Integrand size = 243, antiderivative size = 26 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=x^2 \log ^2\left (\frac {4-x+\frac {1}{e^5+x+x^2}}{x}\right ) \]
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 15.81 (sec) , antiderivative size = 146774, normalized size of antiderivative = 5645.15 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=\text {Result too large to show} \]
Integrate[((8*E^10*x + 4*x^2 + 14*x^3 + 16*x^4 + 8*x^5 + E^5*(2*x + 16*x^2 + 16*x^3))*Log[(1 + E^5*(4 - x) + 4*x + 3*x^2 - x^3)/(E^5*x + x^2 + x^3)] + (-2*x^2 - 10*x^3 - 14*x^4 - 4*x^5 + 2*x^6 + E^10*(-8*x + 2*x^2) + E^5*( -2*x - 16*x^2 - 12*x^3 + 4*x^4))*Log[(1 + E^5*(4 - x) + 4*x + 3*x^2 - x^3) /(E^5*x + x^2 + x^3)]^2)/(E^10*(-4 + x) - x - 5*x^2 - 7*x^3 - 2*x^4 + x^5 + E^5*(-1 - 8*x - 6*x^2 + 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.
| \(\displaystyle \int \frac {\left (8 x^5+16 x^4+14 x^3+4 x^2+e^5 \left (16 x^3+16 x^2+2 x\right )+8 e^{10} x\right ) \log \left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x^3+x^2+e^5 x}\right )+\left (2 x^6-4 x^5-14 x^4-10 x^3-2 x^2+e^{10} \left (2 x^2-8 x\right )+e^5 \left (4 x^4-12 x^3-16 x^2-2 x\right )\right ) \log ^2\left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x^3+x^2+e^5 x}\right )}{x^5-2 x^4-7 x^3-5 x^2+e^5 \left (2 x^3-6 x^2-8 x-1\right )-x+e^{10} (x-4)} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (8 x^5+16 x^4+14 x^3+4 x^2+e^5 \left (16 x^3+16 x^2+2 x\right )+8 e^{10} x\right ) \log \left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x^3+x^2+e^5 x}\right )+\left (2 x^6-4 x^5-14 x^4-10 x^3-2 x^2+e^{10} \left (2 x^2-8 x\right )+e^5 \left (4 x^4-12 x^3-16 x^2-2 x\right )\right ) \log ^2\left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x^3+x^2+e^5 x}\right )}{-x^2-x-e^5}+\frac {(4-x) \left (\left (8 x^5+16 x^4+14 x^3+4 x^2+e^5 \left (16 x^3+16 x^2+2 x\right )+8 e^{10} x\right ) \log \left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x^3+x^2+e^5 x}\right )+\left (2 x^6-4 x^5-14 x^4-10 x^3-2 x^2+e^{10} \left (2 x^2-8 x\right )+e^5 \left (4 x^4-12 x^3-16 x^2-2 x\right )\right ) \log ^2\left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x^3+x^2+e^5 x}\right )\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (-4 x^4-8 x^3-7 x^2-e^5 \left (8 x^2+8 x+1\right )-\left (e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )+e^{10} (x-4)\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-2 x-4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {x \left (4 x^4+8 x^3+7 x^2+2 x+e^5 \left (8 x^2+8 x+1\right )-\left (e^{10} (4-x)+e^5 \left (-2 x^3+6 x^2+8 x+1\right )+x \left (-x^4+2 x^3+7 x^2+5 x+1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {x \left (4 x^4+8 x^3+7 x^2+2 x+e^5 \left (8 x^2+8 x+1\right )-\left (e^{10} (4-x)+e^5 \left (-2 x^3+6 x^2+8 x+1\right )+x \left (-x^4+2 x^3+7 x^2+5 x+1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x+e^5 (4-x)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle -2 \int \left (\frac {(4-x) x \left (-\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5+2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4-4 x^4+7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3-8 x^3+5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2-7 \left (1+\frac {8 e^5}{7}\right ) x^2+\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x-2 \left (1+4 e^5\right ) x+e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )-e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}+\frac {x \left (\log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^5-2 \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^4+4 x^4-7 \left (1-\frac {2 e^5}{7}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^3+8 x^3-5 \left (1+\frac {6 e^5}{5}\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x^2+7 \left (1+\frac {8 e^5}{7}\right ) x^2-\left (1-e^5 \left (-8+e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right ) x+2 \left (1+4 e^5\right ) x-e^5 \left (1+4 e^5\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+e^5 \left (1+4 e^5\right )\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{x^2+x+e^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (e^5 \left (8 x^2+8 x+1\right )+x \left (4 x^3+8 x^2+7 x+2\right )+\left (e^{10} (x-4)+e^5 \left (2 x^3-6 x^2-8 x-1\right )+x \left (x^4-2 x^3-7 x^2-5 x-1\right )\right ) \log \left (\frac {-x^3+3 x^2+4 x-e^5 (x-4)+1}{x \left (x^2+x+e^5\right )}\right )+4 e^{10}\right ) \log \left (\frac {-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1}{x \left (x^2+x+e^5\right )}\right )}{\left (x^2+x+e^5\right ) \left (-x^3+3 x^2+\left (4-e^5\right ) x+4 e^5+1\right )}dx\) |
Int[((8*E^10*x + 4*x^2 + 14*x^3 + 16*x^4 + 8*x^5 + E^5*(2*x + 16*x^2 + 16* x^3))*Log[(1 + E^5*(4 - x) + 4*x + 3*x^2 - x^3)/(E^5*x + x^2 + x^3)] + (-2 *x^2 - 10*x^3 - 14*x^4 - 4*x^5 + 2*x^6 + E^10*(-8*x + 2*x^2) + E^5*(-2*x - 16*x^2 - 12*x^3 + 4*x^4))*Log[(1 + E^5*(4 - x) + 4*x + 3*x^2 - x^3)/(E^5* x + x^2 + x^3)]^2)/(E^10*(-4 + x) - x - 5*x^2 - 7*x^3 - 2*x^4 + x^5 + E^5* (-1 - 8*x - 6*x^2 + 2*x^3)),x]
3.30.56.3.1 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[(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[(u_)/((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.)), x_Symbol] :> With[ {v = RationalFunctionExpand[u/(a + b*x^n + c*x^(2*n)), x]}, Int[v, x] /; Su mQ[v]] /; FreeQ[{a, b, c}, x] && EqQ[n2, 2*n] && IGtQ[n, 0]
Time = 3.09 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.73
| method | result | size |
| norman | \(x^{2} \ln \left (\frac {\left (-x +4\right ) {\mathrm e}^{5}-x^{3}+3 x^{2}+4 x +1}{x \,{\mathrm e}^{5}+x^{3}+x^{2}}\right )^{2}\) | \(45\) |
| risch | \(x^{2} \ln \left (\frac {\left (-x +4\right ) {\mathrm e}^{5}-x^{3}+3 x^{2}+4 x +1}{x \,{\mathrm e}^{5}+x^{3}+x^{2}}\right )^{2}\) | \(45\) |
| parallelrisch | \(-\frac {\left (-16 x^{2} \ln \left (\frac {\left (-x +4\right ) {\mathrm e}^{5}-x^{3}+3 x^{2}+4 x +1}{x \left (x^{2}+{\mathrm e}^{5}+x \right )}\right )^{2} {\mathrm e}^{20}-8 \,{\mathrm e}^{15} x^{2} \ln \left (\frac {\left (-x +4\right ) {\mathrm e}^{5}-x^{3}+3 x^{2}+4 x +1}{x \left (x^{2}+{\mathrm e}^{5}+x \right )}\right )^{2}-{\mathrm e}^{10} x^{2} \ln \left (\frac {\left (-x +4\right ) {\mathrm e}^{5}-x^{3}+3 x^{2}+4 x +1}{x \left (x^{2}+{\mathrm e}^{5}+x \right )}\right )^{2}\right ) {\mathrm e}^{-10}}{\left (4 \,{\mathrm e}^{5}+1\right )^{2}}\) | \(160\) |
int((((2*x^2-8*x)*exp(5)^2+(4*x^4-12*x^3-16*x^2-2*x)*exp(5)+2*x^6-4*x^5-14 *x^4-10*x^3-2*x^2)*ln(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3+x^2))^ 2+(8*x*exp(5)^2+(16*x^3+16*x^2+2*x)*exp(5)+8*x^5+16*x^4+14*x^3+4*x^2)*ln(( (-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3+x^2)))/((x-4)*exp(5)^2+(2*x^3 -6*x^2-8*x-1)*exp(5)+x^5-2*x^4-7*x^3-5*x^2-x),x,method=_RETURNVERBOSE)
Time = 0.25 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=x^{2} \log \left (-\frac {x^{3} - 3 \, x^{2} + {\left (x - 4\right )} e^{5} - 4 \, x - 1}{x^{3} + x^{2} + x e^{5}}\right )^{2} \]
integrate((((2*x^2-8*x)*exp(5)^2+(4*x^4-12*x^3-16*x^2-2*x)*exp(5)+2*x^6-4* x^5-14*x^4-10*x^3-2*x^2)*log(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3 +x^2))^2+(8*x*exp(5)^2+(16*x^3+16*x^2+2*x)*exp(5)+8*x^5+16*x^4+14*x^3+4*x^ 2)*log(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3+x^2)))/((x-4)*exp(5)^ 2+(2*x^3-6*x^2-8*x-1)*exp(5)+x^5-2*x^4-7*x^3-5*x^2-x),x, algorithm=\
Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=x^{2} \log {\left (\frac {- x^{3} + 3 x^{2} + 4 x + \left (4 - x\right ) e^{5} + 1}{x^{3} + x^{2} + x e^{5}} \right )}^{2} \]
integrate((((2*x**2-8*x)*exp(5)**2+(4*x**4-12*x**3-16*x**2-2*x)*exp(5)+2*x **6-4*x**5-14*x**4-10*x**3-2*x**2)*ln(((-x+4)*exp(5)-x**3+3*x**2+4*x+1)/(x *exp(5)+x**3+x**2))**2+(8*x*exp(5)**2+(16*x**3+16*x**2+2*x)*exp(5)+8*x**5+ 16*x**4+14*x**3+4*x**2)*ln(((-x+4)*exp(5)-x**3+3*x**2+4*x+1)/(x*exp(5)+x** 3+x**2)))/((x-4)*exp(5)**2+(2*x**3-6*x**2-8*x-1)*exp(5)+x**5-2*x**4-7*x**3 -5*x**2-x),x)
Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (26) = 52\).
Time = 0.26 (sec) , antiderivative size = 113, normalized size of antiderivative = 4.35 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=x^{2} \log \left (-x^{3} + 3 \, x^{2} - x {\left (e^{5} - 4\right )} + 4 \, e^{5} + 1\right )^{2} + x^{2} \log \left (x^{2} + x + e^{5}\right )^{2} + 2 \, x^{2} \log \left (x^{2} + x + e^{5}\right ) \log \left (x\right ) + x^{2} \log \left (x\right )^{2} - 2 \, {\left (x^{2} \log \left (x^{2} + x + e^{5}\right ) + x^{2} \log \left (x\right )\right )} \log \left (-x^{3} + 3 \, x^{2} - x {\left (e^{5} - 4\right )} + 4 \, e^{5} + 1\right ) \]
integrate((((2*x^2-8*x)*exp(5)^2+(4*x^4-12*x^3-16*x^2-2*x)*exp(5)+2*x^6-4* x^5-14*x^4-10*x^3-2*x^2)*log(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3 +x^2))^2+(8*x*exp(5)^2+(16*x^3+16*x^2+2*x)*exp(5)+8*x^5+16*x^4+14*x^3+4*x^ 2)*log(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3+x^2)))/((x-4)*exp(5)^ 2+(2*x^3-6*x^2-8*x-1)*exp(5)+x^5-2*x^4-7*x^3-5*x^2-x),x, algorithm=\
x^2*log(-x^3 + 3*x^2 - x*(e^5 - 4) + 4*e^5 + 1)^2 + x^2*log(x^2 + x + e^5) ^2 + 2*x^2*log(x^2 + x + e^5)*log(x) + x^2*log(x)^2 - 2*(x^2*log(x^2 + x + e^5) + x^2*log(x))*log(-x^3 + 3*x^2 - x*(e^5 - 4) + 4*e^5 + 1)
Time = 2.21 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.65 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=x^{2} \log \left (-\frac {x^{3} - 3 \, x^{2} + x e^{5} - 4 \, x - 4 \, e^{5} - 1}{x^{3} + x^{2} + x e^{5}}\right )^{2} \]
integrate((((2*x^2-8*x)*exp(5)^2+(4*x^4-12*x^3-16*x^2-2*x)*exp(5)+2*x^6-4* x^5-14*x^4-10*x^3-2*x^2)*log(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3 +x^2))^2+(8*x*exp(5)^2+(16*x^3+16*x^2+2*x)*exp(5)+8*x^5+16*x^4+14*x^3+4*x^ 2)*log(((-x+4)*exp(5)-x^3+3*x^2+4*x+1)/(x*exp(5)+x^3+x^2)))/((x-4)*exp(5)^ 2+(2*x^3-6*x^2-8*x-1)*exp(5)+x^5-2*x^4-7*x^3-5*x^2-x),x, algorithm=\
Time = 12.55 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.65 \[ \int \frac {\left (8 e^{10} x+4 x^2+14 x^3+16 x^4+8 x^5+e^5 \left (2 x+16 x^2+16 x^3\right )\right ) \log \left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )+\left (-2 x^2-10 x^3-14 x^4-4 x^5+2 x^6+e^{10} \left (-8 x+2 x^2\right )+e^5 \left (-2 x-16 x^2-12 x^3+4 x^4\right )\right ) \log ^2\left (\frac {1+e^5 (4-x)+4 x+3 x^2-x^3}{e^5 x+x^2+x^3}\right )}{e^{10} (-4+x)-x-5 x^2-7 x^3-2 x^4+x^5+e^5 \left (-1-8 x-6 x^2+2 x^3\right )} \, dx=x^2\,{\ln \left (\frac {4\,x-{\mathrm {e}}^5\,\left (x-4\right )+3\,x^2-x^3+1}{x^3+x^2+{\mathrm {e}}^5\,x}\right )}^2 \]
int((log((4*x - exp(5)*(x - 4) + 3*x^2 - x^3 + 1)/(x*exp(5) + x^2 + x^3))^ 2*(exp(10)*(8*x - 2*x^2) + exp(5)*(2*x + 16*x^2 + 12*x^3 - 4*x^4) + 2*x^2 + 10*x^3 + 14*x^4 + 4*x^5 - 2*x^6) - log((4*x - exp(5)*(x - 4) + 3*x^2 - x ^3 + 1)/(x*exp(5) + x^2 + x^3))*(8*x*exp(10) + exp(5)*(2*x + 16*x^2 + 16*x ^3) + 4*x^2 + 14*x^3 + 16*x^4 + 8*x^5))/(x + exp(5)*(8*x + 6*x^2 - 2*x^3 + 1) - exp(10)*(x - 4) + 5*x^2 + 7*x^3 + 2*x^4 - x^5),x)