Integrand size = 134, antiderivative size = 19 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx=\log ^2\left (3 x \log \left (2-\frac {1}{(-5+x) x^2}\right )\right ) \]
Time = 0.07 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.47 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx=\log ^2\left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{(-5+x) x^2}\right )\right ) \]
Integrate[((-20 + 6*x + (10 - 2*x + 100*x^2 - 40*x^3 + 4*x^4)*Log[(-1 - 10 *x^2 + 2*x^3)/(-5*x^2 + x^3)])*Log[3*x*Log[(-1 - 10*x^2 + 2*x^3)/(-5*x^2 + x^3)]])/((5*x - x^2 + 50*x^3 - 20*x^4 + 2*x^5)*Log[(-1 - 10*x^2 + 2*x^3)/ (-5*x^2 + 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.
| \(\displaystyle \int \frac {\left (\left (4 x^4-40 x^3+100 x^2-2 x+10\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )+6 x-20\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )\right )}{\left (2 x^5-20 x^4+50 x^3-x^2+5 x\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (\left (4 x^4-40 x^3+100 x^2-2 x+10\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )+6 x-20\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )\right )}{x \left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (\left (4 x^4-40 x^3+100 x^2-2 x+10\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )+6 x-20\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )\right )}{(5-x) x \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )}+\frac {2 x \left (\left (4 x^4-40 x^3+100 x^2-2 x+10\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )+6 x-20\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{x^3-5 x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+3 x-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {-2 x^3+10 x^2+1}{(5-x) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {-2 x^3+10 x^2+1}{(5-x) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {-2 x^3+10 x^2+1}{(5-x) x^2}\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {-2 x^3+10 x^2+1}{(5-x) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {-2 x^3+10 x^2+1}{(5-x) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {-2 x^3+10 x^2+1}{(5-x) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (-3 x-\left (2 x^4-20 x^3+50 x^2-x+5\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )+10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{(5-x) x \left (-2 x^3+10 x^2+1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 (x-5) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {\left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{5 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}-\frac {2 x \left (2 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^4-20 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^3+50 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x^2-\log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right ) x+3 x+5 \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )-10\right ) \log \left (3 x \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )\right )}{\left (2 x^3-10 x^2-1\right ) \log \left (\frac {2 x^3-10 x^2-1}{(x-5) x^2}\right )}\right )dx\) |
Int[((-20 + 6*x + (10 - 2*x + 100*x^2 - 40*x^3 + 4*x^4)*Log[(-1 - 10*x^2 + 2*x^3)/(-5*x^2 + x^3)])*Log[3*x*Log[(-1 - 10*x^2 + 2*x^3)/(-5*x^2 + x^3)] ])/((5*x - x^2 + 50*x^3 - 20*x^4 + 2*x^5)*Log[(-1 - 10*x^2 + 2*x^3)/(-5*x^ 2 + x^3)]),x]
3.12.20.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
\[\int \frac {\left (\left (4 x^{4}-40 x^{3}+100 x^{2}-2 x +10\right ) \ln \left (\frac {2 x^{3}-10 x^{2}-1}{x^{3}-5 x^{2}}\right )+6 x -20\right ) \ln \left (3 x \ln \left (\frac {2 x^{3}-10 x^{2}-1}{x^{3}-5 x^{2}}\right )\right )}{\left (2 x^{5}-20 x^{4}+50 x^{3}-x^{2}+5 x \right ) \ln \left (\frac {2 x^{3}-10 x^{2}-1}{x^{3}-5 x^{2}}\right )}d x\]
int(((4*x^4-40*x^3+100*x^2-2*x+10)*ln((2*x^3-10*x^2-1)/(x^3-5*x^2))+6*x-20 )*ln(3*x*ln((2*x^3-10*x^2-1)/(x^3-5*x^2)))/(2*x^5-20*x^4+50*x^3-x^2+5*x)/l n((2*x^3-10*x^2-1)/(x^3-5*x^2)),x)
int(((4*x^4-40*x^3+100*x^2-2*x+10)*ln((2*x^3-10*x^2-1)/(x^3-5*x^2))+6*x-20 )*ln(3*x*ln((2*x^3-10*x^2-1)/(x^3-5*x^2)))/(2*x^5-20*x^4+50*x^3-x^2+5*x)/l n((2*x^3-10*x^2-1)/(x^3-5*x^2)),x)
Time = 0.26 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.63 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx=\log \left (3 \, x \log \left (\frac {2 \, x^{3} - 10 \, x^{2} - 1}{x^{3} - 5 \, x^{2}}\right )\right )^{2} \]
integrate(((4*x^4-40*x^3+100*x^2-2*x+10)*log((2*x^3-10*x^2-1)/(x^3-5*x^2)) +6*x-20)*log(3*x*log((2*x^3-10*x^2-1)/(x^3-5*x^2)))/(2*x^5-20*x^4+50*x^3-x ^2+5*x)/log((2*x^3-10*x^2-1)/(x^3-5*x^2)),x, algorithm=\
Time = 0.22 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.42 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx=\log {\left (3 x \log {\left (\frac {2 x^{3} - 10 x^{2} - 1}{x^{3} - 5 x^{2}} \right )} \right )}^{2} \]
integrate(((4*x**4-40*x**3+100*x**2-2*x+10)*ln((2*x**3-10*x**2-1)/(x**3-5* x**2))+6*x-20)*ln(3*x*ln((2*x**3-10*x**2-1)/(x**3-5*x**2)))/(2*x**5-20*x** 4+50*x**3-x**2+5*x)/ln((2*x**3-10*x**2-1)/(x**3-5*x**2)),x)
Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (19) = 38\).
Time = 0.24 (sec) , antiderivative size = 124, normalized size of antiderivative = 6.53 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx=2 \, {\left (\log \left (x\right ) + \log \left (\log \left (2 \, x^{3} - 10 \, x^{2} - 1\right ) - \log \left (x - 5\right ) - 2 \, \log \left (x\right )\right )\right )} \log \left (3 \, x \log \left (\frac {2 \, x^{3} - 10 \, x^{2} - 1}{x^{3} - 5 \, x^{2}}\right )\right ) - \log \left (x\right )^{2} - 2 \, \log \left (x\right ) \log \left (\log \left (2 \, x^{3} - 10 \, x^{2} - 1\right ) - \log \left (x - 5\right ) - 2 \, \log \left (x\right )\right ) - \log \left (\log \left (2 \, x^{3} - 10 \, x^{2} - 1\right ) - \log \left (x - 5\right ) - 2 \, \log \left (x\right )\right )^{2} \]
integrate(((4*x^4-40*x^3+100*x^2-2*x+10)*log((2*x^3-10*x^2-1)/(x^3-5*x^2)) +6*x-20)*log(3*x*log((2*x^3-10*x^2-1)/(x^3-5*x^2)))/(2*x^5-20*x^4+50*x^3-x ^2+5*x)/log((2*x^3-10*x^2-1)/(x^3-5*x^2)),x, algorithm=\
2*(log(x) + log(log(2*x^3 - 10*x^2 - 1) - log(x - 5) - 2*log(x)))*log(3*x* log((2*x^3 - 10*x^2 - 1)/(x^3 - 5*x^2))) - log(x)^2 - 2*log(x)*log(log(2*x ^3 - 10*x^2 - 1) - log(x - 5) - 2*log(x)) - log(log(2*x^3 - 10*x^2 - 1) - log(x - 5) - 2*log(x))^2
Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (19) = 38\).
Time = 0.80 (sec) , antiderivative size = 92, normalized size of antiderivative = 4.84 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx=\log \left (x\right )^{2} + 2 \, {\left (\log \left (x\right ) + \log \left (\log \left (2 \, x^{3} - 10 \, x^{2} - 1\right ) - \log \left (x - 5\right ) - 2 \, \log \left (x\right )\right )\right )} \log \left (3 \, \log \left (\frac {2 \, x^{3} - 10 \, x^{2} - 1}{x^{3} - 5 \, x^{2}}\right )\right ) - \log \left (\log \left (2 \, x^{3} - 10 \, x^{2} - 1\right ) - \log \left (x - 5\right ) - 2 \, \log \left (x\right )\right )^{2} \]
integrate(((4*x^4-40*x^3+100*x^2-2*x+10)*log((2*x^3-10*x^2-1)/(x^3-5*x^2)) +6*x-20)*log(3*x*log((2*x^3-10*x^2-1)/(x^3-5*x^2)))/(2*x^5-20*x^4+50*x^3-x ^2+5*x)/log((2*x^3-10*x^2-1)/(x^3-5*x^2)),x, algorithm=\
log(x)^2 + 2*(log(x) + log(log(2*x^3 - 10*x^2 - 1) - log(x - 5) - 2*log(x) ))*log(3*log((2*x^3 - 10*x^2 - 1)/(x^3 - 5*x^2))) - log(log(2*x^3 - 10*x^2 - 1) - log(x - 5) - 2*log(x))^2
Time = 14.16 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.74 \[ \int \frac {\left (-20+6 x+\left (10-2 x+100 x^2-40 x^3+4 x^4\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right ) \log \left (3 x \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )\right )}{\left (5 x-x^2+50 x^3-20 x^4+2 x^5\right ) \log \left (\frac {-1-10 x^2+2 x^3}{-5 x^2+x^3}\right )} \, dx={\ln \left (3\,x\,\ln \left (\frac {-2\,x^3+10\,x^2+1}{5\,x^2-x^3}\right )\right )}^2 \]