Integrand size = 172, antiderivative size = 28 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=e^{\frac {36}{x^2}-\frac {x \left (x+\log \left (e^e-x\right )\right )}{-1+e x}} \] Output:
exp(36/x^2-(x+ln(exp(exp(1))-x))/(x*exp(1)-1)*x)
Time = 0.24 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=e^{\frac {36-36 e x+x^4}{x^2-e x^3}} \left (e^e-x\right )^{\frac {x}{1-e x}} \] Input:
Integrate[(E^((-36 + 36*E*x - x^4 - x^3*Log[E^E - x])/(-x^2 + E*x^3))*(72* x + 72*E^2*x^3 - x^4 - 2*x^5 + E*(-144*x^2 + x^5 + x^6) + E^E*(-72 - 72*E^ 2*x^2 + 2*x^4 + E*(144*x - x^5)) + (E^E*x^3 - x^4)*Log[E^E - x]))/(-x^4 + 2*E*x^5 - E^2*x^6 + E^E*(x^3 - 2*E*x^4 + E^2*x^5)),x]
Output:
E^((36 - 36*E*x + x^4)/(x^2 - E*x^3))*(E^E - x)^(x/(1 - E*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.
| \(\displaystyle \int \frac {\left (-2 x^5-x^4+72 e^2 x^3+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )+e \left (x^6+x^5-144 x^2\right )+e^e \left (e \left (144 x-x^5\right )+2 x^4-72 e^2 x^2-72\right )+72 x\right ) \exp \left (\frac {-x^4-x^3 \log \left (e^e-x\right )+36 e x-36}{e x^3-x^2}\right )}{-e^2 x^6+2 e x^5-x^4+e^e \left (e^2 x^5-2 e x^4+x^3\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (-2 x^5-x^4+72 e^2 x^3+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )+e \left (x^6+x^5-144 x^2\right )+e^e \left (e \left (144 x-x^5\right )+2 x^4-72 e^2 x^2-72\right )+72 x\right ) \exp \left (\frac {-x^4-x^3 \log \left (e^e-x\right )+36 e x-36}{e x^3-x^2}\right )}{x^3 \left (-e^2 x^3+e \left (2+e^{1+e}\right ) x^2-\left (1+2 e^{1+e}\right ) x+e^e\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (-2 x^5-x^4+72 e^2 x^3+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )+e \left (x^6+x^5-144 x^2\right )+e^e \left (e \left (144 x-x^5\right )+2 x^4-72 e^2 x^2-72\right )+72 x\right ) \exp \left (\frac {-x^4-x^3 \log \left (e^e-x\right )+36 e x-36}{e x^3-x^2}+1\right )}{\left (e^{1+e}-1\right )^2 x^3 (e x-1)}+\frac {\left (-2 x^5-x^4+72 e^2 x^3+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )+e \left (x^6+x^5-144 x^2\right )+e^e \left (e \left (144 x-x^5\right )+2 x^4-72 e^2 x^2-72\right )+72 x\right ) \exp \left (\frac {-x^4-x^3 \log \left (e^e-x\right )+36 e x-36}{e x^3-x^2}+1\right )}{\left (e^{1+e}-1\right ) x^3 (e x-1)^2}+\frac {\left (-2 x^5-x^4+72 e^2 x^3+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )+e \left (x^6+x^5-144 x^2\right )+e^e \left (e \left (144 x-x^5\right )+2 x^4-72 e^2 x^2-72\right )+72 x\right ) \exp \left (\frac {-x^4-x^3 \log \left (e^e-x\right )+36 e x-36}{e x^3-x^2}\right )}{\left (e^{1+e}-1\right )^2 \left (e^e-x\right ) x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{1-\frac {(1+e) x-1}{e x-1}} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{-\frac {(1+e) x-1}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}} \left (-e^{1+e} \left (x^4-144\right ) x+2 e^e \left (x^4-36\right )+72 e^2 x^3+\left (e^e-x\right ) x^3 \log \left (e^e-x\right )-72 e^{2+e} x^2-\left (2 x^4+x^3-72\right ) x+e \left (x^4+x^3-144\right ) x^2\right )}{x^3 (1-e x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+1} \left (x^2-12\right ) \left (x^2+12\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{(e x-1)^2}-\frac {72 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e+2} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}+1} \log \left (e^e-x\right )}{(e x-1)^2}+\frac {2 e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+e} \left (x^2-6\right ) \left (x^2+6\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^3 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}} \left (-2 x^4-x^3+72\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x^2 (e x-1)^2}+\frac {e^{\frac {x^4-36 e x+36}{x^2 (1-e x)}+1} \left (x^4+x^3-144\right ) \left (e^e-x\right )^{\frac {1-(1+e) x}{e x-1}}}{x (e x-1)^2}\right )dx\) |
Input:
Int[(E^((-36 + 36*E*x - x^4 - x^3*Log[E^E - x])/(-x^2 + E*x^3))*(72*x + 72 *E^2*x^3 - x^4 - 2*x^5 + E*(-144*x^2 + x^5 + x^6) + E^E*(-72 - 72*E^2*x^2 + 2*x^4 + E*(144*x - x^5)) + (E^E*x^3 - x^4)*Log[E^E - x]))/(-x^4 + 2*E*x^ 5 - E^2*x^6 + E^E*(x^3 - 2*E*x^4 + E^2*x^5)),x]
Output:
$Aborted
Time = 24.09 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32
| method | result | size |
| parallelrisch | \({\mathrm e}^{-\frac {x^{3} \ln \left ({\mathrm e}^{{\mathrm e}}-x \right )+x^{4}-36 x \,{\mathrm e}+36}{x^{2} \left (x \,{\mathrm e}-1\right )}}\) | \(37\) |
| risch | \({\mathrm e}^{\frac {-x^{3} \ln \left ({\mathrm e}^{{\mathrm e}}-x \right )+36 x \,{\mathrm e}-x^{4}-36}{x^{2} \left (x \,{\mathrm e}-1\right )}}\) | \(39\) |
Input:
int(((x^3*exp(exp(1))-x^4)*ln(exp(exp(1))-x)+(-72*x^2*exp(1)^2+(-x^5+144*x )*exp(1)+2*x^4-72)*exp(exp(1))+72*x^3*exp(1)^2+(x^6+x^5-144*x^2)*exp(1)-2* x^5-x^4+72*x)*exp((-x^3*ln(exp(exp(1))-x)+36*x*exp(1)-x^4-36)/(x^3*exp(1)- x^2))/((x^5*exp(1)^2-2*x^4*exp(1)+x^3)*exp(exp(1))-x^6*exp(1)^2+2*x^5*exp( 1)-x^4),x,method=_RETURNVERBOSE)
Output:
exp(-(x^3*ln(exp(exp(1))-x)+x^4-36*x*exp(1)+36)/x^2/(x*exp(1)-1))
Time = 0.12 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=e^{\left (-\frac {x^{4} + x^{3} \log \left (-x + e^{e}\right ) - 36 \, x e + 36}{x^{3} e - x^{2}}\right )} \] Input:
integrate(((x^3*exp(exp(1))-x^4)*log(exp(exp(1))-x)+(-72*x^2*exp(1)^2+(-x^ 5+144*x)*exp(1)+2*x^4-72)*exp(exp(1))+72*x^3*exp(1)^2+(x^6+x^5-144*x^2)*ex p(1)-2*x^5-x^4+72*x)*exp((-x^3*log(exp(exp(1))-x)+36*exp(1)*x-x^4-36)/(x^3 *exp(1)-x^2))/((x^5*exp(1)^2-2*x^4*exp(1)+x^3)*exp(exp(1))-x^6*exp(1)^2+2* x^5*exp(1)-x^4),x, algorithm="fricas")
Output:
e^(-(x^4 + x^3*log(-x + e^e) - 36*x*e + 36)/(x^3*e - x^2))
Time = 7.58 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=e^{\frac {- x^{4} - x^{3} \log {\left (- x + e^{e} \right )} + 36 e x - 36}{e x^{3} - x^{2}}} \] Input:
integrate(((x**3*exp(exp(1))-x**4)*ln(exp(exp(1))-x)+(-72*x**2*exp(1)**2+( -x**5+144*x)*exp(1)+2*x**4-72)*exp(exp(1))+72*x**3*exp(1)**2+(x**6+x**5-14 4*x**2)*exp(1)-2*x**5-x**4+72*x)*exp((-x**3*ln(exp(exp(1))-x)+36*exp(1)*x- x**4-36)/(x**3*exp(1)-x**2))/((x**5*exp(1)**2-2*x**4*exp(1)+x**3)*exp(exp( 1))-x**6*exp(1)**2+2*x**5*exp(1)-x**4),x)
Output:
exp((-x**4 - x**3*log(-x + exp(E)) + 36*E*x - 36)/(E*x**3 - x**2))
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (28) = 56\).
Time = 0.23 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.21 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=e^{\left (-x e^{\left (-1\right )} - e^{\left (-1\right )} \log \left (-x + e^{e}\right ) - \frac {\log \left (-x + e^{e}\right )}{x e^{2} - e} - \frac {1}{x e^{3} - e^{2}} + \frac {36}{x^{2}} - e^{\left (-2\right )}\right )} \] Input:
integrate(((x^3*exp(exp(1))-x^4)*log(exp(exp(1))-x)+(-72*x^2*exp(1)^2+(-x^ 5+144*x)*exp(1)+2*x^4-72)*exp(exp(1))+72*x^3*exp(1)^2+(x^6+x^5-144*x^2)*ex p(1)-2*x^5-x^4+72*x)*exp((-x^3*log(exp(exp(1))-x)+36*exp(1)*x-x^4-36)/(x^3 *exp(1)-x^2))/((x^5*exp(1)^2-2*x^4*exp(1)+x^3)*exp(exp(1))-x^6*exp(1)^2+2* x^5*exp(1)-x^4),x, algorithm="maxima")
Output:
e^(-x*e^(-1) - e^(-1)*log(-x + e^e) - log(-x + e^e)/(x*e^2 - e) - 1/(x*e^3 - e^2) + 36/x^2 - e^(-2))
Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (28) = 56\).
Time = 0.32 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.96 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=e^{\left (-\frac {x^{4}}{x^{3} e - x^{2}} - \frac {x^{3} \log \left (-x + e^{e}\right )}{x^{3} e - x^{2}} + \frac {36 \, x e}{x^{3} e - x^{2}} - \frac {36}{x^{3} e - x^{2}}\right )} \] Input:
integrate(((x^3*exp(exp(1))-x^4)*log(exp(exp(1))-x)+(-72*x^2*exp(1)^2+(-x^ 5+144*x)*exp(1)+2*x^4-72)*exp(exp(1))+72*x^3*exp(1)^2+(x^6+x^5-144*x^2)*ex p(1)-2*x^5-x^4+72*x)*exp((-x^3*log(exp(exp(1))-x)+36*exp(1)*x-x^4-36)/(x^3 *exp(1)-x^2))/((x^5*exp(1)^2-2*x^4*exp(1)+x^3)*exp(exp(1))-x^6*exp(1)^2+2* x^5*exp(1)-x^4),x, algorithm="giac")
Output:
e^(-x^4/(x^3*e - x^2) - x^3*log(-x + e^e)/(x^3*e - x^2) + 36*x*e/(x^3*e - x^2) - 36/(x^3*e - x^2))
Time = 4.87 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.43 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=\frac {{\mathrm {e}}^{-\frac {36}{x^3\,\mathrm {e}-x^2}}\,{\mathrm {e}}^{-\frac {x^2}{x\,\mathrm {e}-1}}\,{\mathrm {e}}^{-\frac {36\,\mathrm {e}}{x-x^2\,\mathrm {e}}}}{{\left ({\mathrm {e}}^{\mathrm {e}}-x\right )}^{\frac {x}{x\,\mathrm {e}-1}}} \] Input:
int((exp(-(x^3*log(exp(exp(1)) - x) - 36*x*exp(1) + x^4 + 36)/(x^3*exp(1) - x^2))*(72*x + exp(1)*(x^5 - 144*x^2 + x^6) + log(exp(exp(1)) - x)*(x^3*e xp(exp(1)) - x^4) + exp(exp(1))*(exp(1)*(144*x - x^5) - 72*x^2*exp(2) + 2* x^4 - 72) + 72*x^3*exp(2) - x^4 - 2*x^5))/(exp(exp(1))*(x^5*exp(2) - 2*x^4 *exp(1) + x^3) + 2*x^5*exp(1) - x^6*exp(2) - x^4),x)
Output:
(exp(-36/(x^3*exp(1) - x^2))*exp(-x^2/(x*exp(1) - 1))*exp(-(36*exp(1))/(x - x^2*exp(1))))/(exp(exp(1)) - x)^(x/(x*exp(1) - 1))
Time = 0.22 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx=\frac {e^{\frac {36 e}{e \,x^{2}-x}}}{e^{\frac {\mathrm {log}\left (e^{e}-x \right ) x^{3}+x^{4}+36}{e \,x^{3}-x^{2}}}} \] Input:
int(((x^3*exp(exp(1))-x^4)*log(exp(exp(1))-x)+(-72*x^2*exp(1)^2+(-x^5+144* x)*exp(1)+2*x^4-72)*exp(exp(1))+72*x^3*exp(1)^2+(x^6+x^5-144*x^2)*exp(1)-2 *x^5-x^4+72*x)*exp((-x^3*log(exp(exp(1))-x)+36*exp(1)*x-x^4-36)/(x^3*exp(1 )-x^2))/((x^5*exp(1)^2-2*x^4*exp(1)+x^3)*exp(exp(1))-x^6*exp(1)^2+2*x^5*ex p(1)-x^4),x)
Output:
e**((36*e)/(e*x**2 - x))/e**((log(e**e - x)*x**3 + x**4 + 36)/(e*x**3 - x* *2))