Integrand size = 398, antiderivative size = 28 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=x+\log (x)-\frac {\log (2+\log (x))}{\left (-x+e^4 x+\frac {\log (x)}{2}\right )^2} \] Output:
x+ln(x)-ln(ln(x)+2)/(x*exp(4)-x+1/2*ln(x))^2
Time = 0.17 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=x+\log (x)-\frac {4 \log (2+\log (x))}{\left (-2 x+2 e^4 x+\log (x)\right )^2} \] Input:
Integrate[(8*x - 16*x^3 - 16*x^4 + E^8*(-48*x^3 - 48*x^4) + E^12*(16*x^3 + 16*x^4) + E^4*(-8*x + 48*x^3 + 48*x^4) + (-4 + 24*x^2 + 16*x^3 - 8*x^4 + E^8*(24*x^2 - 24*x^4) + E^12*(8*x^3 + 8*x^4) + E^4*(-48*x^2 - 24*x^3 + 24* x^4))*Log[x] + (-12*x + 12*x^3 + E^4*(12*x - 12*x^2 - 24*x^3) + E^8*(12*x^ 2 + 12*x^3))*Log[x]^2 + (2 - 4*x - 6*x^2 + E^4*(6*x + 6*x^2))*Log[x]^3 + ( 1 + x)*Log[x]^4 + (16 - 32*x + 32*E^4*x + (8 - 16*x + 16*E^4*x)*Log[x])*Lo g[2 + Log[x]])/(-16*x^4 + 48*E^4*x^4 - 48*E^8*x^4 + 16*E^12*x^4 + (24*x^3 - 8*x^4 + 8*E^12*x^4 + E^8*(24*x^3 - 24*x^4) + E^4*(-48*x^3 + 24*x^4))*Log [x] + (-12*x^2 + 12*x^3 + 12*E^8*x^3 + E^4*(12*x^2 - 24*x^3))*Log[x]^2 + ( 2*x - 6*x^2 + 6*E^4*x^2)*Log[x]^3 + x*Log[x]^4),x]
Output:
x + Log[x] - (4*Log[2 + Log[x]])/(-2*x + 2*E^4*x + Log[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.
| \(\displaystyle \int \frac {-16 x^4-16 x^3+\left (-6 x^2+e^4 \left (6 x^2+6 x\right )-4 x+2\right ) \log ^3(x)+e^8 \left (-48 x^4-48 x^3\right )+e^{12} \left (16 x^4+16 x^3\right )+e^4 \left (48 x^4+48 x^3-8 x\right )+\left (12 x^3+e^4 \left (-24 x^3-12 x^2+12 x\right )+e^8 \left (12 x^3+12 x^2\right )-12 x\right ) \log ^2(x)+\left (-8 x^4+16 x^3+24 x^2+e^{12} \left (8 x^4+8 x^3\right )+e^8 \left (24 x^2-24 x^4\right )+e^4 \left (24 x^4-24 x^3-48 x^2\right )-4\right ) \log (x)+8 x+(x+1) \log ^4(x)+\left (32 e^4 x-32 x+\left (16 e^4 x-16 x+8\right ) \log (x)+16\right ) \log (\log (x)+2)}{16 e^{12} x^4-48 e^8 x^4+48 e^4 x^4-16 x^4+\left (6 e^4 x^2-6 x^2+2 x\right ) \log ^3(x)+\left (8 e^{12} x^4-8 x^4+24 x^3+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (24 x^4-48 x^3\right )\right ) \log (x)+\left (12 e^8 x^3+12 x^3-12 x^2+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+x \log ^4(x)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-16 x^4-16 x^3+\left (-6 x^2+e^4 \left (6 x^2+6 x\right )-4 x+2\right ) \log ^3(x)+e^8 \left (-48 x^4-48 x^3\right )+e^{12} \left (16 x^4+16 x^3\right )+e^4 \left (48 x^4+48 x^3-8 x\right )+\left (12 x^3+e^4 \left (-24 x^3-12 x^2+12 x\right )+e^8 \left (12 x^3+12 x^2\right )-12 x\right ) \log ^2(x)+\left (-8 x^4+16 x^3+24 x^2+e^{12} \left (8 x^4+8 x^3\right )+e^8 \left (24 x^2-24 x^4\right )+e^4 \left (24 x^4-24 x^3-48 x^2\right )-4\right ) \log (x)+8 x+(x+1) \log ^4(x)+\left (32 e^4 x-32 x+\left (16 e^4 x-16 x+8\right ) \log (x)+16\right ) \log (\log (x)+2)}{\left (48 e^4-16\right ) x^4+16 e^{12} x^4-48 e^8 x^4+\left (6 e^4 x^2-6 x^2+2 x\right ) \log ^3(x)+\left (8 e^{12} x^4-8 x^4+24 x^3+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (24 x^4-48 x^3\right )\right ) \log (x)+\left (12 e^8 x^3+12 x^3-12 x^2+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+x \log ^4(x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-16 x^4-16 x^3+\left (-6 x^2+e^4 \left (6 x^2+6 x\right )-4 x+2\right ) \log ^3(x)+e^8 \left (-48 x^4-48 x^3\right )+e^{12} \left (16 x^4+16 x^3\right )+e^4 \left (48 x^4+48 x^3-8 x\right )+\left (12 x^3+e^4 \left (-24 x^3-12 x^2+12 x\right )+e^8 \left (12 x^3+12 x^2\right )-12 x\right ) \log ^2(x)+\left (-8 x^4+16 x^3+24 x^2+e^{12} \left (8 x^4+8 x^3\right )+e^8 \left (24 x^2-24 x^4\right )+e^4 \left (24 x^4-24 x^3-48 x^2\right )-4\right ) \log (x)+8 x+(x+1) \log ^4(x)+\left (32 e^4 x-32 x+\left (16 e^4 x-16 x+8\right ) \log (x)+16\right ) \log (\log (x)+2)}{\left (16 e^{12}-48 e^8\right ) x^4+\left (48 e^4-16\right ) x^4+\left (6 e^4 x^2-6 x^2+2 x\right ) \log ^3(x)+\left (8 e^{12} x^4-8 x^4+24 x^3+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (24 x^4-48 x^3\right )\right ) \log (x)+\left (12 e^8 x^3+12 x^3-12 x^2+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+x \log ^4(x)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-16 x^4-16 x^3+\left (-6 x^2+e^4 \left (6 x^2+6 x\right )-4 x+2\right ) \log ^3(x)+e^8 \left (-48 x^4-48 x^3\right )+e^{12} \left (16 x^4+16 x^3\right )+e^4 \left (48 x^4+48 x^3-8 x\right )+\left (12 x^3+e^4 \left (-24 x^3-12 x^2+12 x\right )+e^8 \left (12 x^3+12 x^2\right )-12 x\right ) \log ^2(x)+\left (-8 x^4+16 x^3+24 x^2+e^{12} \left (8 x^4+8 x^3\right )+e^8 \left (24 x^2-24 x^4\right )+e^4 \left (24 x^4-24 x^3-48 x^2\right )-4\right ) \log (x)+8 x+(x+1) \log ^4(x)+\left (32 e^4 x-32 x+\left (16 e^4 x-16 x+8\right ) \log (x)+16\right ) \log (\log (x)+2)}{\left (-16+48 e^4-48 e^8+16 e^{12}\right ) x^4+\left (6 e^4 x^2-6 x^2+2 x\right ) \log ^3(x)+\left (8 e^{12} x^4-8 x^4+24 x^3+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (24 x^4-48 x^3\right )\right ) \log (x)+\left (12 e^8 x^3+12 x^3-12 x^2+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+x \log ^4(x)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {8 \left (1-e^4\right )^3 x^3 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 \left (-2-e^4\right ) \left (1-e^4\right )^2 x^2 \log (x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {8 (1-e) (1+e) \left (1+e^2\right ) \left (2 \left (1-e^4\right )^2 x^3+2 \left (1-e^4\right )^2 x^2-1\right )}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {(-x-1) \log ^4(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {2 (x+1) \left (3 \left (1-e^4\right ) x-1\right ) \log ^3(x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {12 (1-e) (1+e) \left (1+e^2\right ) (x+1) \left (1-\left (1-e^4\right ) x\right ) \log ^2(x)}{\left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {4 \log (x)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3 (\log (x)+2)}+\frac {24 \left (1-e^4\right )^2 x \log (x)}{(\log (x)+2) \left (\log (x)-2 \left (1-e^4\right ) x\right )^3}+\frac {8 \left (2 \left (1-e^4\right ) x-1\right ) \log (\log (x)+2)}{x \left (2 \left (1-e^4\right ) x-\log (x)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (\left (e^4-1\right ) x \left (2 \left (e^4-1\right )^2 x^3+2 \left (e^4-1\right )^2 x^2-1\right )+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)\right )+4 \left (2 \left (e^4-1\right )^3 x^4+2 \left (2-3 e^4+e^{12}\right ) x^3+6 \left (e^4-1\right )^2 x^2+\left (4 \left (e^4-1\right ) x+2\right ) \log (\log (x)+2)-1\right ) \log (x)+(x+1) \log ^4(x)+2 (x+1) \left (3 \left (e^4-1\right ) x+1\right ) \log ^3(x)+12 \left (e^4-1\right ) x (x+1) \left (\left (e^4-1\right ) x+1\right ) \log ^2(x)}{x (\log (x)+2) \left (2 \left (e^4-1\right ) x+\log (x)\right )^3}dx\) |
Input:
Int[(8*x - 16*x^3 - 16*x^4 + E^8*(-48*x^3 - 48*x^4) + E^12*(16*x^3 + 16*x^ 4) + E^4*(-8*x + 48*x^3 + 48*x^4) + (-4 + 24*x^2 + 16*x^3 - 8*x^4 + E^8*(2 4*x^2 - 24*x^4) + E^12*(8*x^3 + 8*x^4) + E^4*(-48*x^2 - 24*x^3 + 24*x^4))* Log[x] + (-12*x + 12*x^3 + E^4*(12*x - 12*x^2 - 24*x^3) + E^8*(12*x^2 + 12 *x^3))*Log[x]^2 + (2 - 4*x - 6*x^2 + E^4*(6*x + 6*x^2))*Log[x]^3 + (1 + x) *Log[x]^4 + (16 - 32*x + 32*E^4*x + (8 - 16*x + 16*E^4*x)*Log[x])*Log[2 + Log[x]])/(-16*x^4 + 48*E^4*x^4 - 48*E^8*x^4 + 16*E^12*x^4 + (24*x^3 - 8*x^ 4 + 8*E^12*x^4 + E^8*(24*x^3 - 24*x^4) + E^4*(-48*x^3 + 24*x^4))*Log[x] + (-12*x^2 + 12*x^3 + 12*E^8*x^3 + E^4*(12*x^2 - 24*x^3))*Log[x]^2 + (2*x - 6*x^2 + 6*E^4*x^2)*Log[x]^3 + x*Log[x]^4),x]
Output:
$Aborted
Time = 14.39 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89
| method | result | size |
| risch | \(-\frac {4 \ln \left (\ln \left (x \right )+2\right )}{\left (2 x \,{\mathrm e}^{4}+\ln \left (x \right )-2 x \right )^{2}}+x +\ln \left (x \right )\) | \(25\) |
| parallelrisch | \(\frac {4 \,{\mathrm e}^{8} x^{3}-8 x^{3} {\mathrm e}^{4}-16 x^{2} {\mathrm e}^{8}+32 x^{2} {\mathrm e}^{4}-3 x \ln \left (x \right )^{2}+16 x \ln \left (x \right )-4 \ln \left (\ln \left (x \right )+2\right )-16 x \,{\mathrm e}^{4} \ln \left (x \right )+\ln \left (x \right )^{3}-4 \ln \left (x \right )^{2}+4 x^{3}-16 x^{2}-4 \,{\mathrm e}^{4} \ln \left (x \right ) x^{2}+4 \,{\mathrm e}^{4} \ln \left (x \right )^{2} x +4 \,{\mathrm e}^{8} \ln \left (x \right ) x^{2}}{4 x^{2} {\mathrm e}^{8}+4 x \,{\mathrm e}^{4} \ln \left (x \right )-8 x^{2} {\mathrm e}^{4}+\ln \left (x \right )^{2}-4 x \ln \left (x \right )+4 x^{2}}\) | \(150\) |
Input:
int((((16*x*exp(4)-16*x+8)*ln(x)+32*x*exp(4)-32*x+16)*ln(ln(x)+2)+(1+x)*ln (x)^4+((6*x^2+6*x)*exp(4)-6*x^2-4*x+2)*ln(x)^3+((12*x^3+12*x^2)*exp(4)^2+( -24*x^3-12*x^2+12*x)*exp(4)+12*x^3-12*x)*ln(x)^2+((8*x^4+8*x^3)*exp(4)^3+( -24*x^4+24*x^2)*exp(4)^2+(24*x^4-24*x^3-48*x^2)*exp(4)-8*x^4+16*x^3+24*x^2 -4)*ln(x)+(16*x^4+16*x^3)*exp(4)^3+(-48*x^4-48*x^3)*exp(4)^2+(48*x^4+48*x^ 3-8*x)*exp(4)-16*x^4-16*x^3+8*x)/(x*ln(x)^4+(6*x^2*exp(4)-6*x^2+2*x)*ln(x) ^3+(12*x^3*exp(4)^2+(-24*x^3+12*x^2)*exp(4)+12*x^3-12*x^2)*ln(x)^2+(8*x^4* exp(4)^3+(-24*x^4+24*x^3)*exp(4)^2+(24*x^4-48*x^3)*exp(4)-8*x^4+24*x^3)*ln (x)+16*x^4*exp(4)^3-48*x^4*exp(4)^2+48*x^4*exp(4)-16*x^4),x,method=_RETURN VERBOSE)
Output:
-4/(2*x*exp(4)+ln(x)-2*x)^2*ln(ln(x)+2)+x+ln(x)
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (24) = 48\).
Time = 0.08 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.64 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\frac {4 \, x^{3} e^{8} - 8 \, x^{3} e^{4} + 4 \, x^{3} + {\left (4 \, x e^{4} - 3 \, x\right )} \log \left (x\right )^{2} + \log \left (x\right )^{3} + 4 \, {\left (x^{2} e^{8} - x^{2} e^{4}\right )} \log \left (x\right ) - 4 \, \log \left (\log \left (x\right ) + 2\right )}{4 \, x^{2} e^{8} - 8 \, x^{2} e^{4} + 4 \, x^{2} + 4 \, {\left (x e^{4} - x\right )} \log \left (x\right ) + \log \left (x\right )^{2}} \] Input:
integrate((((16*x*exp(4)-16*x+8)*log(x)+32*x*exp(4)-32*x+16)*log(log(x)+2) +(1+x)*log(x)^4+((6*x^2+6*x)*exp(4)-6*x^2-4*x+2)*log(x)^3+((12*x^3+12*x^2) *exp(4)^2+(-24*x^3-12*x^2+12*x)*exp(4)+12*x^3-12*x)*log(x)^2+((8*x^4+8*x^3 )*exp(4)^3+(-24*x^4+24*x^2)*exp(4)^2+(24*x^4-24*x^3-48*x^2)*exp(4)-8*x^4+1 6*x^3+24*x^2-4)*log(x)+(16*x^4+16*x^3)*exp(4)^3+(-48*x^4-48*x^3)*exp(4)^2+ (48*x^4+48*x^3-8*x)*exp(4)-16*x^4-16*x^3+8*x)/(x*log(x)^4+(6*x^2*exp(4)-6* x^2+2*x)*log(x)^3+(12*x^3*exp(4)^2+(-24*x^3+12*x^2)*exp(4)+12*x^3-12*x^2)* log(x)^2+(8*x^4*exp(4)^3+(-24*x^4+24*x^3)*exp(4)^2+(24*x^4-48*x^3)*exp(4)- 8*x^4+24*x^3)*log(x)+16*x^4*exp(4)^3-48*x^4*exp(4)^2+48*x^4*exp(4)-16*x^4) ,x, algorithm="fricas")
Output:
(4*x^3*e^8 - 8*x^3*e^4 + 4*x^3 + (4*x*e^4 - 3*x)*log(x)^2 + log(x)^3 + 4*( x^2*e^8 - x^2*e^4)*log(x) - 4*log(log(x) + 2))/(4*x^2*e^8 - 8*x^2*e^4 + 4* x^2 + 4*(x*e^4 - x)*log(x) + log(x)^2)
Exception generated. \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate((((16*x*exp(4)-16*x+8)*ln(x)+32*x*exp(4)-32*x+16)*ln(ln(x)+2)+(1 +x)*ln(x)**4+((6*x**2+6*x)*exp(4)-6*x**2-4*x+2)*ln(x)**3+((12*x**3+12*x**2 )*exp(4)**2+(-24*x**3-12*x**2+12*x)*exp(4)+12*x**3-12*x)*ln(x)**2+((8*x**4 +8*x**3)*exp(4)**3+(-24*x**4+24*x**2)*exp(4)**2+(24*x**4-24*x**3-48*x**2)* exp(4)-8*x**4+16*x**3+24*x**2-4)*ln(x)+(16*x**4+16*x**3)*exp(4)**3+(-48*x* *4-48*x**3)*exp(4)**2+(48*x**4+48*x**3-8*x)*exp(4)-16*x**4-16*x**3+8*x)/(x *ln(x)**4+(6*x**2*exp(4)-6*x**2+2*x)*ln(x)**3+(12*x**3*exp(4)**2+(-24*x**3 +12*x**2)*exp(4)+12*x**3-12*x**2)*ln(x)**2+(8*x**4*exp(4)**3+(-24*x**4+24* x**3)*exp(4)**2+(24*x**4-48*x**3)*exp(4)-8*x**4+24*x**3)*ln(x)+16*x**4*exp (4)**3-48*x**4*exp(4)**2+48*x**4*exp(4)-16*x**4),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (24) = 48\).
Time = 0.17 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.89 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\frac {4 \, x^{3} {\left (e^{8} - 2 \, e^{4} + 1\right )} + 4 \, x^{2} {\left (e^{8} - e^{4}\right )} \log \left (x\right ) + x {\left (4 \, e^{4} - 3\right )} \log \left (x\right )^{2} + \log \left (x\right )^{3} - 4 \, \log \left (\log \left (x\right ) + 2\right )}{4 \, x^{2} {\left (e^{8} - 2 \, e^{4} + 1\right )} + 4 \, x {\left (e^{4} - 1\right )} \log \left (x\right ) + \log \left (x\right )^{2}} \] Input:
integrate((((16*x*exp(4)-16*x+8)*log(x)+32*x*exp(4)-32*x+16)*log(log(x)+2) +(1+x)*log(x)^4+((6*x^2+6*x)*exp(4)-6*x^2-4*x+2)*log(x)^3+((12*x^3+12*x^2) *exp(4)^2+(-24*x^3-12*x^2+12*x)*exp(4)+12*x^3-12*x)*log(x)^2+((8*x^4+8*x^3 )*exp(4)^3+(-24*x^4+24*x^2)*exp(4)^2+(24*x^4-24*x^3-48*x^2)*exp(4)-8*x^4+1 6*x^3+24*x^2-4)*log(x)+(16*x^4+16*x^3)*exp(4)^3+(-48*x^4-48*x^3)*exp(4)^2+ (48*x^4+48*x^3-8*x)*exp(4)-16*x^4-16*x^3+8*x)/(x*log(x)^4+(6*x^2*exp(4)-6* x^2+2*x)*log(x)^3+(12*x^3*exp(4)^2+(-24*x^3+12*x^2)*exp(4)+12*x^3-12*x^2)* log(x)^2+(8*x^4*exp(4)^3+(-24*x^4+24*x^3)*exp(4)^2+(24*x^4-48*x^3)*exp(4)- 8*x^4+24*x^3)*log(x)+16*x^4*exp(4)^3-48*x^4*exp(4)^2+48*x^4*exp(4)-16*x^4) ,x, algorithm="maxima")
Output:
(4*x^3*(e^8 - 2*e^4 + 1) + 4*x^2*(e^8 - e^4)*log(x) + x*(4*e^4 - 3)*log(x) ^2 + log(x)^3 - 4*log(log(x) + 2))/(4*x^2*(e^8 - 2*e^4 + 1) + 4*x*(e^4 - 1 )*log(x) + log(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (24) = 48\).
Time = 0.94 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.71 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\frac {4 \, x^{3} e^{8} - 8 \, x^{3} e^{4} + 4 \, x^{2} e^{8} \log \left (x\right ) - 4 \, x^{2} e^{4} \log \left (x\right ) + 4 \, x e^{4} \log \left (x\right )^{2} + 4 \, x^{3} - 3 \, x \log \left (x\right )^{2} + \log \left (x\right )^{3} - 4 \, \log \left (\log \left (x\right ) + 2\right )}{4 \, x^{2} e^{8} - 8 \, x^{2} e^{4} + 4 \, x e^{4} \log \left (x\right ) + 4 \, x^{2} - 4 \, x \log \left (x\right ) + \log \left (x\right )^{2}} \] Input:
integrate((((16*x*exp(4)-16*x+8)*log(x)+32*x*exp(4)-32*x+16)*log(log(x)+2) +(1+x)*log(x)^4+((6*x^2+6*x)*exp(4)-6*x^2-4*x+2)*log(x)^3+((12*x^3+12*x^2) *exp(4)^2+(-24*x^3-12*x^2+12*x)*exp(4)+12*x^3-12*x)*log(x)^2+((8*x^4+8*x^3 )*exp(4)^3+(-24*x^4+24*x^2)*exp(4)^2+(24*x^4-24*x^3-48*x^2)*exp(4)-8*x^4+1 6*x^3+24*x^2-4)*log(x)+(16*x^4+16*x^3)*exp(4)^3+(-48*x^4-48*x^3)*exp(4)^2+ (48*x^4+48*x^3-8*x)*exp(4)-16*x^4-16*x^3+8*x)/(x*log(x)^4+(6*x^2*exp(4)-6* x^2+2*x)*log(x)^3+(12*x^3*exp(4)^2+(-24*x^3+12*x^2)*exp(4)+12*x^3-12*x^2)* log(x)^2+(8*x^4*exp(4)^3+(-24*x^4+24*x^3)*exp(4)^2+(24*x^4-48*x^3)*exp(4)- 8*x^4+24*x^3)*log(x)+16*x^4*exp(4)^3-48*x^4*exp(4)^2+48*x^4*exp(4)-16*x^4) ,x, algorithm="giac")
Output:
(4*x^3*e^8 - 8*x^3*e^4 + 4*x^2*e^8*log(x) - 4*x^2*e^4*log(x) + 4*x*e^4*log (x)^2 + 4*x^3 - 3*x*log(x)^2 + log(x)^3 - 4*log(log(x) + 2))/(4*x^2*e^8 - 8*x^2*e^4 + 4*x*e^4*log(x) + 4*x^2 - 4*x*log(x) + log(x)^2)
Time = 2.87 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.82 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\frac {{\ln \left (x\right )}^3-3\,x\,{\ln \left (x\right )}^2-4\,\ln \left (\ln \left (x\right )+2\right )-8\,x^3\,{\mathrm {e}}^4+4\,x^3\,{\mathrm {e}}^8+4\,x^3+4\,x\,{\mathrm {e}}^4\,{\ln \left (x\right )}^2-4\,x^2\,{\mathrm {e}}^4\,\ln \left (x\right )+4\,x^2\,{\mathrm {e}}^8\,\ln \left (x\right )}{{\left (\ln \left (x\right )-2\,x+2\,x\,{\mathrm {e}}^4\right )}^2} \] Input:
int((8*x - log(x)^2*(12*x + exp(4)*(12*x^2 - 12*x + 24*x^3) - exp(8)*(12*x ^2 + 12*x^3) - 12*x^3) + log(x)*(exp(12)*(8*x^3 + 8*x^4) + exp(8)*(24*x^2 - 24*x^4) - exp(4)*(48*x^2 + 24*x^3 - 24*x^4) + 24*x^2 + 16*x^3 - 8*x^4 - 4) + log(log(x) + 2)*(32*x*exp(4) - 32*x + log(x)*(16*x*exp(4) - 16*x + 8) + 16) - log(x)^3*(4*x - exp(4)*(6*x + 6*x^2) + 6*x^2 - 2) + exp(4)*(48*x^ 3 - 8*x + 48*x^4) + log(x)^4*(x + 1) + exp(12)*(16*x^3 + 16*x^4) - exp(8)* (48*x^3 + 48*x^4) - 16*x^3 - 16*x^4)/(x*log(x)^4 + 48*x^4*exp(4) - 48*x^4* exp(8) + 16*x^4*exp(12) + log(x)^2*(exp(4)*(12*x^2 - 24*x^3) + 12*x^3*exp( 8) - 12*x^2 + 12*x^3) + log(x)^3*(2*x + 6*x^2*exp(4) - 6*x^2) + log(x)*(ex p(8)*(24*x^3 - 24*x^4) - exp(4)*(48*x^3 - 24*x^4) + 8*x^4*exp(12) + 24*x^3 - 8*x^4) - 16*x^4),x)
Output:
(log(x)^3 - 3*x*log(x)^2 - 4*log(log(x) + 2) - 8*x^3*exp(4) + 4*x^3*exp(8) + 4*x^3 + 4*x*exp(4)*log(x)^2 - 4*x^2*exp(4)*log(x) + 4*x^2*exp(8)*log(x) )/(log(x) - 2*x + 2*x*exp(4))^2
Time = 0.20 (sec) , antiderivative size = 112, normalized size of antiderivative = 4.00 \[ \int \frac {8 x-16 x^3-16 x^4+e^8 \left (-48 x^3-48 x^4\right )+e^{12} \left (16 x^3+16 x^4\right )+e^4 \left (-8 x+48 x^3+48 x^4\right )+\left (-4+24 x^2+16 x^3-8 x^4+e^8 \left (24 x^2-24 x^4\right )+e^{12} \left (8 x^3+8 x^4\right )+e^4 \left (-48 x^2-24 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x+12 x^3+e^4 \left (12 x-12 x^2-24 x^3\right )+e^8 \left (12 x^2+12 x^3\right )\right ) \log ^2(x)+\left (2-4 x-6 x^2+e^4 \left (6 x+6 x^2\right )\right ) \log ^3(x)+(1+x) \log ^4(x)+\left (16-32 x+32 e^4 x+\left (8-16 x+16 e^4 x\right ) \log (x)\right ) \log (2+\log (x))}{-16 x^4+48 e^4 x^4-48 e^8 x^4+16 e^{12} x^4+\left (24 x^3-8 x^4+8 e^{12} x^4+e^8 \left (24 x^3-24 x^4\right )+e^4 \left (-48 x^3+24 x^4\right )\right ) \log (x)+\left (-12 x^2+12 x^3+12 e^8 x^3+e^4 \left (12 x^2-24 x^3\right )\right ) \log ^2(x)+\left (2 x-6 x^2+6 e^4 x^2\right ) \log ^3(x)+x \log ^4(x)} \, dx=\frac {-4 \,\mathrm {log}\left (\mathrm {log}\left (x \right )+2\right )+\mathrm {log}\left (x \right )^{3}+4 \mathrm {log}\left (x \right )^{2} e^{4} x -3 \mathrm {log}\left (x \right )^{2} x +4 \,\mathrm {log}\left (x \right ) e^{8} x^{2}-4 \,\mathrm {log}\left (x \right ) e^{4} x^{2}+4 e^{8} x^{3}-8 e^{4} x^{3}+4 x^{3}}{\mathrm {log}\left (x \right )^{2}+4 \,\mathrm {log}\left (x \right ) e^{4} x -4 \,\mathrm {log}\left (x \right ) x +4 e^{8} x^{2}-8 e^{4} x^{2}+4 x^{2}} \] Input:
int((((16*x*exp(4)-16*x+8)*log(x)+32*x*exp(4)-32*x+16)*log(log(x)+2)+(1+x) *log(x)^4+((6*x^2+6*x)*exp(4)-6*x^2-4*x+2)*log(x)^3+((12*x^3+12*x^2)*exp(4 )^2+(-24*x^3-12*x^2+12*x)*exp(4)+12*x^3-12*x)*log(x)^2+((8*x^4+8*x^3)*exp( 4)^3+(-24*x^4+24*x^2)*exp(4)^2+(24*x^4-24*x^3-48*x^2)*exp(4)-8*x^4+16*x^3+ 24*x^2-4)*log(x)+(16*x^4+16*x^3)*exp(4)^3+(-48*x^4-48*x^3)*exp(4)^2+(48*x^ 4+48*x^3-8*x)*exp(4)-16*x^4-16*x^3+8*x)/(x*log(x)^4+(6*x^2*exp(4)-6*x^2+2* x)*log(x)^3+(12*x^3*exp(4)^2+(-24*x^3+12*x^2)*exp(4)+12*x^3-12*x^2)*log(x) ^2+(8*x^4*exp(4)^3+(-24*x^4+24*x^3)*exp(4)^2+(24*x^4-48*x^3)*exp(4)-8*x^4+ 24*x^3)*log(x)+16*x^4*exp(4)^3-48*x^4*exp(4)^2+48*x^4*exp(4)-16*x^4),x)
Output:
( - 4*log(log(x) + 2) + log(x)**3 + 4*log(x)**2*e**4*x - 3*log(x)**2*x + 4 *log(x)*e**8*x**2 - 4*log(x)*e**4*x**2 + 4*e**8*x**3 - 8*e**4*x**3 + 4*x** 3)/(log(x)**2 + 4*log(x)*e**4*x - 4*log(x)*x + 4*e**8*x**2 - 8*e**4*x**2 + 4*x**2)