Integrand size = 188, antiderivative size = 28 \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=2 x \log \left (-x+\frac {x}{3 \left (e^{4 e^{1171875/x}}+x\right )}\right ) \]
Time = 0.60 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=2 x \log \left (-\frac {x \left (-1+3 e^{4 e^{1171875/x}}+3 x\right )}{3 \left (e^{4 e^{1171875/x}}+x\right )}\right ) \]
Integrate[(6*E^(8*E^(1171875/x))*x + 6*x^3 + E^(4*E^(1171875/x))*(-9375000 *E^(1171875/x) - 2*x + 12*x^2) + (6*E^(8*E^(1171875/x))*x - 2*x^2 + 6*x^3 + E^(4*E^(1171875/x))*(-2*x + 12*x^2))*Log[(x - 3*E^(4*E^(1171875/x))*x - 3*x^2)/(3*E^(4*E^(1171875/x)) + 3*x)])/(3*E^(8*E^(1171875/x))*x - x^2 + 3* x^3 + E^(4*E^(1171875/x))*(-x + 6*x^2)),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {6 x^3+e^{4 e^{1171875/x}} \left (12 x^2-2 x-9375000 e^{1171875/x}\right )+\left (6 x^3-2 x^2+e^{4 e^{1171875/x}} \left (12 x^2-2 x\right )+6 e^{8 e^{1171875/x}} x\right ) \log \left (\frac {-3 x^2-3 e^{4 e^{1171875/x}} x+x}{3 x+3 e^{4 e^{1171875/x}}}\right )+6 e^{8 e^{1171875/x}} x}{3 x^3-x^2+e^{4 e^{1171875/x}} \left (6 x^2-x\right )+3 e^{8 e^{1171875/x}} x} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 x^2}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right ) x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {12 e^{4 e^{1171875/x}} x}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}} \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {2 e^{4 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}+\frac {6 e^{8 e^{1171875/x}}}{3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}}-\frac {9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}}{\left (3 x^2+6 e^{4 e^{1171875/x}} x-x-e^{4 e^{1171875/x}}+3 e^{8 e^{1171875/x}}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 x^3+6 e^{8 e^{1171875/x}} x+2 e^{4 e^{1171875/x}} (6 x-1) x-9375000 e^{4 e^{1171875/x}+\frac {1171875}{x}}+2 \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right ) x \log \left (-\frac {x \left (3 x+3 e^{4 e^{1171875/x}}-1\right )}{3 \left (x+e^{4 e^{1171875/x}}\right )}\right )}{x \left (x (3 x-1)+3 e^{8 e^{1171875/x}}+e^{4 e^{1171875/x}} (6 x-1)\right )}dx\) |
Int[(6*E^(8*E^(1171875/x))*x + 6*x^3 + E^(4*E^(1171875/x))*(-9375000*E^(11 71875/x) - 2*x + 12*x^2) + (6*E^(8*E^(1171875/x))*x - 2*x^2 + 6*x^3 + E^(4 *E^(1171875/x))*(-2*x + 12*x^2))*Log[(x - 3*E^(4*E^(1171875/x))*x - 3*x^2) /(3*E^(4*E^(1171875/x)) + 3*x)])/(3*E^(8*E^(1171875/x))*x - x^2 + 3*x^3 + E^(4*E^(1171875/x))*(-x + 6*x^2)),x]
3.30.40.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 6.14 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32
| method | result | size |
| parallelrisch | \(2 \ln \left (-\frac {x \left (3 \,{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+3 x -1\right )}{3 \left ({\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x \right )}\right ) x\) | \(37\) |
| risch | \(2 x \ln \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )-2 x \ln \left ({\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x \right )-2 i \pi x {\operatorname {csgn}\left (\frac {i x \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{2}-i \pi x {\operatorname {csgn}\left (\frac {i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{3}-i \pi x \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right ) \operatorname {csgn}\left (i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )\right ) \operatorname {csgn}\left (\frac {i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )-i \pi x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right ) \operatorname {csgn}\left (\frac {i x \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )+i \pi x \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right ) {\operatorname {csgn}\left (\frac {i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{2}+i \pi x \,\operatorname {csgn}\left (i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )\right ) {\operatorname {csgn}\left (\frac {i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{2}+i \pi x \,\operatorname {csgn}\left (\frac {i \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right ) {\operatorname {csgn}\left (\frac {i x \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{2}+i \pi x \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (\frac {i x \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{2}+i \pi x {\operatorname {csgn}\left (\frac {i x \left (x +{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}-\frac {1}{3}\right )}{{\mathrm e}^{4 \,{\mathrm e}^{\frac {1171875}{x}}}+x}\right )}^{3}+2 i x \pi +2 x \ln \left (x \right )\) | \(502\) |
int(((6*x*exp(4*exp(1171875/x))^2+(12*x^2-2*x)*exp(4*exp(1171875/x))+6*x^3 -2*x^2)*ln((-3*x*exp(4*exp(1171875/x))-3*x^2+x)/(3*exp(4*exp(1171875/x))+3 *x))+6*x*exp(4*exp(1171875/x))^2+(-9375000*exp(1171875/x)+12*x^2-2*x)*exp( 4*exp(1171875/x))+6*x^3)/(3*x*exp(4*exp(1171875/x))^2+(6*x^2-x)*exp(4*exp( 1171875/x))+3*x^3-x^2),x,method=_RETURNVERBOSE)
Time = 0.24 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.43 \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=2 \, x \log \left (-\frac {3 \, x^{2} + 3 \, x e^{\left (4 \, e^{\frac {1171875}{x}}\right )} - x}{3 \, {\left (x + e^{\left (4 \, e^{\frac {1171875}{x}}\right )}\right )}}\right ) \]
integrate(((6*x*exp(4*exp(1171875/x))^2+(12*x^2-2*x)*exp(4*exp(1171875/x)) +6*x^3-2*x^2)*log((-3*x*exp(4*exp(1171875/x))-3*x^2+x)/(3*exp(4*exp(117187 5/x))+3*x))+6*x*exp(4*exp(1171875/x))^2+(-9375000*exp(1171875/x)+12*x^2-2* x)*exp(4*exp(1171875/x))+6*x^3)/(3*x*exp(4*exp(1171875/x))^2+(6*x^2-x)*exp (4*exp(1171875/x))+3*x^3-x^2),x, algorithm=\
Time = 0.94 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=2 x \log {\left (\frac {- 3 x^{2} - 3 x e^{4 e^{\frac {1171875}{x}}} + x}{3 x + 3 e^{4 e^{\frac {1171875}{x}}}} \right )} \]
integrate(((6*x*exp(4*exp(1171875/x))**2+(12*x**2-2*x)*exp(4*exp(1171875/x ))+6*x**3-2*x**2)*ln((-3*x*exp(4*exp(1171875/x))-3*x**2+x)/(3*exp(4*exp(11 71875/x))+3*x))+6*x*exp(4*exp(1171875/x))**2+(-9375000*exp(1171875/x)+12*x **2-2*x)*exp(4*exp(1171875/x))+6*x**3)/(3*x*exp(4*exp(1171875/x))**2+(6*x* *2-x)*exp(4*exp(1171875/x))+3*x**3-x**2),x)
Time = 0.33 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=-2 \, x \log \left (3\right ) - 2 \, x \log \left (x + e^{\left (4 \, e^{\frac {1171875}{x}}\right )}\right ) + 2 \, x \log \left (x\right ) + 2 \, x \log \left (-3 \, x - 3 \, e^{\left (4 \, e^{\frac {1171875}{x}}\right )} + 1\right ) \]
integrate(((6*x*exp(4*exp(1171875/x))^2+(12*x^2-2*x)*exp(4*exp(1171875/x)) +6*x^3-2*x^2)*log((-3*x*exp(4*exp(1171875/x))-3*x^2+x)/(3*exp(4*exp(117187 5/x))+3*x))+6*x*exp(4*exp(1171875/x))^2+(-9375000*exp(1171875/x)+12*x^2-2* x)*exp(4*exp(1171875/x))+6*x^3)/(3*x*exp(4*exp(1171875/x))^2+(6*x^2-x)*exp (4*exp(1171875/x))+3*x^3-x^2),x, algorithm=\
-2*x*log(3) - 2*x*log(x + e^(4*e^(1171875/x))) + 2*x*log(x) + 2*x*log(-3*x - 3*e^(4*e^(1171875/x)) + 1)
Exception generated. \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=\text {Exception raised: TypeError} \]
integrate(((6*x*exp(4*exp(1171875/x))^2+(12*x^2-2*x)*exp(4*exp(1171875/x)) +6*x^3-2*x^2)*log((-3*x*exp(4*exp(1171875/x))-3*x^2+x)/(3*exp(4*exp(117187 5/x))+3*x))+6*x*exp(4*exp(1171875/x))^2+(-9375000*exp(1171875/x)+12*x^2-2* x)*exp(4*exp(1171875/x))+6*x^3)/(3*x*exp(4*exp(1171875/x))^2+(6*x^2-x)*exp (4*exp(1171875/x))+3*x^3-x^2),x, algorithm=\
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Polynomial exponent overflow. Error : Bad Argument Value
Time = 11.56 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.57 \[ \int \frac {6 e^{8 e^{1171875/x}} x+6 x^3+e^{4 e^{1171875/x}} \left (-9375000 e^{1171875/x}-2 x+12 x^2\right )+\left (6 e^{8 e^{1171875/x}} x-2 x^2+6 x^3+e^{4 e^{1171875/x}} \left (-2 x+12 x^2\right )\right ) \log \left (\frac {x-3 e^{4 e^{1171875/x}} x-3 x^2}{3 e^{4 e^{1171875/x}}+3 x}\right )}{3 e^{8 e^{1171875/x}} x-x^2+3 x^3+e^{4 e^{1171875/x}} \left (-x+6 x^2\right )} \, dx=2\,x\,\ln \left (-\frac {3\,x\,{\mathrm {e}}^{4\,{\mathrm {e}}^{1171875/x}}-x+3\,x^2}{3\,x+3\,{\mathrm {e}}^{4\,{\mathrm {e}}^{1171875/x}}}\right ) \]
int(-(exp(4*exp(1171875/x))*(2*x + 9375000*exp(1171875/x) - 12*x^2) - 6*x* exp(8*exp(1171875/x)) + log(-(3*x*exp(4*exp(1171875/x)) - x + 3*x^2)/(3*x + 3*exp(4*exp(1171875/x))))*(exp(4*exp(1171875/x))*(2*x - 12*x^2) - 6*x*ex p(8*exp(1171875/x)) + 2*x^2 - 6*x^3) - 6*x^3)/(3*x*exp(8*exp(1171875/x)) - exp(4*exp(1171875/x))*(x - 6*x^2) - x^2 + 3*x^3),x)