Integrand size = 264, antiderivative size = 32 \[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=10+x+x^2+\frac {x^2}{(3+x)^2 \left (-x+\log \left (\frac {e^2}{3 x}\right )\right )^2} \]
\[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=\int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx \]
Integrate[(6*x + 2*x^2 - 25*x^3 - 81*x^4 - 63*x^5 - 19*x^6 - 2*x^7 + (6*x + 81*x^2 + 243*x^3 + 189*x^4 + 57*x^5 + 6*x^6)*Log[E^2/(3*x)] + (-81*x - 2 43*x^2 - 189*x^3 - 57*x^4 - 6*x^5)*Log[E^2/(3*x)]^2 + (27 + 81*x + 63*x^2 + 19*x^3 + 2*x^4)*Log[E^2/(3*x)]^3)/(-27*x^3 - 27*x^4 - 9*x^5 - x^6 + (81* x^2 + 81*x^3 + 27*x^4 + 3*x^5)*Log[E^2/(3*x)] + (-81*x - 81*x^2 - 27*x^3 - 3*x^4)*Log[E^2/(3*x)]^2 + (27 + 27*x + 9*x^2 + x^3)*Log[E^2/(3*x)]^3),x]
Integrate[(6*x + 2*x^2 - 25*x^3 - 81*x^4 - 63*x^5 - 19*x^6 - 2*x^7 + (6*x + 81*x^2 + 243*x^3 + 189*x^4 + 57*x^5 + 6*x^6)*Log[E^2/(3*x)] + (-81*x - 2 43*x^2 - 189*x^3 - 57*x^4 - 6*x^5)*Log[E^2/(3*x)]^2 + (27 + 81*x + 63*x^2 + 19*x^3 + 2*x^4)*Log[E^2/(3*x)]^3)/(-27*x^3 - 27*x^4 - 9*x^5 - x^6 + (81* x^2 + 81*x^3 + 27*x^4 + 3*x^5)*Log[E^2/(3*x)] + (-81*x - 81*x^2 - 27*x^3 - 3*x^4)*Log[E^2/(3*x)]^2 + (27 + 27*x + 9*x^2 + x^3)*Log[E^2/(3*x)]^3), x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-2 x^7-19 x^6-63 x^5-81 x^4-25 x^3+2 x^2+\left (2 x^4+19 x^3+63 x^2+81 x+27\right ) \log ^3\left (\frac {e^2}{3 x}\right )+\left (-6 x^5-57 x^4-189 x^3-243 x^2-81 x\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (6 x^6+57 x^5+189 x^4+243 x^3+81 x^2+6 x\right ) \log \left (\frac {e^2}{3 x}\right )+6 x}{-x^6-9 x^5-27 x^4-27 x^3+\left (x^3+9 x^2+27 x+27\right ) \log ^3\left (\frac {e^2}{3 x}\right )+\left (-3 x^4-27 x^3-81 x^2-81 x\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (3 x^5+27 x^4+81 x^3+81 x^2\right ) \log \left (\frac {e^2}{3 x}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^7+7 x^6-27 x^5-85 x^4+143 x^3+304 x^2+3 (x+3)^3 \left (2 x^2-3 x-2\right ) \log ^2\left (\frac {1}{3 x}\right )-3 \left (2 x^6+11 x^5-5 x^4-95 x^3-45 x^2+218 x+108\right ) \log \left (\frac {1}{3 x}\right )-342 x-(x+3)^3 (2 x+1) \log ^3\left (\frac {1}{3 x}\right )-216}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^7}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log \left (\frac {1}{3 x}\right ) x^6}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {7 x^6}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {6 \log ^2\left (\frac {1}{3 x}\right ) x^5}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {33 \log \left (\frac {1}{3 x}\right ) x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 x^5}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {2 \log ^3\left (\frac {1}{3 x}\right ) x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {45 \log ^2\left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {15 \log \left (\frac {1}{3 x}\right ) x^4}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {85 x^4}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {19 \log ^3\left (\frac {1}{3 x}\right ) x^3}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {75 \log ^2\left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {285 \log \left (\frac {1}{3 x}\right ) x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {143 x^3}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {63 \log ^3\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log ^2\left (\frac {1}{3 x}\right ) x^2}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {135 \log \left (\frac {1}{3 x}\right ) x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {304 x^2}{(x+3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {81 \log ^3\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {405 \log ^2\left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {654 \log \left (\frac {1}{3 x}\right ) x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {342 x}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {27 \log ^3\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {162 \log ^2\left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {324 \log \left (\frac {1}{3 x}\right )}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}+\frac {216}{(-x-3)^3 \left (x-\log \left (\frac {1}{x}\right )-2 \left (1-\frac {\log (3)}{2}\right )\right )^3}\right )dx\) |
Int[(6*x + 2*x^2 - 25*x^3 - 81*x^4 - 63*x^5 - 19*x^6 - 2*x^7 + (6*x + 81*x ^2 + 243*x^3 + 189*x^4 + 57*x^5 + 6*x^6)*Log[E^2/(3*x)] + (-81*x - 243*x^2 - 189*x^3 - 57*x^4 - 6*x^5)*Log[E^2/(3*x)]^2 + (27 + 81*x + 63*x^2 + 19*x ^3 + 2*x^4)*Log[E^2/(3*x)]^3)/(-27*x^3 - 27*x^4 - 9*x^5 - x^6 + (81*x^2 + 81*x^3 + 27*x^4 + 3*x^5)*Log[E^2/(3*x)] + (-81*x - 81*x^2 - 27*x^3 - 3*x^4 )*Log[E^2/(3*x)]^2 + (27 + 27*x + 9*x^2 + x^3)*Log[E^2/(3*x)]^3),x]
3.4.51.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 7.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06
| method | result | size |
| risch | \(x^{2}+x +\frac {x^{2}}{\left (x^{2}+6 x +9\right ) {\left (x -\ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )\right )}^{2}}\) | \(34\) |
| derivativedivides | \(x +x^{2}+\frac {1}{x^{2} \left (\frac {3 \ln \left (3\right )}{x^{2}}-\frac {3 \ln \left (\frac {1}{x}\right )}{x^{2}}+\frac {\ln \left (3\right )}{x}-\frac {6}{x^{2}}-\frac {\ln \left (\frac {1}{x}\right )}{x}+\frac {1}{x}+1\right )^{2}}\) | \(53\) |
| default | \(x +x^{2}+\frac {1}{x^{2} \left (\frac {3 \ln \left (3\right )}{x^{2}}-\frac {3 \ln \left (\frac {1}{x}\right )}{x^{2}}+\frac {\ln \left (3\right )}{x}-\frac {6}{x^{2}}-\frac {\ln \left (\frac {1}{x}\right )}{x}+\frac {1}{x}+1\right )^{2}}\) | \(53\) |
| parallelrisch | \(\frac {-81 x^{3}-134 x^{2}+x^{6}+7 x^{5}-135 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2}+\ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2} x^{4}-2 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right ) x^{5}+7 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2} x^{3}-14 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right ) x^{4}-81 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2} x +162 x^{2} \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )+270 x \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )}{x^{4}-2 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right ) x^{3}+\ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2} x^{2}+6 x^{3}-12 x^{2} \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )+6 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2} x +9 x^{2}-18 x \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )+9 \ln \left (\frac {{\mathrm e}^{2}}{3 x}\right )^{2}}\) | \(217\) |
int(((2*x^4+19*x^3+63*x^2+81*x+27)*ln(1/3*exp(2)/x)^3+(-6*x^5-57*x^4-189*x ^3-243*x^2-81*x)*ln(1/3*exp(2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+81*x^2+6 *x)*ln(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*x)/((x^3+9* x^2+27*x+27)*ln(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*ln(1/3*exp(2)/ x)^2+(3*x^5+27*x^4+81*x^3+81*x^2)*ln(1/3*exp(2)/x)-x^6-9*x^5-27*x^4-27*x^3 ),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 137 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 137, normalized size of antiderivative = 4.28 \[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=\frac {x^{6} + 7 \, x^{5} + 15 \, x^{4} + 9 \, x^{3} + {\left (x^{4} + 7 \, x^{3} + 15 \, x^{2} + 9 \, x\right )} \log \left (\frac {e^{2}}{3 \, x}\right )^{2} + x^{2} - 2 \, {\left (x^{5} + 7 \, x^{4} + 15 \, x^{3} + 9 \, x^{2}\right )} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{4} + 6 \, x^{3} + {\left (x^{2} + 6 \, x + 9\right )} \log \left (\frac {e^{2}}{3 \, x}\right )^{2} + 9 \, x^{2} - 2 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} \log \left (\frac {e^{2}}{3 \, x}\right )} \]
integrate(((2*x^4+19*x^3+63*x^2+81*x+27)*log(1/3*exp(2)/x)^3+(-6*x^5-57*x^ 4-189*x^3-243*x^2-81*x)*log(1/3*exp(2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+ 81*x^2+6*x)*log(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*x) /((x^3+9*x^2+27*x+27)*log(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*log( 1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x^3+81*x^2)*log(1/3*exp(2)/x)-x^6-9*x^5-2 7*x^4-27*x^3),x, algorithm=\
(x^6 + 7*x^5 + 15*x^4 + 9*x^3 + (x^4 + 7*x^3 + 15*x^2 + 9*x)*log(1/3*e^2/x )^2 + x^2 - 2*(x^5 + 7*x^4 + 15*x^3 + 9*x^2)*log(1/3*e^2/x))/(x^4 + 6*x^3 + (x^2 + 6*x + 9)*log(1/3*e^2/x)^2 + 9*x^2 - 2*(x^3 + 6*x^2 + 9*x)*log(1/3 *e^2/x))
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (26) = 52\).
Time = 0.23 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.97 \[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=x^{2} + \frac {x^{2}}{x^{4} + 6 x^{3} + 9 x^{2} + \left (x^{2} + 6 x + 9\right ) \log {\left (\frac {e^{2}}{3 x} \right )}^{2} + \left (- 2 x^{3} - 12 x^{2} - 18 x\right ) \log {\left (\frac {e^{2}}{3 x} \right )}} + x \]
integrate(((2*x**4+19*x**3+63*x**2+81*x+27)*ln(1/3*exp(2)/x)**3+(-6*x**5-5 7*x**4-189*x**3-243*x**2-81*x)*ln(1/3*exp(2)/x)**2+(6*x**6+57*x**5+189*x** 4+243*x**3+81*x**2+6*x)*ln(1/3*exp(2)/x)-2*x**7-19*x**6-63*x**5-81*x**4-25 *x**3+2*x**2+6*x)/((x**3+9*x**2+27*x+27)*ln(1/3*exp(2)/x)**3+(-3*x**4-27*x **3-81*x**2-81*x)*ln(1/3*exp(2)/x)**2+(3*x**5+27*x**4+81*x**3+81*x**2)*ln( 1/3*exp(2)/x)-x**6-9*x**5-27*x**4-27*x**3),x)
x**2 + x**2/(x**4 + 6*x**3 + 9*x**2 + (x**2 + 6*x + 9)*log(exp(2)/(3*x))** 2 + (-2*x**3 - 12*x**2 - 18*x)*log(exp(2)/(3*x))) + x
Leaf count of result is larger than twice the leaf count of optimal. 236 vs. \(2 (29) = 58\).
Time = 0.34 (sec) , antiderivative size = 236, normalized size of antiderivative = 7.38 \[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=\frac {x^{6} + x^{5} {\left (2 \, \log \left (3\right ) + 3\right )} + {\left (\log \left (3\right )^{2} + 10 \, \log \left (3\right ) - 9\right )} x^{4} + {\left (7 \, \log \left (3\right )^{2} + 2 \, \log \left (3\right ) - 23\right )} x^{3} + {\left (15 \, \log \left (3\right )^{2} - 42 \, \log \left (3\right ) + 25\right )} x^{2} + {\left (x^{4} + 7 \, x^{3} + 15 \, x^{2} + 9 \, x\right )} \log \left (x\right )^{2} + 9 \, {\left (\log \left (3\right )^{2} - 4 \, \log \left (3\right ) + 4\right )} x + 2 \, {\left (x^{5} + x^{4} {\left (\log \left (3\right ) + 5\right )} + x^{3} {\left (7 \, \log \left (3\right ) + 1\right )} + 3 \, x^{2} {\left (5 \, \log \left (3\right ) - 7\right )} + 9 \, x {\left (\log \left (3\right ) - 2\right )}\right )} \log \left (x\right )}{x^{4} + 2 \, x^{3} {\left (\log \left (3\right ) + 1\right )} + {\left (\log \left (3\right )^{2} + 8 \, \log \left (3\right ) - 11\right )} x^{2} + {\left (x^{2} + 6 \, x + 9\right )} \log \left (x\right )^{2} + 6 \, {\left (\log \left (3\right )^{2} - \log \left (3\right ) - 2\right )} x + 9 \, \log \left (3\right )^{2} + 2 \, {\left (x^{3} + x^{2} {\left (\log \left (3\right ) + 4\right )} + 3 \, x {\left (2 \, \log \left (3\right ) - 1\right )} + 9 \, \log \left (3\right ) - 18\right )} \log \left (x\right ) - 36 \, \log \left (3\right ) + 36} \]
integrate(((2*x^4+19*x^3+63*x^2+81*x+27)*log(1/3*exp(2)/x)^3+(-6*x^5-57*x^ 4-189*x^3-243*x^2-81*x)*log(1/3*exp(2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+ 81*x^2+6*x)*log(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*x) /((x^3+9*x^2+27*x+27)*log(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*log( 1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x^3+81*x^2)*log(1/3*exp(2)/x)-x^6-9*x^5-2 7*x^4-27*x^3),x, algorithm=\
(x^6 + x^5*(2*log(3) + 3) + (log(3)^2 + 10*log(3) - 9)*x^4 + (7*log(3)^2 + 2*log(3) - 23)*x^3 + (15*log(3)^2 - 42*log(3) + 25)*x^2 + (x^4 + 7*x^3 + 15*x^2 + 9*x)*log(x)^2 + 9*(log(3)^2 - 4*log(3) + 4)*x + 2*(x^5 + x^4*(log (3) + 5) + x^3*(7*log(3) + 1) + 3*x^2*(5*log(3) - 7) + 9*x*(log(3) - 2))*l og(x))/(x^4 + 2*x^3*(log(3) + 1) + (log(3)^2 + 8*log(3) - 11)*x^2 + (x^2 + 6*x + 9)*log(x)^2 + 6*(log(3)^2 - log(3) - 2)*x + 9*log(3)^2 + 2*(x^3 + x ^2*(log(3) + 4) + 3*x*(2*log(3) - 1) + 9*log(3) - 18)*log(x) - 36*log(3) + 36)
Leaf count of result is larger than twice the leaf count of optimal. 283 vs. \(2 (29) = 58\).
Time = 0.42 (sec) , antiderivative size = 283, normalized size of antiderivative = 8.84 \[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=-\frac {{\left (\frac {2 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x} - \frac {e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{2}} - \frac {7 \, e^{14}}{x} + \frac {14 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{2}} - \frac {7 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{3}} - \frac {15 \, e^{14}}{x^{2}} + \frac {30 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{3}} - \frac {15 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{4}} - \frac {9 \, e^{14}}{x^{3}} + \frac {18 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{4}} - \frac {9 \, e^{14} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{5}} - \frac {e^{14}}{x^{4}} - e^{14}\right )} e^{\left (-2\right )}}{\frac {e^{12}}{x^{2}} - \frac {2 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{3}} + \frac {e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{4}} + \frac {6 \, e^{12}}{x^{3}} - \frac {12 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{4}} + \frac {6 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{5}} + \frac {9 \, e^{12}}{x^{4}} - \frac {18 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )}{x^{5}} + \frac {9 \, e^{12} \log \left (\frac {e^{2}}{3 \, x}\right )^{2}}{x^{6}}} \]
integrate(((2*x^4+19*x^3+63*x^2+81*x+27)*log(1/3*exp(2)/x)^3+(-6*x^5-57*x^ 4-189*x^3-243*x^2-81*x)*log(1/3*exp(2)/x)^2+(6*x^6+57*x^5+189*x^4+243*x^3+ 81*x^2+6*x)*log(1/3*exp(2)/x)-2*x^7-19*x^6-63*x^5-81*x^4-25*x^3+2*x^2+6*x) /((x^3+9*x^2+27*x+27)*log(1/3*exp(2)/x)^3+(-3*x^4-27*x^3-81*x^2-81*x)*log( 1/3*exp(2)/x)^2+(3*x^5+27*x^4+81*x^3+81*x^2)*log(1/3*exp(2)/x)-x^6-9*x^5-2 7*x^4-27*x^3),x, algorithm=\
-(2*e^14*log(1/3*e^2/x)/x - e^14*log(1/3*e^2/x)^2/x^2 - 7*e^14/x + 14*e^14 *log(1/3*e^2/x)/x^2 - 7*e^14*log(1/3*e^2/x)^2/x^3 - 15*e^14/x^2 + 30*e^14* log(1/3*e^2/x)/x^3 - 15*e^14*log(1/3*e^2/x)^2/x^4 - 9*e^14/x^3 + 18*e^14*l og(1/3*e^2/x)/x^4 - 9*e^14*log(1/3*e^2/x)^2/x^5 - e^14/x^4 - e^14)*e^(-2)/ (e^12/x^2 - 2*e^12*log(1/3*e^2/x)/x^3 + e^12*log(1/3*e^2/x)^2/x^4 + 6*e^12 /x^3 - 12*e^12*log(1/3*e^2/x)/x^4 + 6*e^12*log(1/3*e^2/x)^2/x^5 + 9*e^12/x ^4 - 18*e^12*log(1/3*e^2/x)/x^5 + 9*e^12*log(1/3*e^2/x)^2/x^6)
Time = 9.33 (sec) , antiderivative size = 206, normalized size of antiderivative = 6.44 \[ \int \frac {6 x+2 x^2-25 x^3-81 x^4-63 x^5-19 x^6-2 x^7+\left (6 x+81 x^2+243 x^3+189 x^4+57 x^5+6 x^6\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-243 x^2-189 x^3-57 x^4-6 x^5\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+81 x+63 x^2+19 x^3+2 x^4\right ) \log ^3\left (\frac {e^2}{3 x}\right )}{-27 x^3-27 x^4-9 x^5-x^6+\left (81 x^2+81 x^3+27 x^4+3 x^5\right ) \log \left (\frac {e^2}{3 x}\right )+\left (-81 x-81 x^2-27 x^3-3 x^4\right ) \log ^2\left (\frac {e^2}{3 x}\right )+\left (27+27 x+9 x^2+x^3\right ) \log ^3\left (\frac {e^2}{3 x}\right )} \, dx=x+\frac {\frac {x^2\,\left (x^2+x+3\right )}{\left (x+1\right )\,{\left (x+3\right )}^3}+\frac {3\,x^2\,\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )}{\left (x+1\right )\,{\left (x+3\right )}^3}}{x^2-2\,x\,\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )+{\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )}^2}+x^2+\frac {\frac {3\,x\,\left (3\,x^4+3\,x^3+x^2+3\,x\right )}{{\left (x+1\right )}^3\,{\left (x+3\right )}^4}+\frac {6\,x^2\,\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )\,\left (-x^2+x+3\right )}{{\left (x+1\right )}^3\,{\left (x+3\right )}^4}}{x-\ln \left (\frac {{\mathrm {e}}^2}{3\,x}\right )}+\frac {-6\,x^4+6\,x^3+18\,x^2}{x^7+15\,x^6+93\,x^5+307\,x^4+579\,x^3+621\,x^2+351\,x+81} \]
int((25*x^3 - log(exp(2)/(3*x))^3*(81*x + 63*x^2 + 19*x^3 + 2*x^4 + 27) - log(exp(2)/(3*x))*(6*x + 81*x^2 + 243*x^3 + 189*x^4 + 57*x^5 + 6*x^6) - 2* x^2 - 6*x + 81*x^4 + 63*x^5 + 19*x^6 + 2*x^7 + log(exp(2)/(3*x))^2*(81*x + 243*x^2 + 189*x^3 + 57*x^4 + 6*x^5))/(log(exp(2)/(3*x))^2*(81*x + 81*x^2 + 27*x^3 + 3*x^4) - log(exp(2)/(3*x))^3*(27*x + 9*x^2 + x^3 + 27) - log(ex p(2)/(3*x))*(81*x^2 + 81*x^3 + 27*x^4 + 3*x^5) + 27*x^3 + 27*x^4 + 9*x^5 + x^6),x)
x + ((x^2*(x + x^2 + 3))/((x + 1)*(x + 3)^3) + (3*x^2*log(exp(2)/(3*x)))/( (x + 1)*(x + 3)^3))/(log(exp(2)/(3*x))^2 + x^2 - 2*x*log(exp(2)/(3*x))) + x^2 + ((3*x*(3*x + x^2 + 3*x^3 + 3*x^4))/((x + 1)^3*(x + 3)^4) + (6*x^2*lo g(exp(2)/(3*x))*(x - x^2 + 3))/((x + 1)^3*(x + 3)^4))/(x - log(exp(2)/(3*x ))) + (18*x^2 + 6*x^3 - 6*x^4)/(351*x + 621*x^2 + 579*x^3 + 307*x^4 + 93*x ^5 + 15*x^6 + x^7 + 81)