(-I*pi + x - log(23/3) + 3)) + sinh(-x^3/log(-I*pi + x - log(23/3) + 3))))
Timed out. \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=\text {Timed out} \] Input:
integrate(((3*x**2*(ln(23/3)+I*pi)-3*x**3-9*x**2)*ln(-ln(23/3)-I*pi+3+x)+x **3)*exp(x**3/ln(-ln(23/3)-I*pi+3+x))*exp(exp(x**3/ln(-ln(23/3)-I*pi+3+x)) )*exp(exp(exp(x**3/ln(-ln(23/3)-I*pi+3+x))))/(ln(23/3)+I*pi-3-x)/ln(-ln(23 /3)-I*pi+3+x)**2,x)
Output:
Timed out
Timed out. \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=\text {Timed out} \] Input:
integrate(((3*x^2*(log(23/3)+I*pi)-3*x^3-9*x^2)*log(-log(23/3)-I*pi+3+x)+x ^3)*exp(x^3/log(-log(23/3)-I*pi+3+x))*exp(exp(x^3/log(-log(23/3)-I*pi+3+x) ))*exp(exp(exp(x^3/log(-log(23/3)-I*pi+3+x))))/(log(23/3)+I*pi-3-x)/log(-l og(23/3)-I*pi+3+x)^2,x, algorithm="maxima")
Output:
Timed out
Timed out. \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=\text {Timed out} \] Input:
integrate(((3*x^2*(log(23/3)+I*pi)-3*x^3-9*x^2)*log(-log(23/3)-I*pi+3+x)+x ^3)*exp(x^3/log(-log(23/3)-I*pi+3+x))*exp(exp(x^3/log(-log(23/3)-I*pi+3+x) ))*exp(exp(exp(x^3/log(-log(23/3)-I*pi+3+x))))/(log(23/3)+I*pi-3-x)/log(-l og(23/3)-I*pi+3+x)^2,x, algorithm="giac")
Output:
Timed out
Timed out. \[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=\int -\frac {{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}}}\,{\mathrm {e}}^{\frac {x^3}{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}}\,\left (\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )\,\left (9\,x^2-3\,x^2\,\left (\ln \left (\frac {23}{3}\right )+\Pi \,1{}\mathrm {i}\right )+3\,x^3\right )-x^3\right )}{{\ln \left (x-\ln \left (\frac {23}{3}\right )+3-\Pi \,1{}\mathrm {i}\right )}^2\,\left (\ln \left (\frac {23}{3}\right )-x-3+\Pi \,1{}\mathrm {i}\right )} \,d x \] Input:
int(-(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3)))*exp(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3))))*exp(x^3/log(x - Pi*1i - log(23/3) + 3))*(log(x - Pi*1i - log(23/3) + 3)*(9*x^2 - 3*x^2*(Pi*1i + log(23/3)) + 3*x^3) - x^3 ))/(log(x - Pi*1i - log(23/3) + 3)^2*(Pi*1i - x + log(23/3) - 3)),x)
Output:
int(-(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3)))*exp(exp(exp(x^3/log(x - Pi*1i - log(23/3) + 3))))*exp(x^3/log(x - Pi*1i - log(23/3) + 3))*(log(x - Pi*1i - log(23/3) + 3)*(9*x^2 - 3*x^2*(Pi*1i + log(23/3)) + 3*x^3) - x^3 ))/(log(x - Pi*1i - log(23/3) + 3)^2*(Pi*1i - x + log(23/3) - 3)), x)
\[ \int \frac {e^{e^{e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}}+e^{\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}}+\frac {x^3}{\log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )}} \left (x^3+\left (-9 x^2-3 x^3+3 x^2 \left (i \pi +\log \left (\frac {23}{3}\right )\right )\right ) \log \left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )\right )}{\left (-3+i \pi -x+\log \left (\frac {23}{3}\right )\right ) \log ^2\left (3-i \pi +x-\log \left (\frac {23}{3}\right )\right )} \, dx=\int \frac {\left (\left (3 x^{2} \left (\mathrm {log}\left (\frac {23}{3}\right )+i \pi \right )-3 x^{3}-9 x^{2}\right ) \mathrm {log}\left (-\mathrm {log}\left (\frac {23}{3}\right )-i \pi +3+x \right )+x^{3}\right ) {\mathrm e}^{\frac {x^{3}}{\mathrm {log}\left (-\mathrm {log}\left (\frac {23}{3}\right )-i \pi +3+x \right )}} {\mathrm e}^{{\mathrm e}^{\frac {x^{3}}{\mathrm {log}\left (-\mathrm {log}\left (\frac {23}{3}\right )-i \pi +3+x \right )}}} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {x^{3}}{\mathrm {log}\left (-\mathrm {log}\left (\frac {23}{3}\right )-i \pi +3+x \right )}}}}}{\left (\mathrm {log}\left (\frac {23}{3}\right )+i \pi -3-x \right ) \mathrm {log}\left (-\mathrm {log}\left (\frac {23}{3}\right )-i \pi +3+x \right )^{2}}d x \] Input:
int(((3*x^2*(log(23/3)+I*Pi)-3*x^3-9*x^2)*log(-log(23/3)-I*Pi+3+x)+x^3)*ex p(x^3/log(-log(23/3)-I*Pi+3+x))*exp(exp(x^3/log(-log(23/3)-I*Pi+3+x)))*exp (exp(exp(x^3/log(-log(23/3)-I*Pi+3+x))))/(log(23/3)+I*Pi-3-x)/log(-log(23/ 3)-I*Pi+3+x)^2,x)
Output:
int(((3*x^2*(log(23/3)+I*Pi)-3*x^3-9*x^2)*log(-log(23/3)-I*Pi+3+x)+x^3)*ex p(x^3/log(-log(23/3)-I*Pi+3+x))*exp(exp(x^3/log(-log(23/3)-I*Pi+3+x)))*exp (exp(exp(x^3/log(-log(23/3)-I*Pi+3+x))))/(log(23/3)+I*Pi-3-x)/log(-log(23/ 3)-I*Pi+3+x)^2,x)