Integrand size = 189, antiderivative size = 28 \[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=e^{e^{\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}}} \] Output:
exp(exp(1/625*(5+ln(x))^2/x^2*exp(x^2)^2*(ln(x)-4)))
Time = 0.41 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.68 \[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=e^{e^{\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}} x^{-\frac {3 e^{2 x^2}}{125 x^2}}} \] Input:
Integrate[(E^(E^((-100*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6*E^(2*x^2)*Log[x ]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2)) + (-100*E^(2*x^2) - 15*E^(2*x^2)*Log[ x] + 6*E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2))*(E^(2*x^2)*(185 - 400*x^2) + E^(2*x^2)*(42 - 60*x^2)*Log[x] + E^(2*x^2)*(-9 + 24*x^2)*Log [x]^2 + E^(2*x^2)*(-2 + 4*x^2)*Log[x]^3))/(625*x^3),x]
Output:
E^(E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2 ))/(125*x^2)))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (4 x^2-2\right ) \log ^3(x)+e^{2 x^2} \left (24 x^2-9\right ) \log ^2(x)+e^{2 x^2} \left (42-60 x^2\right ) \log (x)\right ) \exp \left (\exp \left (\frac {-100 e^{2 x^2}+e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)-15 e^{2 x^2} \log (x)}{625 x^2}\right )+\frac {-100 e^{2 x^2}+e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)-15 e^{2 x^2} \log (x)}{625 x^2}\right )}{625 x^3} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{625} \int \frac {\exp \left (\exp \left (-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+100 e^{2 x^2}}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+15 e^{2 x^2} \log (x)+100 e^{2 x^2}}{625 x^2}\right ) \left (-2 e^{2 x^2} \left (1-2 x^2\right ) \log ^3(x)-3 e^{2 x^2} \left (3-8 x^2\right ) \log ^2(x)+6 e^{2 x^2} \left (7-10 x^2\right ) \log (x)+5 e^{2 x^2} \left (37-80 x^2\right )\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \frac {1}{625} \int \frac {\exp \left (\exp \left (-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+100 e^{2 x^2}}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+2 x^2-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+15 e^{2 x^2} \log (x)+100 e^{2 x^2}}{625 x^2}\right ) (\log (x)+5) \left (4 \log ^2(x) x^2+4 \log (x) x^2-80 x^2-2 \log ^2(x)+\log (x)+37\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (\frac {2 \exp \left (\exp \left (-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+100 e^{2 x^2}}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+2 x^2-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+15 e^{2 x^2} \log (x)+100 e^{2 x^2}}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x)}{x^3}+\frac {3 \exp \left (\exp \left (-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+100 e^{2 x^2}}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+2 x^2-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+15 e^{2 x^2} \log (x)+100 e^{2 x^2}}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x)}{x^3}-\frac {6 \exp \left (\exp \left (-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+100 e^{2 x^2}}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+2 x^2-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+15 e^{2 x^2} \log (x)+100 e^{2 x^2}}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x)}{x^3}-\frac {5 \exp \left (\exp \left (-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+100 e^{2 x^2}}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+2 x^2-\frac {-e^{2 x^2} \log ^3(x)-6 e^{2 x^2} \log ^2(x)+15 e^{2 x^2} \log (x)+100 e^{2 x^2}}{625 x^2}\right ) \left (80 x^2-37\right )}{x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{625} \int \left (2 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (2 x^2-1\right ) \log ^3(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}+3 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (8 x^2-3\right ) \log ^2(x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-5 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (80 x^2-37\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}-6 \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) \left (10 x^2-7\right ) \log (x) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {1}{625} \int \exp \left (\frac {e^{2 x^2} \log ^3(x)+6 e^{2 x^2} \log ^2(x)+25 \left (25 e^{\frac {e^{2 x^2} \left (\log ^3(x)+6 \log ^2(x)-100\right )}{625 x^2}} x^{2-\frac {3 e^{2 x^2}}{125 x^2}}+50 x^4-4 e^{2 x^2}\right )}{625 x^2}\right ) x^{-3-\frac {3 e^{2 x^2}}{125 x^2}} (\log (x)+5) \left (-80 x^2+\left (4 x^2-2\right ) \log ^2(x)+\left (4 x^2+1\right ) \log (x)+37\right )dx\) |
Input:
Int[(E^(E^((-100*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6*E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2)) + (-100*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6 *E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2))*(E^(2*x^2)*(185 - 400 *x^2) + E^(2*x^2)*(42 - 60*x^2)*Log[x] + E^(2*x^2)*(-9 + 24*x^2)*Log[x]^2 + E^(2*x^2)*(-2 + 4*x^2)*Log[x]^3))/(625*x^3),x]
Output:
$Aborted
Time = 34.78 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86
| method | result | size |
| risch | \({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x^{2}} \left (\ln \left (x \right )-4\right ) \left (5+\ln \left (x \right )\right )^{2}}{625 x^{2}}}}\) | \(24\) |
| parallelrisch | \({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x^{2}} \left (\ln \left (x \right )^{3}+6 \ln \left (x \right )^{2}-15 \ln \left (x \right )-100\right )}{625 x^{2}}}}\) | \(30\) |
Input:
int(1/625*((4*x^2-2)*exp(x^2)^2*ln(x)^3+(24*x^2-9)*exp(x^2)^2*ln(x)^2+(-60 *x^2+42)*exp(x^2)^2*ln(x)+(-400*x^2+185)*exp(x^2)^2)*exp(1/625*(exp(x^2)^2 *ln(x)^3+6*exp(x^2)^2*ln(x)^2-15*exp(x^2)^2*ln(x)-100*exp(x^2)^2)/x^2)*exp (exp(1/625*(exp(x^2)^2*ln(x)^3+6*exp(x^2)^2*ln(x)^2-15*exp(x^2)^2*ln(x)-10 0*exp(x^2)^2)/x^2))/x^3,x,method=_RETURNVERBOSE)
Output:
exp(exp(1/625*exp(2*x^2)*(ln(x)-4)*(5+ln(x))^2/x^2))
Leaf count of result is larger than twice the leaf count of optimal. 149 vs. \(2 (23) = 46\).
Time = 0.11 (sec) , antiderivative size = 149, normalized size of antiderivative = 5.32 \[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 625 \, x^{2} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}} - \frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )} \] Input:
integrate(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x )^2+(-60*x^2+42)*exp(x^2)^2*log(x)+(-400*x^2+185)*exp(x^2)^2)*exp(1/625*(e xp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2) ^2)/x^2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x ^2)^2*log(x)-100*exp(x^2)^2)/x^2))/x^3,x, algorithm="fricas")
Output:
e^(1/625*(e^(2*x^2)*log(x)^3 + 625*x^2*e^(1/625*(e^(2*x^2)*log(x)^3 + 6*e^ (2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2) + 6*e^(2*x^2) *log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2 - 1/625*(e^(2*x^2)*lo g(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (26) = 52\).
Time = 12.55 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=e^{e^{\frac {\frac {e^{2 x^{2}} \log {\left (x \right )}^{3}}{625} + \frac {6 e^{2 x^{2}} \log {\left (x \right )}^{2}}{625} - \frac {3 e^{2 x^{2}} \log {\left (x \right )}}{125} - \frac {4 e^{2 x^{2}}}{25}}{x^{2}}}} \] Input:
integrate(1/625*((4*x**2-2)*exp(x**2)**2*ln(x)**3+(24*x**2-9)*exp(x**2)**2 *ln(x)**2+(-60*x**2+42)*exp(x**2)**2*ln(x)+(-400*x**2+185)*exp(x**2)**2)*e xp(1/625*(exp(x**2)**2*ln(x)**3+6*exp(x**2)**2*ln(x)**2-15*exp(x**2)**2*ln (x)-100*exp(x**2)**2)/x**2)*exp(exp(1/625*(exp(x**2)**2*ln(x)**3+6*exp(x** 2)**2*ln(x)**2-15*exp(x**2)**2*ln(x)-100*exp(x**2)**2)/x**2))/x**3,x)
Output:
exp(exp((exp(2*x**2)*log(x)**3/625 + 6*exp(2*x**2)*log(x)**2/625 - 3*exp(2 *x**2)*log(x)/125 - 4*exp(2*x**2)/25)/x**2))
Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (23) = 46\).
Time = 1.41 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.04 \[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=e^{\left (e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3}}{625 \, x^{2}} + \frac {6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2}}{625 \, x^{2}} - \frac {3 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )}{125 \, x^{2}} - \frac {4 \, e^{\left (2 \, x^{2}\right )}}{25 \, x^{2}}\right )}\right )} \] Input:
integrate(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x )^2+(-60*x^2+42)*exp(x^2)^2*log(x)+(-400*x^2+185)*exp(x^2)^2)*exp(1/625*(e xp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2) ^2)/x^2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x ^2)^2*log(x)-100*exp(x^2)^2)/x^2))/x^3,x, algorithm="maxima")
Output:
e^(e^(1/625*e^(2*x^2)*log(x)^3/x^2 + 6/625*e^(2*x^2)*log(x)^2/x^2 - 3/125* e^(2*x^2)*log(x)/x^2 - 4/25*e^(2*x^2)/x^2))
\[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=\int { \frac {{\left (2 \, {\left (2 \, x^{2} - 1\right )} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 3 \, {\left (8 \, x^{2} - 3\right )} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 6 \, {\left (10 \, x^{2} - 7\right )} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 5 \, {\left (80 \, x^{2} - 37\right )} e^{\left (2 \, x^{2}\right )}\right )} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}} + e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )}\right )}}{625 \, x^{3}} \,d x } \] Input:
integrate(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x )^2+(-60*x^2+42)*exp(x^2)^2*log(x)+(-400*x^2+185)*exp(x^2)^2)*exp(1/625*(e xp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2) ^2)/x^2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x ^2)^2*log(x)-100*exp(x^2)^2)/x^2))/x^3,x, algorithm="giac")
Output:
integrate(1/625*(2*(2*x^2 - 1)*e^(2*x^2)*log(x)^3 + 3*(8*x^2 - 3)*e^(2*x^2 )*log(x)^2 - 6*(10*x^2 - 7)*e^(2*x^2)*log(x) - 5*(80*x^2 - 37)*e^(2*x^2))* e^(1/625*(e^(2*x^2)*log(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2 + e^(1/625*(e^(2*x^2)*log(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2))/x^3, x)
Time = 3.07 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14 \[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx={\mathrm {e}}^{{\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^{2\,x^2}\,\ln \left (x\right )}{125\,x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^2}}{25\,x^2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^3}{625\,x^2}}\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^2}{625\,x^2}}} \] Input:
int(-(exp(-((4*exp(2*x^2))/25 - (6*exp(2*x^2)*log(x)^2)/625 - (exp(2*x^2)* log(x)^3)/625 + (3*exp(2*x^2)*log(x))/125)/x^2)*exp(exp(-((4*exp(2*x^2))/2 5 - (6*exp(2*x^2)*log(x)^2)/625 - (exp(2*x^2)*log(x)^3)/625 + (3*exp(2*x^2 )*log(x))/125)/x^2))*(exp(2*x^2)*(400*x^2 - 185) + exp(2*x^2)*log(x)*(60*x ^2 - 42) - exp(2*x^2)*log(x)^3*(4*x^2 - 2) - exp(2*x^2)*log(x)^2*(24*x^2 - 9)))/(625*x^3),x)
Output:
exp(exp(-(3*exp(2*x^2)*log(x))/(125*x^2))*exp(-(4*exp(2*x^2))/(25*x^2))*ex p((exp(2*x^2)*log(x)^3)/(625*x^2))*exp((6*exp(2*x^2)*log(x)^2)/(625*x^2)))
\[ \int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx=\text {too large to display} \] Input:
int(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x)^2+(- 60*x^2+42)*exp(x^2)^2*log(x)+(-400*x^2+185)*exp(x^2)^2)*exp(1/625*(exp(x^2 )^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2)^2)/x^ 2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2* log(x)-100*exp(x^2)^2)/x^2))/x^3,x)
Output:
(185*int(e**((e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2) + 250*x**4)/(125* x**2))*log(x)**3 + 6*e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2) + 250*x**4 )/(125*x**2))*log(x)**2 + 1250*e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2)) /(125*x**2))*x**4 + 625*e**((e**(2*x**2)*log(x)**3 + 6*e**(2*x**2)*log(x)* *2)/(625*x**2))*x**2)/(625*e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2))/(12 5*x**2))*x**2))/(e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2))/(125*x**2))*x **3),x) - 400*int(e**((e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2) + 250*x* *4)/(125*x**2))*log(x)**3 + 6*e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2) + 250*x**4)/(125*x**2))*log(x)**2 + 1250*e**((3*e**(2*x**2)*log(x) + 20*e** (2*x**2))/(125*x**2))*x**4 + 625*e**((e**(2*x**2)*log(x)**3 + 6*e**(2*x**2 )*log(x)**2)/(625*x**2))*x**2)/(625*e**((3*e**(2*x**2)*log(x) + 20*e**(2*x **2))/(125*x**2))*x**2))/(e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2))/(125 *x**2))*x),x) - 2*int((e**((e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2) + 2 50*x**4)/(125*x**2))*log(x)**3 + 6*e**((3*e**(2*x**2)*log(x) + 20*e**(2*x* *2) + 250*x**4)/(125*x**2))*log(x)**2 + 1250*e**((3*e**(2*x**2)*log(x) + 2 0*e**(2*x**2))/(125*x**2))*x**4 + 625*e**((e**(2*x**2)*log(x)**3 + 6*e**(2 *x**2)*log(x)**2)/(625*x**2))*x**2)/(625*e**((3*e**(2*x**2)*log(x) + 20*e* *(2*x**2))/(125*x**2))*x**2))*log(x)**3)/(e**((3*e**(2*x**2)*log(x) + 20*e **(2*x**2))/(125*x**2))*x**3),x) + 4*int((e**((e**((3*e**(2*x**2)*log(x) + 20*e**(2*x**2) + 250*x**4)/(125*x**2))*log(x)**3 + 6*e**((3*e**(2*x**2...