Integrand size = 460, antiderivative size = 30 \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\frac {3+x}{-3+x-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(-3+x)^2}\right )\right )} \] Output:
(3+x)/(x-3-ln(ln(ln(x^2+3/ln(5))/(-3+x)^2)))
Leaf count is larger than twice the leaf count of optimal. \(142\) vs. \(2(30)=60\).
Time = 0.12 (sec) , antiderivative size = 142, normalized size of antiderivative = 4.73 \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\frac {18 x \log (5)-x^3 \log (25)+(3+x) \left (3+x^2 \log (5)\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left (2+(-3+x) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(-3+x)^2}\right )\right )}{\left (-2 (-3+x) x \log (5)+\left (3+x^2 \log (5)\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left (2+(-3+x) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(-3+x)^2}\right )\right )\right ) \left (-3+x-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(-3+x)^2}\right )\right )\right )} \] Input:
Integrate[((-18*x + 2*x^3)*Log[5] + (-18 - 6*x + (-6*x^2 - 2*x^3)*Log[5])* Log[(3 + x^2*Log[5])/Log[5]] + (54 - 18*x + (18*x^2 - 6*x^3)*Log[5])*Log[( 3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)] + (9 - 3*x + (3*x^2 - x^3)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)]*Log[Log[Log[(3 + x^2*Log[5])/Log[5 ]]/(9 - 6*x + x^2)]])/((-81 + 81*x - 27*x^2 + 3*x^3 + (-27*x^2 + 27*x^3 - 9*x^4 + x^5)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5]) /Log[5]]/(9 - 6*x + x^2)] + (-54 + 36*x - 6*x^2 + (-18*x^2 + 12*x^3 - 2*x^ 4)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5]]/( 9 - 6*x + x^2)]*Log[Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)]] + ( -9 + 3*x + (-3*x^2 + x^3)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)]*Log[Log[Log[(3 + x^2*Log[5])/Log[5] ]/(9 - 6*x + x^2)]]^2),x]
Output:
(18*x*Log[5] - x^3*Log[25] + (3 + x)*(3 + x^2*Log[5])*Log[x^2 + 3/Log[5]]* (2 + (-3 + x)*Log[Log[x^2 + 3/Log[5]]/(-3 + x)^2]))/((-2*(-3 + x)*x*Log[5] + (3 + x^2*Log[5])*Log[x^2 + 3/Log[5]]*(2 + (-3 + x)*Log[Log[x^2 + 3/Log[ 5]]/(-3 + x)^2]))*(-3 + x - Log[Log[Log[x^2 + 3/Log[5]]/(-3 + x)^2]]))
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.
| \(\displaystyle \int \frac {\left (2 x^3-18 x\right ) \log (5)+\left (\left (-2 x^3-6 x^2\right ) \log (5)-6 x-18\right ) \log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )+\left (\left (18 x^2-6 x^3\right ) \log (5)-18 x+54\right ) \log \left (\frac {x^2 \log (5)+3}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right )+\left (\left (3 x^2-x^3\right ) \log (5)-3 x+9\right ) \log \left (\frac {x^2 \log (5)+3}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right ) \log \left (\log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right )\right )}{\left (\left (x^3-3 x^2\right ) \log (5)+3 x-9\right ) \log \left (\frac {x^2 \log (5)+3}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right )\right )+\left (-6 x^2+\left (-2 x^4+12 x^3-18 x^2\right ) \log (5)+36 x-54\right ) \log \left (\frac {x^2 \log (5)+3}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right ) \log \left (\log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right )\right )+\left (3 x^3-27 x^2+\left (x^5-9 x^4+27 x^3-27 x^2\right ) \log (5)+81 x-81\right ) \log \left (\frac {x^2 \log (5)+3}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {x^2 \log (5)+3}{\log (5)}\right )}{x^2-6 x+9}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^3 (-\log (25))+\left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \left ((x-3) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+6\right )+2 (x+3)\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle \int \left (\frac {1}{-\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )+x-3}+\frac {-x^3 \log (25)+6 x^2 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+3 x^2 (1-3 \log (5)) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+6 x \log \left (x^2+\frac {3}{\log (5)}\right )+18 \log \left (x^2+\frac {3}{\log (5)}\right )-27 \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+x^4 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )+2 x^3 \log (5) \log \left (x^2+\frac {3}{\log (5)}\right )+18 x \log (5)}{(3-x) \left (x^2 \log (5)+3\right ) \log \left (x^2+\frac {3}{\log (5)}\right ) \log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right ) \left (\log \left (\log \left (\frac {\log \left (x^2+\frac {3}{\log (5)}\right )}{(x-3)^2}\right )\right )-x+3\right )^2}\right )dx\) |
Input:
Int[((-18*x + 2*x^3)*Log[5] + (-18 - 6*x + (-6*x^2 - 2*x^3)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]] + (54 - 18*x + (18*x^2 - 6*x^3)*Log[5])*Log[(3 + x^ 2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)] + (9 - 3*x + (3*x^2 - x^3)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2 *Log[5])/Log[5]]/(9 - 6*x + x^2)]*Log[Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)]])/((-81 + 81*x - 27*x^2 + 3*x^3 + (-27*x^2 + 27*x^3 - 9*x^4 + x^5)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5 ]]/(9 - 6*x + x^2)] + (-54 + 36*x - 6*x^2 + (-18*x^2 + 12*x^3 - 2*x^4)*Log [5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6* x + x^2)]*Log[Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)]] + (-9 + 3 *x + (-3*x^2 + x^3)*Log[5])*Log[(3 + x^2*Log[5])/Log[5]]*Log[Log[(3 + x^2* Log[5])/Log[5]]/(9 - 6*x + x^2)]*Log[Log[Log[(3 + x^2*Log[5])/Log[5]]/(9 - 6*x + x^2)]]^2),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.05 (sec) , antiderivative size = 175, normalized size of antiderivative = 5.83
\[\frac {3+x}{x -\ln \left (\ln \left (\ln \left (\frac {x^{2} \ln \left (5\right )+3}{\ln \left (5\right )}\right )\right )-2 \ln \left (-3+x \right )+\frac {i \pi \,\operatorname {csgn}\left (i \left (-3+x \right )^{2}\right ) {\left (-\operatorname {csgn}\left (i \left (-3+x \right )^{2}\right )+\operatorname {csgn}\left (i \left (-3+x \right )\right )\right )}^{2}}{2}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \ln \left (\frac {x^{2} \ln \left (5\right )+3}{\ln \left (5\right )}\right )}{\left (-3+x \right )^{2}}\right ) \left (-\operatorname {csgn}\left (\frac {i \ln \left (\frac {x^{2} \ln \left (5\right )+3}{\ln \left (5\right )}\right )}{\left (-3+x \right )^{2}}\right )+\operatorname {csgn}\left (i \ln \left (\frac {x^{2} \ln \left (5\right )+3}{\ln \left (5\right )}\right )\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \ln \left (\frac {x^{2} \ln \left (5\right )+3}{\ln \left (5\right )}\right )}{\left (-3+x \right )^{2}}\right )+\operatorname {csgn}\left (\frac {i}{\left (-3+x \right )^{2}}\right )\right )}{2}\right )-3}\]
Input:
int((((-x^3+3*x^2)*ln(5)-3*x+9)*ln((x^2*ln(5)+3)/ln(5))*ln(ln((x^2*ln(5)+3 )/ln(5))/(x^2-6*x+9))*ln(ln(ln((x^2*ln(5)+3)/ln(5))/(x^2-6*x+9)))+((-6*x^3 +18*x^2)*ln(5)-18*x+54)*ln((x^2*ln(5)+3)/ln(5))*ln(ln((x^2*ln(5)+3)/ln(5)) /(x^2-6*x+9))+((-2*x^3-6*x^2)*ln(5)-6*x-18)*ln((x^2*ln(5)+3)/ln(5))+(2*x^3 -18*x)*ln(5))/(((x^3-3*x^2)*ln(5)+3*x-9)*ln((x^2*ln(5)+3)/ln(5))*ln(ln((x^ 2*ln(5)+3)/ln(5))/(x^2-6*x+9))*ln(ln(ln((x^2*ln(5)+3)/ln(5))/(x^2-6*x+9))) ^2+((-2*x^4+12*x^3-18*x^2)*ln(5)-6*x^2+36*x-54)*ln((x^2*ln(5)+3)/ln(5))*ln (ln((x^2*ln(5)+3)/ln(5))/(x^2-6*x+9))*ln(ln(ln((x^2*ln(5)+3)/ln(5))/(x^2-6 *x+9)))+((x^5-9*x^4+27*x^3-27*x^2)*ln(5)+3*x^3-27*x^2+81*x-81)*ln((x^2*ln( 5)+3)/ln(5))*ln(ln((x^2*ln(5)+3)/ln(5))/(x^2-6*x+9))),x)
Output:
(3+x)/(x-ln(ln(ln((x^2*ln(5)+3)/ln(5)))-2*ln(-3+x)+1/2*I*Pi*csgn(I*(-3+x)^ 2)*(-csgn(I*(-3+x)^2)+csgn(I*(-3+x)))^2-1/2*I*Pi*csgn(I*ln((x^2*ln(5)+3)/l n(5))/(-3+x)^2)*(-csgn(I*ln((x^2*ln(5)+3)/ln(5))/(-3+x)^2)+csgn(I*ln((x^2* ln(5)+3)/ln(5))))*(-csgn(I*ln((x^2*ln(5)+3)/ln(5))/(-3+x)^2)+csgn(I/(-3+x) ^2)))-3)
Time = 0.10 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27 \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\frac {x + 3}{x - \log \left (\log \left (\frac {\log \left (\frac {x^{2} \log \left (5\right ) + 3}{\log \left (5\right )}\right )}{x^{2} - 6 \, x + 9}\right )\right ) - 3} \] Input:
integrate((((-x^3+3*x^2)*log(5)-3*x+9)*log((x^2*log(5)+3)/log(5))*log(log( (x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^ 2-6*x+9)))+((-6*x^3+18*x^2)*log(5)-18*x+54)*log((x^2*log(5)+3)/log(5))*log (log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))+((-2*x^3-6*x^2)*log(5)-6*x-18)*lo g((x^2*log(5)+3)/log(5))+(2*x^3-18*x)*log(5))/(((x^3-3*x^2)*log(5)+3*x-9)* log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log (log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))^2+((-2*x^4+12*x^3-18*x^2)*lo g(5)-6*x^2+36*x-54)*log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log( 5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))+((x^5-9* x^4+27*x^3-27*x^2)*log(5)+3*x^3-27*x^2+81*x-81)*log((x^2*log(5)+3)/log(5)) *log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))),x, algorithm="fricas")
Output:
(x + 3)/(x - log(log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9))) - 3)
Time = 2.16 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\frac {- x - 3}{- x + \log {\left (\log {\left (\frac {\log {\left (\frac {x^{2} \log {\left (5 \right )} + 3}{\log {\left (5 \right )}} \right )}}{x^{2} - 6 x + 9} \right )} \right )} + 3} \] Input:
integrate((((-x**3+3*x**2)*ln(5)-3*x+9)*ln((x**2*ln(5)+3)/ln(5))*ln(ln((x* *2*ln(5)+3)/ln(5))/(x**2-6*x+9))*ln(ln(ln((x**2*ln(5)+3)/ln(5))/(x**2-6*x+ 9)))+((-6*x**3+18*x**2)*ln(5)-18*x+54)*ln((x**2*ln(5)+3)/ln(5))*ln(ln((x** 2*ln(5)+3)/ln(5))/(x**2-6*x+9))+((-2*x**3-6*x**2)*ln(5)-6*x-18)*ln((x**2*l n(5)+3)/ln(5))+(2*x**3-18*x)*ln(5))/(((x**3-3*x**2)*ln(5)+3*x-9)*ln((x**2* ln(5)+3)/ln(5))*ln(ln((x**2*ln(5)+3)/ln(5))/(x**2-6*x+9))*ln(ln(ln((x**2*l n(5)+3)/ln(5))/(x**2-6*x+9)))**2+((-2*x**4+12*x**3-18*x**2)*ln(5)-6*x**2+3 6*x-54)*ln((x**2*ln(5)+3)/ln(5))*ln(ln((x**2*ln(5)+3)/ln(5))/(x**2-6*x+9)) *ln(ln(ln((x**2*ln(5)+3)/ln(5))/(x**2-6*x+9)))+((x**5-9*x**4+27*x**3-27*x* *2)*ln(5)+3*x**3-27*x**2+81*x-81)*ln((x**2*ln(5)+3)/ln(5))*ln(ln((x**2*ln( 5)+3)/ln(5))/(x**2-6*x+9))),x)
Output:
(-x - 3)/(-x + log(log(log((x**2*log(5) + 3)/log(5))/(x**2 - 6*x + 9))) + 3)
Time = 0.37 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\frac {x + 3}{x - \log \left (-2 \, \log \left (x - 3\right ) + \log \left (\log \left (x^{2} \log \left (5\right ) + 3\right ) - \log \left (\log \left (5\right )\right )\right )\right ) - 3} \] Input:
integrate((((-x^3+3*x^2)*log(5)-3*x+9)*log((x^2*log(5)+3)/log(5))*log(log( (x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^ 2-6*x+9)))+((-6*x^3+18*x^2)*log(5)-18*x+54)*log((x^2*log(5)+3)/log(5))*log (log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))+((-2*x^3-6*x^2)*log(5)-6*x-18)*lo g((x^2*log(5)+3)/log(5))+(2*x^3-18*x)*log(5))/(((x^3-3*x^2)*log(5)+3*x-9)* log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log (log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))^2+((-2*x^4+12*x^3-18*x^2)*lo g(5)-6*x^2+36*x-54)*log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log( 5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))+((x^5-9* x^4+27*x^3-27*x^2)*log(5)+3*x^3-27*x^2+81*x-81)*log((x^2*log(5)+3)/log(5)) *log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))),x, algorithm="maxima")
Output:
(x + 3)/(x - log(-2*log(x - 3) + log(log(x^2*log(5) + 3) - log(log(5)))) - 3)
Exception generated. \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((-x^3+3*x^2)*log(5)-3*x+9)*log((x^2*log(5)+3)/log(5))*log(log( (x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^ 2-6*x+9)))+((-6*x^3+18*x^2)*log(5)-18*x+54)*log((x^2*log(5)+3)/log(5))*log (log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))+((-2*x^3-6*x^2)*log(5)-6*x-18)*lo g((x^2*log(5)+3)/log(5))+(2*x^3-18*x)*log(5))/(((x^3-3*x^2)*log(5)+3*x-9)* log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log (log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))^2+((-2*x^4+12*x^3-18*x^2)*lo g(5)-6*x^2+36*x-54)*log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log( 5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))+((x^5-9* x^4+27*x^3-27*x^2)*log(5)+3*x^3-27*x^2+81*x-81)*log((x^2*log(5)+3)/log(5)) *log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))),x, algorithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value
Timed out. \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\int \frac {\ln \left (5\right )\,\left (18\,x-2\,x^3\right )+\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )\,\left (6\,x+\ln \left (5\right )\,\left (2\,x^3+6\,x^2\right )+18\right )-\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )\,\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\,\left (\ln \left (5\right )\,\left (18\,x^2-6\,x^3\right )-18\,x+54\right )-\ln \left (\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\right )\,\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )\,\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\,\left (\ln \left (5\right )\,\left (3\,x^2-x^3\right )-3\,x+9\right )}{\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )\,\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\,\left (\ln \left (5\right )\,\left (3\,x^2-x^3\right )-3\,x+9\right )\,{\ln \left (\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\right )}^2+\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )\,\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\,\left (\ln \left (5\right )\,\left (2\,x^4-12\,x^3+18\,x^2\right )-36\,x+6\,x^2+54\right )\,\ln \left (\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\right )+\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )\,\ln \left (\frac {\ln \left (\frac {\ln \left (5\right )\,x^2+3}{\ln \left (5\right )}\right )}{x^2-6\,x+9}\right )\,\left (\ln \left (5\right )\,\left (-x^5+9\,x^4-27\,x^3+27\,x^2\right )-81\,x+27\,x^2-3\,x^3+81\right )} \,d x \] Input:
int((log(5)*(18*x - 2*x^3) + log((x^2*log(5) + 3)/log(5))*(6*x + log(5)*(6 *x^2 + 2*x^3) + 18) - log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3 )/log(5))/(x^2 - 6*x + 9))*(log(5)*(18*x^2 - 6*x^3) - 18*x + 54) - log(log (log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9)))*log((x^2*log(5) + 3)/log(5 ))*log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9))*(log(5)*(3*x^2 - x^3) - 3*x + 9))/(log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3)/log(5) )/(x^2 - 6*x + 9))*(log(5)*(27*x^2 - 27*x^3 + 9*x^4 - x^5) - 81*x + 27*x^2 - 3*x^3 + 81) + log(log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9)))^2* log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9))*(log(5)*(3*x^2 - x^3) - 3*x + 9) + log(log(log((x^2*log(5) + 3)/log(5 ))/(x^2 - 6*x + 9)))*log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3) /log(5))/(x^2 - 6*x + 9))*(log(5)*(18*x^2 - 12*x^3 + 2*x^4) - 36*x + 6*x^2 + 54)),x)
Output:
int((log(5)*(18*x - 2*x^3) + log((x^2*log(5) + 3)/log(5))*(6*x + log(5)*(6 *x^2 + 2*x^3) + 18) - log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3 )/log(5))/(x^2 - 6*x + 9))*(log(5)*(18*x^2 - 6*x^3) - 18*x + 54) - log(log (log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9)))*log((x^2*log(5) + 3)/log(5 ))*log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9))*(log(5)*(3*x^2 - x^3) - 3*x + 9))/(log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3)/log(5) )/(x^2 - 6*x + 9))*(log(5)*(27*x^2 - 27*x^3 + 9*x^4 - x^5) - 81*x + 27*x^2 - 3*x^3 + 81) + log(log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9)))^2* log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3)/log(5))/(x^2 - 6*x + 9))*(log(5)*(3*x^2 - x^3) - 3*x + 9) + log(log(log((x^2*log(5) + 3)/log(5 ))/(x^2 - 6*x + 9)))*log((x^2*log(5) + 3)/log(5))*log(log((x^2*log(5) + 3) /log(5))/(x^2 - 6*x + 9))*(log(5)*(18*x^2 - 12*x^3 + 2*x^4) - 36*x + 6*x^2 + 54)), x)
Time = 0.37 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.20 \[ \int \frac {\left (-18 x+2 x^3\right ) \log (5)+\left (-18-6 x+\left (-6 x^2-2 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )+\left (54-18 x+\left (18 x^2-6 x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (9-3 x+\left (3 x^2-x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )}{\left (-81+81 x-27 x^2+3 x^3+\left (-27 x^2+27 x^3-9 x^4+x^5\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )+\left (-54+36 x-6 x^2+\left (-18 x^2+12 x^3-2 x^4\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log \left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )+\left (-9+3 x+\left (-3 x^2+x^3\right ) \log (5)\right ) \log \left (\frac {3+x^2 \log (5)}{\log (5)}\right ) \log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right ) \log ^2\left (\log \left (\frac {\log \left (\frac {3+x^2 \log (5)}{\log (5)}\right )}{9-6 x+x^2}\right )\right )} \, dx=\frac {-\mathrm {log}\left (\mathrm {log}\left (\frac {\mathrm {log}\left (\frac {\mathrm {log}\left (5\right ) x^{2}+3}{\mathrm {log}\left (5\right )}\right )}{x^{2}-6 x +9}\right )\right )-6}{\mathrm {log}\left (\mathrm {log}\left (\frac {\mathrm {log}\left (\frac {\mathrm {log}\left (5\right ) x^{2}+3}{\mathrm {log}\left (5\right )}\right )}{x^{2}-6 x +9}\right )\right )-x +3} \] Input:
int((((-x^3+3*x^2)*log(5)-3*x+9)*log((x^2*log(5)+3)/log(5))*log(log((x^2*l og(5)+3)/log(5))/(x^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+ 9)))+((-6*x^3+18*x^2)*log(5)-18*x+54)*log((x^2*log(5)+3)/log(5))*log(log(( x^2*log(5)+3)/log(5))/(x^2-6*x+9))+((-2*x^3-6*x^2)*log(5)-6*x-18)*log((x^2 *log(5)+3)/log(5))+(2*x^3-18*x)*log(5))/(((x^3-3*x^2)*log(5)+3*x-9)*log((x ^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9))*log(log(l og((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))^2+((-2*x^4+12*x^3-18*x^2)*log(5)-6 *x^2+36*x-54)*log((x^2*log(5)+3)/log(5))*log(log((x^2*log(5)+3)/log(5))/(x ^2-6*x+9))*log(log(log((x^2*log(5)+3)/log(5))/(x^2-6*x+9)))+((x^5-9*x^4+27 *x^3-27*x^2)*log(5)+3*x^3-27*x^2+81*x-81)*log((x^2*log(5)+3)/log(5))*log(l og((x^2*log(5)+3)/log(5))/(x^2-6*x+9))),x)
Output:
( - log(log(log((log(5)*x**2 + 3)/log(5))/(x**2 - 6*x + 9))) - 6)/(log(log (log((log(5)*x**2 + 3)/log(5))/(x**2 - 6*x + 9))) - x + 3)