Integrand size = 318, antiderivative size = 32 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=4-e^{\frac {6}{-e^{e^{5 x}}+x^2 (x+\log (5)+\log (x))^2}} \] Output:
4-exp(3/(x^2*(ln(5)+x+ln(x))^2-exp(exp(5*x))))^2
\[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=\int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx \] Input:
Integrate[(-30*E^(E^(5*x) + 5*x) + 12*x^2 + 24*x^3 + (12*x + 36*x^2)*Log[5 ] + 12*x*Log[5]^2 + (12*x + 36*x^2 + 24*x*Log[5])*Log[x] + 12*x*Log[x]^2)/ (E^(6/(E^E^(5*x) - x^4 - 2*x^3*Log[5] - x^2*Log[5]^2 + (-2*x^3 - 2*x^2*Log [5])*Log[x] - x^2*Log[x]^2))*(E^(2*E^(5*x)) + x^8 + 4*x^7*Log[5] + 6*x^6*L og[5]^2 + 4*x^5*Log[5]^3 + x^4*Log[5]^4 + (4*x^7 + 12*x^6*Log[5] + 12*x^5* Log[5]^2 + 4*x^4*Log[5]^3)*Log[x] + (6*x^6 + 12*x^5*Log[5] + 6*x^4*Log[5]^ 2)*Log[x]^2 + (4*x^5 + 4*x^4*Log[5])*Log[x]^3 + x^4*Log[x]^4 + E^E^(5*x)*( -2*x^4 - 4*x^3*Log[5] - 2*x^2*Log[5]^2 + (-4*x^3 - 4*x^2*Log[5])*Log[x] - 2*x^2*Log[x]^2))),x]
Output:
Integrate[(-30*E^(E^(5*x) + 5*x) + 12*x^2 + 24*x^3 + (12*x + 36*x^2)*Log[5 ] + 12*x*Log[5]^2 + (12*x + 36*x^2 + 24*x*Log[5])*Log[x] + 12*x*Log[x]^2)/ (E^(6/(E^E^(5*x) - x^4 - 2*x^3*Log[5] - x^2*Log[5]^2 + (-2*x^3 - 2*x^2*Log [5])*Log[x] - x^2*Log[x]^2))*(E^(2*E^(5*x)) + x^8 + 4*x^7*Log[5] + 6*x^6*L og[5]^2 + 4*x^5*Log[5]^3 + x^4*Log[5]^4 + (4*x^7 + 12*x^6*Log[5] + 12*x^5* Log[5]^2 + 4*x^4*Log[5]^3)*Log[x] + (6*x^6 + 12*x^5*Log[5] + 6*x^4*Log[5]^ 2)*Log[x]^2 + (4*x^5 + 4*x^4*Log[5])*Log[x]^3 + x^4*Log[x]^4 + E^E^(5*x)*( -2*x^4 - 4*x^3*Log[5] - 2*x^2*Log[5]^2 + (-4*x^3 - 4*x^2*Log[5])*Log[x] - 2*x^2*Log[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.
| \(\displaystyle \int \frac {\left (24 x^3+12 x^2+\left (36 x^2+12 x+24 x \log (5)\right ) \log (x)+\left (36 x^2+12 x\right ) \log (5)-30 e^{5 x+e^{5 x}}+12 x \log ^2(x)+12 x \log ^2(5)\right ) \exp \left (-\frac {6}{-x^4-2 x^3 \log (5)-x^2 \log ^2(x)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)+e^{e^{5 x}}}\right )}{x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(x)+x^4 \log ^4(5)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(x)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)\right )+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+e^{2 e^{5 x}}} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 \left (2 x \left (2 x^2+x+3 x \log (5)+\log ^2(5)+\log (5)\right )-5 e^{5 x+e^{5 x}}+2 x \log ^2(x)+2 x (3 x+1+\log (25)) \log (x)\right ) \exp \left (-\frac {6}{-x^2 \log ^2(x)+x^2 \left (-(x+\log (5))^2\right )-2 x^2 (x+\log (5)) \log (x)+e^{e^{5 x}}}\right )}{\left (-x^2 \log ^2(x)+x^2 \left (-(x+\log (5))^2\right )-2 x^2 (x+\log (5)) \log (x)+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 6 \int -\frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log (5) (1+\log (5))\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log (5) (1+\log (5))\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6 \int \frac {\exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) \left (-2 x \log ^2(x)-2 x (3 x+\log (25)+1) \log (x)+5 e^{5 x+e^{5 x}}-2 x \left (2 x^2+3 \log (5) x+x+\log ^2(5)+\log (5)\right )\right )}{\left (-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x \log ^2(x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (3 x+\log (25)+1) \log (x)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}+\frac {5 \exp \left (5 x+e^{5 x}-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right )}{\left (-x^4-2 \log (x) x^3-2 \log (5) x^3-\log ^2(x) x^2-2 \log (5) \log (x) x^2-\log ^2(5) x^2+e^{e^{5 x}}\right )^2}-\frac {2 \exp \left (-\frac {6}{-(x+\log (5))^2 x^2-\log ^2(x) x^2-2 (x+\log (5)) \log (x) x^2+e^{e^{5 x}}}\right ) x (x+\log (5)) (2 x+\log (5)+1)}{\left (x^4+2 \log (x) x^3+2 \log (5) x^3+\log ^2(x) x^2+2 \log (5) \log (x) x^2+\log ^2(5) x^2-e^{e^{5 x}}\right )^2}\right )dx\) |
Input:
Int[(-30*E^(E^(5*x) + 5*x) + 12*x^2 + 24*x^3 + (12*x + 36*x^2)*Log[5] + 12 *x*Log[5]^2 + (12*x + 36*x^2 + 24*x*Log[5])*Log[x] + 12*x*Log[x]^2)/(E^(6/ (E^E^(5*x) - x^4 - 2*x^3*Log[5] - x^2*Log[5]^2 + (-2*x^3 - 2*x^2*Log[5])*L og[x] - x^2*Log[x]^2))*(E^(2*E^(5*x)) + x^8 + 4*x^7*Log[5] + 6*x^6*Log[5]^ 2 + 4*x^5*Log[5]^3 + x^4*Log[5]^4 + (4*x^7 + 12*x^6*Log[5] + 12*x^5*Log[5] ^2 + 4*x^4*Log[5]^3)*Log[x] + (6*x^6 + 12*x^5*Log[5] + 6*x^4*Log[5]^2)*Log [x]^2 + (4*x^5 + 4*x^4*Log[5])*Log[x]^3 + x^4*Log[x]^4 + E^E^(5*x)*(-2*x^4 - 4*x^3*Log[5] - 2*x^2*Log[5]^2 + (-4*x^3 - 4*x^2*Log[5])*Log[x] - 2*x^2* Log[x]^2))),x]
Output:
$Aborted
Time = 0.06 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.81
\[-{\mathrm e}^{\frac {6}{x^{2} \ln \left (x \right )^{2}+2 x^{2} \ln \left (5\right ) \ln \left (x \right )+2 x^{3} \ln \left (x \right )+x^{2} \ln \left (5\right )^{2}+2 x^{3} \ln \left (5\right )+x^{4}-{\mathrm e}^{{\mathrm e}^{5 x}}}}\]
Input:
int((-30*exp(5*x)*exp(exp(5*x))+12*x*ln(x)^2+(24*x*ln(5)+36*x^2+12*x)*ln(x )+12*x*ln(5)^2+(36*x^2+12*x)*ln(5)+24*x^3+12*x^2)*exp(-3/(exp(exp(5*x))-x^ 2*ln(x)^2+(-2*x^2*ln(5)-2*x^3)*ln(x)-x^2*ln(5)^2-2*x^3*ln(5)-x^4))^2/(exp( exp(5*x))^2+(-2*x^2*ln(x)^2+(-4*x^2*ln(5)-4*x^3)*ln(x)-2*x^2*ln(5)^2-4*x^3 *ln(5)-2*x^4)*exp(exp(5*x))+x^4*ln(x)^4+(4*x^4*ln(5)+4*x^5)*ln(x)^3+(6*x^4 *ln(5)^2+12*x^5*ln(5)+6*x^6)*ln(x)^2+(4*x^4*ln(5)^3+12*x^5*ln(5)^2+12*x^6* ln(5)+4*x^7)*ln(x)+x^4*ln(5)^4+4*x^5*ln(5)^3+6*x^6*ln(5)^2+4*x^7*ln(5)+x^8 ),x)
Output:
-exp(6/(x^2*ln(x)^2+2*x^2*ln(5)*ln(x)+2*x^3*ln(x)+x^2*ln(5)^2+2*x^3*ln(5)+ x^4-exp(exp(5*x))))
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (29) = 58\).
Time = 0.11 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.41 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-e^{\left (\frac {6 \, e^{\left (5 \, x\right )}}{x^{2} e^{\left (5 \, x\right )} \log \left (x\right )^{2} + 2 \, {\left (x^{3} + x^{2} \log \left (5\right )\right )} e^{\left (5 \, x\right )} \log \left (x\right ) + {\left (x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (5\right )^{2}\right )} e^{\left (5 \, x\right )} - e^{\left (5 \, x + e^{\left (5 \, x\right )}\right )}}\right )} \] Input:
integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12 *x)*log(x)+12*x*log(5)^2+(36*x^2+12*x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(e xp(5*x))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*log( 5)-x^4))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)- 2*x^2*log(5)^2-4*x^3*log(5)-2*x^4)*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5 )+4*x^5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4*log (5)^3+12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5 )^3+6*x^6*log(5)^2+4*x^7*log(5)+x^8),x, algorithm="fricas")
Output:
-e^(6*e^(5*x)/(x^2*e^(5*x)*log(x)^2 + 2*(x^3 + x^2*log(5))*e^(5*x)*log(x) + (x^4 + 2*x^3*log(5) + x^2*log(5)^2)*e^(5*x) - e^(5*x + e^(5*x))))
Timed out. \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=\text {Timed out} \] Input:
integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*ln(x)**2+(24*x*ln(5)+36*x**2+12 *x)*ln(x)+12*x*ln(5)**2+(36*x**2+12*x)*ln(5)+24*x**3+12*x**2)*exp(-3/(exp( exp(5*x))-x**2*ln(x)**2+(-2*x**2*ln(5)-2*x**3)*ln(x)-x**2*ln(5)**2-2*x**3* ln(5)-x**4))**2/(exp(exp(5*x))**2+(-2*x**2*ln(x)**2+(-4*x**2*ln(5)-4*x**3) *ln(x)-2*x**2*ln(5)**2-4*x**3*ln(5)-2*x**4)*exp(exp(5*x))+x**4*ln(x)**4+(4 *x**4*ln(5)+4*x**5)*ln(x)**3+(6*x**4*ln(5)**2+12*x**5*ln(5)+6*x**6)*ln(x)* *2+(4*x**4*ln(5)**3+12*x**5*ln(5)**2+12*x**6*ln(5)+4*x**7)*ln(x)+x**4*ln(5 )**4+4*x**5*ln(5)**3+6*x**6*ln(5)**2+4*x**7*ln(5)+x**8),x)
Output:
Timed out
Time = 0.29 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.72 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-e^{\left (\frac {6}{x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (5\right )^{2} + x^{2} \log \left (x\right )^{2} + 2 \, {\left (x^{3} + x^{2} \log \left (5\right )\right )} \log \left (x\right ) - e^{\left (e^{\left (5 \, x\right )}\right )}}\right )} \] Input:
integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12 *x)*log(x)+12*x*log(5)^2+(36*x^2+12*x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(e xp(5*x))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*log( 5)-x^4))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)- 2*x^2*log(5)^2-4*x^3*log(5)-2*x^4)*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5 )+4*x^5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4*log (5)^3+12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5 )^3+6*x^6*log(5)^2+4*x^7*log(5)+x^8),x, algorithm="maxima")
Output:
-e^(6/(x^4 + 2*x^3*log(5) + x^2*log(5)^2 + x^2*log(x)^2 + 2*(x^3 + x^2*log (5))*log(x) - e^(e^(5*x))))
Time = 0.12 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.78 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-e^{\left (\frac {6}{x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (5\right )^{2} + 2 \, x^{3} \log \left (x\right ) + 2 \, x^{2} \log \left (5\right ) \log \left (x\right ) + x^{2} \log \left (x\right )^{2} - e^{\left (e^{\left (5 \, x\right )}\right )}}\right )} \] Input:
integrate((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12 *x)*log(x)+12*x*log(5)^2+(36*x^2+12*x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(e xp(5*x))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*log( 5)-x^4))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)- 2*x^2*log(5)^2-4*x^3*log(5)-2*x^4)*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5 )+4*x^5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4*log (5)^3+12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5 )^3+6*x^6*log(5)^2+4*x^7*log(5)+x^8),x, algorithm="giac")
Output:
-e^(6/(x^4 + 2*x^3*log(5) + x^2*log(5)^2 + 2*x^3*log(x) + 2*x^2*log(5)*log (x) + x^2*log(x)^2 - e^(e^(5*x))))
Time = 21.58 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.78 \[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=-{\mathrm {e}}^{\frac {6}{x^2\,{\ln \left (5\right )}^2-{\mathrm {e}}^{{\mathrm {e}}^{5\,x}}+2\,x^3\,\ln \left (x\right )+x^2\,{\ln \left (x\right )}^2+2\,x^3\,\ln \left (5\right )+x^4+2\,x^2\,\ln \left (5\right )\,\ln \left (x\right )}} \] Input:
int((exp(6/(x^2*log(5)^2 - exp(exp(5*x)) + x^2*log(x)^2 + log(x)*(2*x^2*lo g(5) + 2*x^3) + 2*x^3*log(5) + x^4))*(12*x*log(x)^2 + log(5)*(12*x + 36*x^ 2) - 30*exp(5*x)*exp(exp(5*x)) + 12*x*log(5)^2 + 12*x^2 + 24*x^3 + log(x)* (12*x + 24*x*log(5) + 36*x^2)))/(exp(2*exp(5*x)) + x^4*log(5)^4 + 4*x^5*lo g(5)^3 + 6*x^6*log(5)^2 - exp(exp(5*x))*(2*x^2*log(5)^2 + 2*x^2*log(x)^2 + log(x)*(4*x^2*log(5) + 4*x^3) + 4*x^3*log(5) + 2*x^4) + x^4*log(x)^4 + lo g(x)*(4*x^4*log(5)^3 + 12*x^5*log(5)^2 + 12*x^6*log(5) + 4*x^7) + 4*x^7*lo g(5) + x^8 + log(x)^3*(4*x^4*log(5) + 4*x^5) + log(x)^2*(6*x^4*log(5)^2 + 12*x^5*log(5) + 6*x^6)),x)
Output:
-exp(6/(x^2*log(5)^2 - exp(exp(5*x)) + 2*x^3*log(x) + x^2*log(x)^2 + 2*x^3 *log(5) + x^4 + 2*x^2*log(5)*log(x)))
\[ \int \frac {e^{-\frac {6}{e^{e^{5 x}}-x^4-2 x^3 \log (5)-x^2 \log ^2(5)+\left (-2 x^3-2 x^2 \log (5)\right ) \log (x)-x^2 \log ^2(x)}} \left (-30 e^{e^{5 x}+5 x}+12 x^2+24 x^3+\left (12 x+36 x^2\right ) \log (5)+12 x \log ^2(5)+\left (12 x+36 x^2+24 x \log (5)\right ) \log (x)+12 x \log ^2(x)\right )}{e^{2 e^{5 x}}+x^8+4 x^7 \log (5)+6 x^6 \log ^2(5)+4 x^5 \log ^3(5)+x^4 \log ^4(5)+\left (4 x^7+12 x^6 \log (5)+12 x^5 \log ^2(5)+4 x^4 \log ^3(5)\right ) \log (x)+\left (6 x^6+12 x^5 \log (5)+6 x^4 \log ^2(5)\right ) \log ^2(x)+\left (4 x^5+4 x^4 \log (5)\right ) \log ^3(x)+x^4 \log ^4(x)+e^{e^{5 x}} \left (-2 x^4-4 x^3 \log (5)-2 x^2 \log ^2(5)+\left (-4 x^3-4 x^2 \log (5)\right ) \log (x)-2 x^2 \log ^2(x)\right )} \, dx=\int \frac {\left (-30 \,{\mathrm e}^{5 x} {\mathrm e}^{{\mathrm e}^{5 x}}+12 \mathrm {log}\left (x \right )^{2} x +\left (24 \,\mathrm {log}\left (5\right ) x +36 x^{2}+12 x \right ) \mathrm {log}\left (x \right )+12 x \mathrm {log}\left (5\right )^{2}+\left (36 x^{2}+12 x \right ) \mathrm {log}\left (5\right )+24 x^{3}+12 x^{2}\right ) \left ({\mathrm e}^{-\frac {3}{{\mathrm e}^{{\mathrm e}^{5 x}}-\mathrm {log}\left (x \right )^{2} x^{2}+\left (-2 \,\mathrm {log}\left (5\right ) x^{2}-2 x^{3}\right ) \mathrm {log}\left (x \right )-\mathrm {log}\left (5\right )^{2} x^{2}-2 \,\mathrm {log}\left (5\right ) x^{3}-x^{4}}}\right )^{2}}{\left ({\mathrm e}^{{\mathrm e}^{5 x}}\right )^{2}+\left (-2 \mathrm {log}\left (x \right )^{2} x^{2}+\left (-4 \,\mathrm {log}\left (5\right ) x^{2}-4 x^{3}\right ) \mathrm {log}\left (x \right )-2 \mathrm {log}\left (5\right )^{2} x^{2}-4 \,\mathrm {log}\left (5\right ) x^{3}-2 x^{4}\right ) {\mathrm e}^{{\mathrm e}^{5 x}}+\mathrm {log}\left (x \right )^{4} x^{4}+\left (4 \,\mathrm {log}\left (5\right ) x^{4}+4 x^{5}\right ) \mathrm {log}\left (x \right )^{3}+\left (6 x^{4} \mathrm {log}\left (5\right )^{2}+12 \,\mathrm {log}\left (5\right ) x^{5}+6 x^{6}\right ) \mathrm {log}\left (x \right )^{2}+\left (4 x^{4} \mathrm {log}\left (5\right )^{3}+12 x^{5} \mathrm {log}\left (5\right )^{2}+12 x^{6} \mathrm {log}\left (5\right )+4 x^{7}\right ) \mathrm {log}\left (x \right )+\mathrm {log}\left (5\right )^{4} x^{4}+4 x^{5} \mathrm {log}\left (5\right )^{3}+6 x^{6} \mathrm {log}\left (5\right )^{2}+4 x^{7} \mathrm {log}\left (5\right )+x^{8}}d x \] Input:
int((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12*x)*lo g(x)+12*x*log(5)^2+(36*x^2+12*x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(exp(5*x ))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*log(5)-x^4 ))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)-2*x^2* log(5)^2-4*x^3*log(5)-2*x^4)*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5)+4*x^ 5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4*log(5)^3+ 12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5)^3+6* x^6*log(5)^2+4*x^7*log(5)+x^8),x)
Output:
int((-30*exp(5*x)*exp(exp(5*x))+12*x*log(x)^2+(24*x*log(5)+36*x^2+12*x)*lo g(x)+12*x*log(5)^2+(36*x^2+12*x)*log(5)+24*x^3+12*x^2)*exp(-3/(exp(exp(5*x ))-x^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*log(x)-x^2*log(5)^2-2*x^3*log(5)-x^4 ))^2/(exp(exp(5*x))^2+(-2*x^2*log(x)^2+(-4*x^2*log(5)-4*x^3)*log(x)-2*x^2* log(5)^2-4*x^3*log(5)-2*x^4)*exp(exp(5*x))+x^4*log(x)^4+(4*x^4*log(5)+4*x^ 5)*log(x)^3+(6*x^4*log(5)^2+12*x^5*log(5)+6*x^6)*log(x)^2+(4*x^4*log(5)^3+ 12*x^5*log(5)^2+12*x^6*log(5)+4*x^7)*log(x)+x^4*log(5)^4+4*x^5*log(5)^3+6* x^6*log(5)^2+4*x^7*log(5)+x^8),x)