Integrand size = 203, antiderivative size = 32 \[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx=e^{x+\frac {\log \left (\frac {x^4}{\log ^2(x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \]
Time = 0.50 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.97 \[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx=e^x \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \]
Integrate[(E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Log[3*x]/Log[x]]))*((2*x^2 + (-4*x^2 + x^5)*Log[x])*Log[3*x] + (-Log[x ] + (1 + 2*x^2*Log[x])*Log[3*x])*Log[x^4/Log[x]^2] + (-2 + (4 - 2*x^3)*Log [x])*Log[3*x]*Log[Log[3*x]/Log[x]] + x*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x] ]^2))/(x^5*Log[x]*Log[3*x] - 2*x^3*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x]] + x*Log[x]*Log[3*x]*Log[Log[3*x]/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.
\(\displaystyle \int \frac {\left (\left (\left (4-2 x^3\right ) \log (x)-2\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+\left (2 x^2+\left (x^5-4 x^2\right ) \log (x)\right ) \log (3 x)+\left (\left (2 x^2 \log (x)+1\right ) \log (3 x)-\log (x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right ) \exp \left (\frac {\log \left (\frac {x^4}{\log ^2(x)}\right )-x^3+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {\left (\left (\left (4-2 x^3\right ) \log (x)-2\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+\left (2 x^2+\left (x^5-4 x^2\right ) \log (x)\right ) \log (3 x)+\left (\left (2 x^2 \log (x)+1\right ) \log (3 x)-\log (x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right ) \exp \left (\frac {\log \left (\frac {x^4}{\log ^2(x)}\right )-x^3+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {2 (2 \log (x)-1) \exp \left (\frac {\log \left (\frac {x^4}{\log ^2(x)}\right )-x^3+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}\right )}{x \log (x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\exp \left (\frac {\log \left (\frac {x^4}{\log ^2(x)}\right )-x^3+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}\right )+\frac {\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right ) \exp \left (\frac {\log \left (\frac {x^4}{\log ^2(x)}\right )-x^3+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}\right )}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (e^{-\frac {x^3}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}}-\frac {2 e^{-\frac {x^3}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}} (2 \log (x)-1) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}}}{x \log (x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{-\frac {x^3}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}}}{x \log (x) \log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \log (x) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^4}-\frac {2 e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} (2 \log (x)-1) \log (3 x) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )}+\frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \log \left (\frac {x^4}{\log ^2(x)}\right ) \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1}}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{\frac {x^3}{x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\frac {x^4}{\log ^2(x)}\right )^{\frac {1}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}+1} \left (\frac {\log (3 x)}{\log (x)}\right )^{\frac {x}{\log \left (\frac {\log (3 x)}{\log (x)}\right )-x^2}-1} \left (\left (2 x^2 \log ^2(x)+x^2 \log (9) \log (x)+\log (3)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\log (3 x) \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right ) \left (\log (x) \left (x^3-x \log \left (\frac {\log (3 x)}{\log (x)}\right )-4\right )+2\right )\right )}{x^5 \left (x^2-\log \left (\frac {\log (3 x)}{\log (x)}\right )\right )^2}dx\) |
Int[(E^((-x^3 + Log[x^4/Log[x]^2] + x*Log[Log[3*x]/Log[x]])/(-x^2 + Log[Lo g[3*x]/Log[x]]))*((2*x^2 + (-4*x^2 + x^5)*Log[x])*Log[3*x] + (-Log[x] + (1 + 2*x^2*Log[x])*Log[3*x])*Log[x^4/Log[x]^2] + (-2 + (4 - 2*x^3)*Log[x])*L og[3*x]*Log[Log[3*x]/Log[x]] + x*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x]]^2))/ (x^5*Log[x]*Log[3*x] - 2*x^3*Log[x]*Log[3*x]*Log[Log[3*x]/Log[x]] + x*Log[ x]*Log[3*x]*Log[Log[3*x]/Log[x]]^2),x]
3.9.76.3.1 Defintions of rubi rules used
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 = 0.19 (sec) , antiderivative size = 622, normalized size of antiderivative = 19.44
\[\text {Expression too large to display}\]
int((x*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))^2+((-2*x^3+4)*ln(x)-2)*ln(3*x)*ln(l n(3*x)/ln(x))+((2*x^2*ln(x)+1)*ln(3*x)-ln(x))*ln(x^4/ln(x)^2)+((x^5-4*x^2) *ln(x)+2*x^2)*ln(3*x))*exp((x*ln(ln(3*x)/ln(x))+ln(x^4/ln(x)^2)-x^3)/(ln(l n(3*x)/ln(x))-x^2))/(x*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))^2-2*x^3*ln(x)*ln(3* x)*ln(ln(3*x)/ln(x))+x^5*ln(x)*ln(3*x)),x)
exp(-(2*I*Pi*csgn(I*x)*csgn(I*x^2)^2+I*x*Pi*csgn(I/ln(x)*(ln(x)+ln(3)))^2* csgn(I/ln(x))+I*x*Pi*csgn(I/ln(x)*(ln(x)+ln(3)))^2*csgn(I*(ln(x)+ln(3)))-2 *x*ln(ln(x))-4*ln(ln(x))+8*ln(x)-2*x^3+I*Pi*csgn(I*x)*csgn(I*x^4)^2-I*Pi*c sgn(I*x)^2*csgn(I*x^2)-2*I*Pi*csgn(I*ln(x))*csgn(I*ln(x)^2)^2+I*Pi*csgn(I* ln(x))^2*csgn(I*ln(x)^2)-I*Pi*csgn(I*x)*csgn(I*x^4)*csgn(I*x^3)-I*Pi*csgn( I*x^4)*csgn(I*x^4/ln(x)^2)*csgn(I/ln(x)^2)+I*Pi*csgn(I*x)*csgn(I*x^3)^2+I* Pi*csgn(I*x^2)*csgn(I*x^3)^2-I*Pi*csgn(I*x^3)^3+I*Pi*csgn(I*x^3)*csgn(I*x^ 4)^2+I*Pi*csgn(I*x^4)*csgn(I*x^4/ln(x)^2)^2+I*Pi*csgn(I*x^4/ln(x)^2)^2*csg n(I/ln(x)^2)-I*Pi*csgn(I*x)*csgn(I*x^2)*csgn(I*x^3)+2*x*ln(ln(x)+ln(3))-I* x*Pi*csgn(I/ln(x)*(ln(x)+ln(3)))^3-I*Pi*csgn(I*x^4)^3-I*Pi*csgn(I*x^4/ln(x )^2)^3-I*Pi*csgn(I*x^2)^3+I*Pi*csgn(I*ln(x)^2)^3-I*x*Pi*csgn(I/ln(x)*(ln(x )+ln(3)))*csgn(I/ln(x))*csgn(I*(ln(x)+ln(3))))/(I*Pi*csgn(I/ln(x)*(ln(x)+l n(3)))^3-I*Pi*csgn(I/ln(x)*(ln(x)+ln(3)))^2*csgn(I/ln(x))-I*Pi*csgn(I/ln(x )*(ln(x)+ln(3)))^2*csgn(I*(ln(x)+ln(3)))+I*Pi*csgn(I/ln(x)*(ln(x)+ln(3)))* csgn(I/ln(x))*csgn(I*(ln(x)+ln(3)))+2*x^2+2*ln(ln(x))-2*ln(ln(x)+ln(3))))
Time = 0.24 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.56 \[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx=e^{\left (\frac {x^{3} - x \log \left (\frac {\log \left (3\right ) + \log \left (x\right )}{\log \left (x\right )}\right ) - \log \left (\frac {x^{4}}{\log \left (x\right )^{2}}\right )}{x^{2} - \log \left (\frac {\log \left (3\right ) + \log \left (x\right )}{\log \left (x\right )}\right )}\right )} \]
integrate((x*log(x)*log(3*x)*log(log(3*x)/log(x))^2+((-2*x^3+4)*log(x)-2)* log(3*x)*log(log(3*x)/log(x))+((2*x^2*log(x)+1)*log(3*x)-log(x))*log(x^4/l og(x)^2)+((x^5-4*x^2)*log(x)+2*x^2)*log(3*x))*exp((x*log(log(3*x)/log(x))+ log(x^4/log(x)^2)-x^3)/(log(log(3*x)/log(x))-x^2))/(x*log(x)*log(3*x)*log( log(3*x)/log(x))^2-2*x^3*log(x)*log(3*x)*log(log(3*x)/log(x))+x^5*log(x)*l og(3*x)),x, algorithm=\
e^((x^3 - x*log((log(3) + log(x))/log(x)) - log(x^4/log(x)^2))/(x^2 - log( (log(3) + log(x))/log(x))))
Time = 24.63 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.31 \[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx=e^{\frac {- x^{3} + x \log {\left (\frac {\log {\left (x \right )} + \log {\left (3 \right )}}{\log {\left (x \right )}} \right )} + \log {\left (\frac {x^{4}}{\log {\left (x \right )}^{2}} \right )}}{- x^{2} + \log {\left (\frac {\log {\left (x \right )} + \log {\left (3 \right )}}{\log {\left (x \right )}} \right )}}} \]
integrate((x*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))**2+((-2*x**3+4)*ln(x)-2)*ln(3 *x)*ln(ln(3*x)/ln(x))+((2*x**2*ln(x)+1)*ln(3*x)-ln(x))*ln(x**4/ln(x)**2)+( (x**5-4*x**2)*ln(x)+2*x**2)*ln(3*x))*exp((x*ln(ln(3*x)/ln(x))+ln(x**4/ln(x )**2)-x**3)/(ln(ln(3*x)/ln(x))-x**2))/(x*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))** 2-2*x**3*ln(x)*ln(3*x)*ln(ln(3*x)/ln(x))+x**5*ln(x)*ln(3*x)),x)
exp((-x**3 + x*log((log(x) + log(3))/log(x)) + log(x**4/log(x)**2))/(-x**2 + log((log(x) + log(3))/log(x))))
\[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx=\int { \frac {{\left (x \log \left (3 \, x\right ) \log \left (x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right )^{2} - 2 \, {\left ({\left (x^{3} - 2\right )} \log \left (x\right ) + 1\right )} \log \left (3 \, x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right ) + {\left ({\left (2 \, x^{2} \log \left (x\right ) + 1\right )} \log \left (3 \, x\right ) - \log \left (x\right )\right )} \log \left (\frac {x^{4}}{\log \left (x\right )^{2}}\right ) + {\left (2 \, x^{2} + {\left (x^{5} - 4 \, x^{2}\right )} \log \left (x\right )\right )} \log \left (3 \, x\right )\right )} e^{\left (\frac {x^{3} - x \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right ) - \log \left (\frac {x^{4}}{\log \left (x\right )^{2}}\right )}{x^{2} - \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right )}\right )}}{x^{5} \log \left (3 \, x\right ) \log \left (x\right ) - 2 \, x^{3} \log \left (3 \, x\right ) \log \left (x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right ) + x \log \left (3 \, x\right ) \log \left (x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right )^{2}} \,d x } \]
integrate((x*log(x)*log(3*x)*log(log(3*x)/log(x))^2+((-2*x^3+4)*log(x)-2)* log(3*x)*log(log(3*x)/log(x))+((2*x^2*log(x)+1)*log(3*x)-log(x))*log(x^4/l og(x)^2)+((x^5-4*x^2)*log(x)+2*x^2)*log(3*x))*exp((x*log(log(3*x)/log(x))+ log(x^4/log(x)^2)-x^3)/(log(log(3*x)/log(x))-x^2))/(x*log(x)*log(3*x)*log( log(3*x)/log(x))^2-2*x^3*log(x)*log(3*x)*log(log(3*x)/log(x))+x^5*log(x)*l og(3*x)),x, algorithm=\
integrate((x*log(3*x)*log(x)*log(log(3*x)/log(x))^2 - 2*((x^3 - 2)*log(x) + 1)*log(3*x)*log(log(3*x)/log(x)) + ((2*x^2*log(x) + 1)*log(3*x) - log(x) )*log(x^4/log(x)^2) + (2*x^2 + (x^5 - 4*x^2)*log(x))*log(3*x))*e^((x^3 - x *log(log(3*x)/log(x)) - log(x^4/log(x)^2))/(x^2 - log(log(3*x)/log(x))))/( x^5*log(3*x)*log(x) - 2*x^3*log(3*x)*log(x)*log(log(3*x)/log(x)) + x*log(3 *x)*log(x)*log(log(3*x)/log(x))^2), x)
\[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx=\int { \frac {{\left (x \log \left (3 \, x\right ) \log \left (x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right )^{2} - 2 \, {\left ({\left (x^{3} - 2\right )} \log \left (x\right ) + 1\right )} \log \left (3 \, x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right ) + {\left ({\left (2 \, x^{2} \log \left (x\right ) + 1\right )} \log \left (3 \, x\right ) - \log \left (x\right )\right )} \log \left (\frac {x^{4}}{\log \left (x\right )^{2}}\right ) + {\left (2 \, x^{2} + {\left (x^{5} - 4 \, x^{2}\right )} \log \left (x\right )\right )} \log \left (3 \, x\right )\right )} e^{\left (\frac {x^{3} - x \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right ) - \log \left (\frac {x^{4}}{\log \left (x\right )^{2}}\right )}{x^{2} - \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right )}\right )}}{x^{5} \log \left (3 \, x\right ) \log \left (x\right ) - 2 \, x^{3} \log \left (3 \, x\right ) \log \left (x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right ) + x \log \left (3 \, x\right ) \log \left (x\right ) \log \left (\frac {\log \left (3 \, x\right )}{\log \left (x\right )}\right )^{2}} \,d x } \]
integrate((x*log(x)*log(3*x)*log(log(3*x)/log(x))^2+((-2*x^3+4)*log(x)-2)* log(3*x)*log(log(3*x)/log(x))+((2*x^2*log(x)+1)*log(3*x)-log(x))*log(x^4/l og(x)^2)+((x^5-4*x^2)*log(x)+2*x^2)*log(3*x))*exp((x*log(log(3*x)/log(x))+ log(x^4/log(x)^2)-x^3)/(log(log(3*x)/log(x))-x^2))/(x*log(x)*log(3*x)*log( log(3*x)/log(x))^2-2*x^3*log(x)*log(3*x)*log(log(3*x)/log(x))+x^5*log(x)*l og(3*x)),x, algorithm=\
Time = 15.16 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.12 \[ \int \frac {e^{\frac {-x^3+\log \left (\frac {x^4}{\log ^2(x)}\right )+x \log \left (\frac {\log (3 x)}{\log (x)}\right )}{-x^2+\log \left (\frac {\log (3 x)}{\log (x)}\right )}} \left (\left (2 x^2+\left (-4 x^2+x^5\right ) \log (x)\right ) \log (3 x)+\left (-\log (x)+\left (1+2 x^2 \log (x)\right ) \log (3 x)\right ) \log \left (\frac {x^4}{\log ^2(x)}\right )+\left (-2+\left (4-2 x^3\right ) \log (x)\right ) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )\right )}{x^5 \log (x) \log (3 x)-2 x^3 \log (x) \log (3 x) \log \left (\frac {\log (3 x)}{\log (x)}\right )+x \log (x) \log (3 x) \log ^2\left (\frac {\log (3 x)}{\log (x)}\right )} \, dx={\mathrm {e}}^{-\frac {x^3}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \left (x\right )}\right )-x^2}}\,{\left (\frac {1}{{\ln \left (x\right )}^2}\right )}^{\frac {1}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \left (x\right )}\right )-x^2}}\,{\left (x^4\right )}^{\frac {1}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \left (x\right )}\right )-x^2}}\,{\left (\frac {\ln \left (3\,x\right )}{\ln \left (x\right )}\right )}^{\frac {x}{\ln \left (\frac {\ln \left (3\,x\right )}{\ln \left (x\right )}\right )-x^2}} \]
int(-(exp((log(x^4/log(x)^2) + x*log(log(3*x)/log(x)) - x^3)/(log(log(3*x) /log(x)) - x^2))*(log(3*x)*(log(x)*(4*x^2 - x^5) - 2*x^2) + log(x^4/log(x) ^2)*(log(x) - log(3*x)*(2*x^2*log(x) + 1)) + log(3*x)*log(log(3*x)/log(x)) *(log(x)*(2*x^3 - 4) + 2) - x*log(3*x)*log(log(3*x)/log(x))^2*log(x)))/(x^ 5*log(3*x)*log(x) + x*log(3*x)*log(log(3*x)/log(x))^2*log(x) - 2*x^3*log(3 *x)*log(log(3*x)/log(x))*log(x)),x)