Integrand size = 349, antiderivative size = 31 \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\frac {e^2}{5+e^x+\frac {15}{x}+\frac {9 x}{\left (-x+3 \log ^2(x)\right )^2}} \] Output:
exp(2)/(15/x+9/(3*ln(x)^2-x)^2*x+exp(x)+5)
Time = 0.21 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.00 \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\frac {e^2 x \left (x-3 \log ^2(x)\right )^2}{x^2 \left (24+\left (5+e^x\right ) x\right )-6 x \left (15+\left (5+e^x\right ) x\right ) \log ^2(x)+9 \left (15+\left (5+e^x\right ) x\right ) \log ^4(x)} \] Input:
Integrate[(24*E^2*x^4 - E^(2 + x)*x^6 - 108*E^2*x^3*Log[x] + (-180*E^2*x^3 + 12*E^(2 + x)*x^5)*Log[x]^2 + 324*E^2*x^2*Log[x]^3 + (729*E^2*x^2 - 54*E ^(2 + x)*x^4)*Log[x]^4 + (-1620*E^2*x + 108*E^(2 + x)*x^3)*Log[x]^6 + (121 5*E^2 - 81*E^(2 + x)*x^2)*Log[x]^8)/(576*x^4 + 240*x^5 + 25*x^6 + E^(2*x)* x^6 + E^x*(48*x^5 + 10*x^6) + (-4320*x^3 - 2340*x^4 - 300*x^5 - 12*E^(2*x) *x^5 + E^x*(-468*x^4 - 120*x^5))*Log[x]^2 + (14580*x^2 + 8910*x^3 + 1350*x ^4 + 54*E^(2*x)*x^4 + E^x*(1782*x^3 + 540*x^4))*Log[x]^4 + (-24300*x - 162 00*x^2 - 2700*x^3 - 108*E^(2*x)*x^3 + E^x*(-3240*x^2 - 1080*x^3))*Log[x]^6 + (18225 + 12150*x + 2025*x^2 + 81*E^(2*x)*x^2 + E^x*(2430*x + 810*x^2))* Log[x]^8),x]
Output:
(E^2*x*(x - 3*Log[x]^2)^2)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x )*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)
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.
| \(\displaystyle \int \frac {-e^{x+2} x^6+24 e^2 x^4+\left (108 e^{x+2} x^3-1620 e^2 x\right ) \log ^6(x)-108 e^2 x^3 \log (x)+\left (1215 e^2-81 e^{x+2} x^2\right ) \log ^8(x)+324 e^2 x^2 \log ^3(x)+\left (12 e^{x+2} x^5-180 e^2 x^3\right ) \log ^2(x)+\left (729 e^2 x^2-54 e^{x+2} x^4\right ) \log ^4(x)}{e^{2 x} x^6+25 x^6+240 x^5+576 x^4+\left (81 e^{2 x} x^2+2025 x^2+e^x \left (810 x^2+2430 x\right )+12150 x+18225\right ) \log ^8(x)+e^x \left (10 x^6+48 x^5\right )+\left (-108 e^{2 x} x^3-2700 x^3-16200 x^2+e^x \left (-1080 x^3-3240 x^2\right )-24300 x\right ) \log ^6(x)+\left (-12 e^{2 x} x^5-300 x^5-2340 x^4-4320 x^3+e^x \left (-120 x^5-468 x^4\right )\right ) \log ^2(x)+\left (54 e^{2 x} x^4+1350 x^4+8910 x^3+14580 x^2+e^x \left (540 x^4+1782 x^3\right )\right ) \log ^4(x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^2 \left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (x^2 \left (\left (e^x+5\right ) x+24\right )+9 \left (\left (e^x+5\right ) x+15\right ) \log ^4(x)-6 x \left (\left (e^x+5\right ) x+15\right ) \log ^2(x)\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (-27 \left (15-e^x x^2\right ) \log ^6(x)+27 x \left (15-e^x x^2\right ) \log ^4(x)-9 x^2 \left (12-e^x x^2\right ) \log ^2(x)-108 x^2 \log (x)+x^3 \left (24-e^x x^2\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle e^2 \int \left (\frac {405 x^2 \log ^8(x)+1215 x \log ^8(x)+1215 \log ^8(x)-540 x^3 \log ^6(x)-1620 x^2 \log ^6(x)-1620 x \log ^6(x)+270 x^4 \log ^4(x)+891 x^3 \log ^4(x)+729 x^2 \log ^4(x)+324 x^2 \log ^3(x)-60 x^5 \log ^2(x)-234 x^4 \log ^2(x)-180 x^3 \log ^2(x)-108 x^3 \log (x)+5 x^6+24 x^5+24 x^4}{\left (9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2\right )^2}-\frac {x \left (x-3 \log ^2(x)\right )^2}{9 e^x x \log ^4(x)+45 x \log ^4(x)+135 \log ^4(x)-6 e^x x^2 \log ^2(x)-30 x^2 \log ^2(x)-90 x \log ^2(x)+e^x x^3+5 x^3+24 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (27 \left (e^x x^2-15\right ) \log ^6(x)-27 x \left (e^x x^2-15\right ) \log ^4(x)+9 x^2 \left (e^x x^2-12\right ) \log ^2(x)-108 x^2 \log (x)-x^3 \left (e^x x^2-24\right )\right )}{\left (9 \left (\left (5+e^x\right ) x+15\right ) \log ^4(x)-6 x \left (\left (5+e^x\right ) x+15\right ) \log ^2(x)+x^2 \left (\left (5+e^x\right ) x+24\right )\right )^2}dx\) |
Input:
Int[(24*E^2*x^4 - E^(2 + x)*x^6 - 108*E^2*x^3*Log[x] + (-180*E^2*x^3 + 12* E^(2 + x)*x^5)*Log[x]^2 + 324*E^2*x^2*Log[x]^3 + (729*E^2*x^2 - 54*E^(2 + x)*x^4)*Log[x]^4 + (-1620*E^2*x + 108*E^(2 + x)*x^3)*Log[x]^6 + (1215*E^2 - 81*E^(2 + x)*x^2)*Log[x]^8)/(576*x^4 + 240*x^5 + 25*x^6 + E^(2*x)*x^6 + E^x*(48*x^5 + 10*x^6) + (-4320*x^3 - 2340*x^4 - 300*x^5 - 12*E^(2*x)*x^5 + E^x*(-468*x^4 - 120*x^5))*Log[x]^2 + (14580*x^2 + 8910*x^3 + 1350*x^4 + 5 4*E^(2*x)*x^4 + E^x*(1782*x^3 + 540*x^4))*Log[x]^4 + (-24300*x - 16200*x^2 - 2700*x^3 - 108*E^(2*x)*x^3 + E^x*(-3240*x^2 - 1080*x^3))*Log[x]^6 + (18 225 + 12150*x + 2025*x^2 + 81*E^(2*x)*x^2 + E^x*(2430*x + 810*x^2))*Log[x] ^8),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(29)=58\).
Time = 0.06 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32
\[\frac {x \,{\mathrm e}^{2}}{{\mathrm e}^{x} x +5 x +15}-\frac {9 x^{3} {\mathrm e}^{2}}{\left ({\mathrm e}^{x} x +5 x +15\right ) \left (9 x \ln \left (x \right )^{4} {\mathrm e}^{x}+45 x \ln \left (x \right )^{4}-6 x^{2} {\mathrm e}^{x} \ln \left (x \right )^{2}+135 \ln \left (x \right )^{4}-30 x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{x} x^{3}-90 x \ln \left (x \right )^{2}+5 x^{3}+24 x^{2}\right )}\]
Input:
int(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*ln(x)^8+(108*x^3*exp(2)*exp(x)-16 20*exp(2)*x)*ln(x)^6+(-54*x^4*exp(2)*exp(x)+729*x^2*exp(2))*ln(x)^4+324*x^ 2*exp(2)*ln(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*ln(x)^2-108*x^3*exp (2)*ln(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+(810*x^2+2430 *x)*exp(x)+2025*x^2+12150*x+18225)*ln(x)^8+(-108*exp(x)^2*x^3+(-1080*x^3-3 240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*ln(x)^6+(54*exp(x)^2*x^4+(540* x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*ln(x)^4+(-12*x^5*exp(x)^ 2+(-120*x^5-468*x^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*ln(x)^2+x^6*exp(x)^ 2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x)
Output:
x*exp(2)/(exp(x)*x+5*x+15)-9*x^3*exp(2)/(exp(x)*x+5*x+15)/(9*x*ln(x)^4*exp (x)+45*x*ln(x)^4-6*x^2*exp(x)*ln(x)^2+135*ln(x)^4-30*x^2*ln(x)^2+exp(x)*x^ 3-90*x*ln(x)^2+5*x^3+24*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (29) = 58\).
Time = 0.17 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.19 \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\frac {9 \, x e^{4} \log \left (x\right )^{4} - 6 \, x^{2} e^{4} \log \left (x\right )^{2} + x^{3} e^{4}}{9 \, {\left (5 \, {\left (x + 3\right )} e^{2} + x e^{\left (x + 2\right )}\right )} \log \left (x\right )^{4} + x^{3} e^{\left (x + 2\right )} - 6 \, {\left (x^{2} e^{\left (x + 2\right )} + 5 \, {\left (x^{2} + 3 \, x\right )} e^{2}\right )} \log \left (x\right )^{2} + {\left (5 \, x^{3} + 24 \, x^{2}\right )} e^{2}} \] Input:
integrate(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*ex p(x)-1620*exp(2)*x)*log(x)^6+(-54*x^4*exp(2)*exp(x)+729*x^2*exp(2))*log(x) ^4+324*x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^2- 108*x^3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+( 810*x^2+2430*x)*exp(x)+2025*x^2+12150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3 +(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*exp( x)^2*x^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+( -12*x^5*exp(x)^2+(-120*x^5-468*x^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log( x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x, algori thm="fricas")
Output:
(9*x*e^4*log(x)^4 - 6*x^2*e^4*log(x)^2 + x^3*e^4)/(9*(5*(x + 3)*e^2 + x*e^ (x + 2))*log(x)^4 + x^3*e^(x + 2) - 6*(x^2*e^(x + 2) + 5*(x^2 + 3*x)*e^2)* log(x)^2 + (5*x^3 + 24*x^2)*e^2)
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (24) = 48\).
Time = 0.55 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\frac {x^{3} e^{2} - 6 x^{2} e^{2} \log {\left (x \right )}^{2} + 9 x e^{2} \log {\left (x \right )}^{4}}{5 x^{3} - 30 x^{2} \log {\left (x \right )}^{2} + 24 x^{2} + 45 x \log {\left (x \right )}^{4} - 90 x \log {\left (x \right )}^{2} + \left (x^{3} - 6 x^{2} \log {\left (x \right )}^{2} + 9 x \log {\left (x \right )}^{4}\right ) e^{x} + 135 \log {\left (x \right )}^{4}} \] Input:
integrate(((-81*x**2*exp(2)*exp(x)+1215*exp(2))*ln(x)**8+(108*x**3*exp(2)* exp(x)-1620*exp(2)*x)*ln(x)**6+(-54*x**4*exp(2)*exp(x)+729*x**2*exp(2))*ln (x)**4+324*x**2*exp(2)*ln(x)**3+(12*x**5*exp(2)*exp(x)-180*x**3*exp(2))*ln (x)**2-108*x**3*exp(2)*ln(x)-x**6*exp(2)*exp(x)+24*x**4*exp(2))/((81*exp(x )**2*x**2+(810*x**2+2430*x)*exp(x)+2025*x**2+12150*x+18225)*ln(x)**8+(-108 *exp(x)**2*x**3+(-1080*x**3-3240*x**2)*exp(x)-2700*x**3-16200*x**2-24300*x )*ln(x)**6+(54*exp(x)**2*x**4+(540*x**4+1782*x**3)*exp(x)+1350*x**4+8910*x **3+14580*x**2)*ln(x)**4+(-12*x**5*exp(x)**2+(-120*x**5-468*x**4)*exp(x)-3 00*x**5-2340*x**4-4320*x**3)*ln(x)**2+x**6*exp(x)**2+(10*x**6+48*x**5)*exp (x)+25*x**6+240*x**5+576*x**4),x)
Output:
(x**3*exp(2) - 6*x**2*exp(2)*log(x)**2 + 9*x*exp(2)*log(x)**4)/(5*x**3 - 3 0*x**2*log(x)**2 + 24*x**2 + 45*x*log(x)**4 - 90*x*log(x)**2 + (x**3 - 6*x **2*log(x)**2 + 9*x*log(x)**4)*exp(x) + 135*log(x)**4)
Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (29) = 58\).
Time = 0.29 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.77 \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\frac {9 \, x e^{2} \log \left (x\right )^{4} - 6 \, x^{2} e^{2} \log \left (x\right )^{2} + x^{3} e^{2}}{45 \, {\left (x + 3\right )} \log \left (x\right )^{4} + 5 \, x^{3} - 30 \, {\left (x^{2} + 3 \, x\right )} \log \left (x\right )^{2} + 24 \, x^{2} + {\left (9 \, x \log \left (x\right )^{4} - 6 \, x^{2} \log \left (x\right )^{2} + x^{3}\right )} e^{x}} \] Input:
integrate(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*ex p(x)-1620*exp(2)*x)*log(x)^6+(-54*x^4*exp(2)*exp(x)+729*x^2*exp(2))*log(x) ^4+324*x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^2- 108*x^3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+( 810*x^2+2430*x)*exp(x)+2025*x^2+12150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3 +(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*exp( x)^2*x^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+( -12*x^5*exp(x)^2+(-120*x^5-468*x^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log( x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x, algori thm="maxima")
Output:
(9*x*e^2*log(x)^4 - 6*x^2*e^2*log(x)^2 + x^3*e^2)/(45*(x + 3)*log(x)^4 + 5 *x^3 - 30*(x^2 + 3*x)*log(x)^2 + 24*x^2 + (9*x*log(x)^4 - 6*x^2*log(x)^2 + x^3)*e^x)
Timed out. \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\text {Timed out} \] Input:
integrate(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*ex p(x)-1620*exp(2)*x)*log(x)^6+(-54*x^4*exp(2)*exp(x)+729*x^2*exp(2))*log(x) ^4+324*x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^2- 108*x^3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+( 810*x^2+2430*x)*exp(x)+2025*x^2+12150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3 +(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*exp( x)^2*x^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+( -12*x^5*exp(x)^2+(-120*x^5-468*x^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log( x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x, algori thm="giac")
Output:
Timed out
Timed out. \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=-\int -\frac {{\ln \left (x\right )}^2\,\left (12\,x^5\,{\mathrm {e}}^{x+2}-180\,x^3\,{\mathrm {e}}^2\right )-{\ln \left (x\right )}^4\,\left (54\,x^4\,{\mathrm {e}}^{x+2}-729\,x^2\,{\mathrm {e}}^2\right )+{\ln \left (x\right )}^8\,\left (1215\,{\mathrm {e}}^2-81\,x^2\,{\mathrm {e}}^{x+2}\right )-x^6\,{\mathrm {e}}^{x+2}+24\,x^4\,{\mathrm {e}}^2-{\ln \left (x\right )}^6\,\left (1620\,x\,{\mathrm {e}}^2-108\,x^3\,{\mathrm {e}}^{x+2}\right )-108\,x^3\,{\mathrm {e}}^2\,\ln \left (x\right )+324\,x^2\,{\mathrm {e}}^2\,{\ln \left (x\right )}^3}{{\mathrm {e}}^x\,\left (10\,x^6+48\,x^5\right )-{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^x\,\left (120\,x^5+468\,x^4\right )+12\,x^5\,{\mathrm {e}}^{2\,x}+4320\,x^3+2340\,x^4+300\,x^5\right )+{\ln \left (x\right )}^4\,\left ({\mathrm {e}}^x\,\left (540\,x^4+1782\,x^3\right )+54\,x^4\,{\mathrm {e}}^{2\,x}+14580\,x^2+8910\,x^3+1350\,x^4\right )+{\ln \left (x\right )}^8\,\left (12150\,x+81\,x^2\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (810\,x^2+2430\,x\right )+2025\,x^2+18225\right )+x^6\,{\mathrm {e}}^{2\,x}-{\ln \left (x\right )}^6\,\left (24300\,x+{\mathrm {e}}^x\,\left (1080\,x^3+3240\,x^2\right )+108\,x^3\,{\mathrm {e}}^{2\,x}+16200\,x^2+2700\,x^3\right )+576\,x^4+240\,x^5+25\,x^6} \,d x \] Input:
int(-(log(x)^2*(180*x^3*exp(2) - 12*x^5*exp(2)*exp(x)) - log(x)^4*(729*x^2 *exp(2) - 54*x^4*exp(2)*exp(x)) - log(x)^8*(1215*exp(2) - 81*x^2*exp(2)*ex p(x)) - 24*x^4*exp(2) + log(x)^6*(1620*x*exp(2) - 108*x^3*exp(2)*exp(x)) + x^6*exp(2)*exp(x) + 108*x^3*exp(2)*log(x) - 324*x^2*exp(2)*log(x)^3)/(exp (x)*(48*x^5 + 10*x^6) - log(x)^2*(exp(x)*(468*x^4 + 120*x^5) + 12*x^5*exp( 2*x) + 4320*x^3 + 2340*x^4 + 300*x^5) + log(x)^4*(exp(x)*(1782*x^3 + 540*x ^4) + 54*x^4*exp(2*x) + 14580*x^2 + 8910*x^3 + 1350*x^4) + log(x)^8*(12150 *x + 81*x^2*exp(2*x) + exp(x)*(2430*x + 810*x^2) + 2025*x^2 + 18225) + x^6 *exp(2*x) - log(x)^6*(24300*x + exp(x)*(3240*x^2 + 1080*x^3) + 108*x^3*exp (2*x) + 16200*x^2 + 2700*x^3) + 576*x^4 + 240*x^5 + 25*x^6),x)
Output:
-int(-(log(x)^2*(12*x^5*exp(x + 2) - 180*x^3*exp(2)) - log(x)^4*(54*x^4*ex p(x + 2) - 729*x^2*exp(2)) + log(x)^8*(1215*exp(2) - 81*x^2*exp(x + 2)) - x^6*exp(x + 2) + 24*x^4*exp(2) - log(x)^6*(1620*x*exp(2) - 108*x^3*exp(x + 2)) - 108*x^3*exp(2)*log(x) + 324*x^2*exp(2)*log(x)^3)/(exp(x)*(48*x^5 + 10*x^6) - log(x)^2*(exp(x)*(468*x^4 + 120*x^5) + 12*x^5*exp(2*x) + 4320*x^ 3 + 2340*x^4 + 300*x^5) + log(x)^4*(exp(x)*(1782*x^3 + 540*x^4) + 54*x^4*e xp(2*x) + 14580*x^2 + 8910*x^3 + 1350*x^4) + log(x)^8*(12150*x + 81*x^2*ex p(2*x) + exp(x)*(2430*x + 810*x^2) + 2025*x^2 + 18225) + x^6*exp(2*x) - lo g(x)^6*(24300*x + exp(x)*(3240*x^2 + 1080*x^3) + 108*x^3*exp(2*x) + 16200* x^2 + 2700*x^3) + 576*x^4 + 240*x^5 + 25*x^6), x)
Time = 0.22 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.00 \[ \int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx=\frac {e^{2} x \left (9 \mathrm {log}\left (x \right )^{4}-6 \mathrm {log}\left (x \right )^{2} x +x^{2}\right )}{9 e^{x} \mathrm {log}\left (x \right )^{4} x -6 e^{x} \mathrm {log}\left (x \right )^{2} x^{2}+e^{x} x^{3}+45 \mathrm {log}\left (x \right )^{4} x +135 \mathrm {log}\left (x \right )^{4}-30 \mathrm {log}\left (x \right )^{2} x^{2}-90 \mathrm {log}\left (x \right )^{2} x +5 x^{3}+24 x^{2}} \] Input:
int(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*exp(x)-1 620*exp(2)*x)*log(x)^6+(-54*x^4*exp(2)*exp(x)+729*x^2*exp(2))*log(x)^4+324 *x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^2-108*x^ 3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+(810*x^ 2+2430*x)*exp(x)+2025*x^2+12150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3+(-108 0*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*exp(x)^2*x ^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+(-12*x^ 5*exp(x)^2+(-120*x^5-468*x^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log(x)^2+x ^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x)
Output:
(e**2*x*(9*log(x)**4 - 6*log(x)**2*x + x**2))/(9*e**x*log(x)**4*x - 6*e**x *log(x)**2*x**2 + e**x*x**3 + 45*log(x)**4*x + 135*log(x)**4 - 30*log(x)** 2*x**2 - 90*log(x)**2*x + 5*x**3 + 24*x**2)