Integrand size = 510, antiderivative size = 33 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\frac {\left (4+\frac {x}{4+3 x+\frac {x^2}{\log (2-x)}}\right )^2}{\left (e^8+x\right )^2} \] Output:
(4+x/(4+3*x+x^2/ln(2-x)))^2/(x+exp(4)^2)^2
Time = 0.12 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.39 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\frac {\left (4 x^2+(16+13 x) \log (2-x)\right )^2}{\left (e^8+x\right )^2 \left (x^2+(4+3 x) \log (2-x)\right )^2} \] Input:
Integrate[(8*E^8*x^5 + 72*x^6 - 32*x^7 + (800*x^4 + 266*x^5 - 312*x^6 + E^ 8*(32*x^3 + 42*x^4 - 8*x^5))*Log[2 - x] + (3072*x^2 + 3328*x^3 - 456*x^4 - 988*x^5 + E^8*(52*x^3 - 26*x^4))*Log[2 - x]^2 + (4096 + 7424*x + 2752*x^2 - 1716*x^3 - 1014*x^4 + E^8*(-256 - 80*x + 104*x^2))*Log[2 - x]^3)/(-2*x^ 9 + x^10 + E^24*(-2*x^6 + x^7) + E^16*(-6*x^7 + 3*x^8) + E^8*(-6*x^8 + 3*x ^9) + (-24*x^7 - 6*x^8 + 9*x^9 + E^24*(-24*x^4 - 6*x^5 + 9*x^6) + E^16*(-7 2*x^5 - 18*x^6 + 27*x^7) + E^8*(-72*x^6 - 18*x^7 + 27*x^8))*Log[2 - x] + ( -96*x^5 - 96*x^6 + 18*x^7 + 27*x^8 + E^24*(-96*x^2 - 96*x^3 + 18*x^4 + 27* x^5) + E^16*(-288*x^3 - 288*x^4 + 54*x^5 + 81*x^6) + E^8*(-288*x^4 - 288*x ^5 + 54*x^6 + 81*x^7))*Log[2 - x]^2 + (-128*x^3 - 224*x^4 - 72*x^5 + 54*x^ 6 + 27*x^7 + E^24*(-128 - 224*x - 72*x^2 + 54*x^3 + 27*x^4) + E^16*(-384*x - 672*x^2 - 216*x^3 + 162*x^4 + 81*x^5) + E^8*(-384*x^2 - 672*x^3 - 216*x ^4 + 162*x^5 + 81*x^6))*Log[2 - x]^3),x]
Output:
(4*x^2 + (16 + 13*x)*Log[2 - x])^2/((E^8 + x)^2*(x^2 + (4 + 3*x)*Log[2 - 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.
| \(\displaystyle \int \frac {-32 x^7+72 x^6+8 e^8 x^5+\left (-1014 x^4-1716 x^3+2752 x^2+e^8 \left (104 x^2-80 x-256\right )+7424 x+4096\right ) \log ^3(2-x)+\left (-312 x^6+266 x^5+800 x^4+e^8 \left (-8 x^5+42 x^4+32 x^3\right )\right ) \log (2-x)+\left (-988 x^5-456 x^4+3328 x^3+3072 x^2+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)}{x^{10}-2 x^9+e^8 \left (3 x^9-6 x^8\right )+e^{16} \left (3 x^8-6 x^7\right )+e^{24} \left (x^7-2 x^6\right )+\left (9 x^9-6 x^8-24 x^7+e^8 \left (27 x^8-18 x^7-72 x^6\right )+e^{16} \left (27 x^7-18 x^6-72 x^5\right )+e^{24} \left (9 x^6-6 x^5-24 x^4\right )\right ) \log (2-x)+\left (27 x^7+54 x^6-72 x^5-224 x^4-128 x^3+e^{24} \left (27 x^4+54 x^3-72 x^2-224 x-128\right )+e^{16} \left (81 x^5+162 x^4-216 x^3-672 x^2-384 x\right )+e^8 \left (81 x^6+162 x^5-216 x^4-672 x^3-384 x^2\right )\right ) \log ^3(2-x)+\left (27 x^8+18 x^7-96 x^6-96 x^5+e^8 \left (81 x^7+54 x^6-288 x^5-288 x^4\right )+e^{16} \left (81 x^6+54 x^5-288 x^4-288 x^3\right )+e^{24} \left (27 x^5+18 x^4-96 x^3-96 x^2\right )\right ) \log ^2(2-x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (4 x^2+(13 x+16) \log (2-x)\right ) \left (\left (x (4 x-9)-e^8\right ) x^3+(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)+(x-2) \left (26 x+e^8+32\right ) x^2 \log (2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (\left ((9-4 x) x+e^8\right ) x^3+(2-x) \left (26 x+e^8+32\right ) \log (2-x) x^2+(2-x) \left (39 x^2+96 x+4 \left (16-e^8\right )\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (\left ((9-4 x) x+e^8\right ) x^3+(2-x) \left (26 x+e^8+32\right ) \log (2-x) x^2+(2-x) \left (39 x^2+96 x+4 \left (16-e^8\right )\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {\left (4 x^2+(13 x+16) \log (2-x)\right ) \left (-\left (\left (x (4 x-9)-e^8\right ) x^3\right )-(x-2) \left (26 x+e^8+32\right ) \log (2-x) x^2-(x-2) \left (39 x^2+96 x-4 e^8+64\right ) \log ^2(2-x)\right )}{(2-x) \left (x+e^8\right )^3 \left (x^2+(3 x+4) \log (2-x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (3 x^3+11 x^2+8 x+16\right ) x^6}{(x-2) \left (x+e^8\right )^2 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^3}+\frac {\left (39 x^5+199 \left (1+\frac {42 e^8}{199}\right ) x^4+264 \left (1+\frac {197 e^8}{264}\right ) x^3+336 \left (1+\frac {16 e^8}{21}\right ) x^2+256 \left (1+\frac {21 e^8}{16}\right ) x+256 e^8\right ) x^3}{(2-x) \left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )^2}+\frac {\left (-39 x^3+\left (8+39 e^8\right ) x^2+16 \left (4+13 e^8\right ) x+192 e^8\right ) x^2}{\left (x+e^8\right )^3 (3 x+4)^3 \left (x^2+3 \log (2-x) x+4 \log (2-x)\right )}+\frac {(13 x+16) \left (39 x^2+96 x+4 \left (16-e^8\right )\right )}{\left (x+e^8\right )^3 (3 x+4)^3}\right )dx\) |
Input:
Int[(8*E^8*x^5 + 72*x^6 - 32*x^7 + (800*x^4 + 266*x^5 - 312*x^6 + E^8*(32* x^3 + 42*x^4 - 8*x^5))*Log[2 - x] + (3072*x^2 + 3328*x^3 - 456*x^4 - 988*x ^5 + E^8*(52*x^3 - 26*x^4))*Log[2 - x]^2 + (4096 + 7424*x + 2752*x^2 - 171 6*x^3 - 1014*x^4 + E^8*(-256 - 80*x + 104*x^2))*Log[2 - x]^3)/(-2*x^9 + x^ 10 + E^24*(-2*x^6 + x^7) + E^16*(-6*x^7 + 3*x^8) + E^8*(-6*x^8 + 3*x^9) + (-24*x^7 - 6*x^8 + 9*x^9 + E^24*(-24*x^4 - 6*x^5 + 9*x^6) + E^16*(-72*x^5 - 18*x^6 + 27*x^7) + E^8*(-72*x^6 - 18*x^7 + 27*x^8))*Log[2 - x] + (-96*x^ 5 - 96*x^6 + 18*x^7 + 27*x^8 + E^24*(-96*x^2 - 96*x^3 + 18*x^4 + 27*x^5) + E^16*(-288*x^3 - 288*x^4 + 54*x^5 + 81*x^6) + E^8*(-288*x^4 - 288*x^5 + 5 4*x^6 + 81*x^7))*Log[2 - x]^2 + (-128*x^3 - 224*x^4 - 72*x^5 + 54*x^6 + 27 *x^7 + E^24*(-128 - 224*x - 72*x^2 + 54*x^3 + 27*x^4) + E^16*(-384*x - 672 *x^2 - 216*x^3 + 162*x^4 + 81*x^5) + E^8*(-384*x^2 - 672*x^3 - 216*x^4 + 1 62*x^5 + 81*x^6))*Log[2 - x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(150\) vs. \(2(34)=68\).
Time = 212.13 (sec) , antiderivative size = 151, normalized size of antiderivative = 4.58
| method | result | size |
| risch | \(\frac {169 x^{2}+416 x +256}{9 x^{2} {\mathrm e}^{16}+24 x \,{\mathrm e}^{16}+18 \,{\mathrm e}^{8} x^{3}+16 \,{\mathrm e}^{16}+48 \,{\mathrm e}^{8} x^{2}+9 x^{4}+32 x \,{\mathrm e}^{8}+24 x^{3}+16 x^{2}}-\frac {\left (25 x^{3}+78 \ln \left (2-x \right ) x^{2}+32 x^{2}+200 x \ln \left (2-x \right )+128 \ln \left (2-x \right )\right ) x^{3}}{\left (x +{\mathrm e}^{8}\right )^{2} \left (x^{2}+3 x \ln \left (2-x \right )+4 \ln \left (2-x \right )\right )^{2} \left (9 x^{2}+24 x +16\right )}\) | \(151\) |
| derivativedivides | \(\frac {169 \ln \left (2-x \right )^{2} \left (2-x \right )^{2}-104 \ln \left (2-x \right ) \left (2-x \right )^{3}+16 \left (2-x \right )^{4}-1092 \ln \left (2-x \right )^{2} \left (2-x \right )+752 \ln \left (2-x \right ) \left (2-x \right )^{2}-128 \left (2-x \right )^{3}+1764 \ln \left (2-x \right )^{2}-1760 \ln \left (2-x \right ) \left (2-x \right )+384 \left (2-x \right )^{2}+1344 \ln \left (2-x \right )-768+512 x}{\left (-{\mathrm e}^{8+2 \ln \left (2-x \right )}+3 \ln \left (2-x \right ) {\mathrm e}^{8+\ln \left (2-x \right )}+\left (2-x \right )^{3}-3 \ln \left (2-x \right ) \left (2-x \right )^{2}+4 \,{\mathrm e}^{8+\ln \left (2-x \right )}-10 \,{\mathrm e}^{8} \ln \left (2-x \right )-6 \left (2-x \right )^{2}+16 \ln \left (2-x \right ) \left (2-x \right )-4 \,{\mathrm e}^{8}+16-12 x -20 \ln \left (2-x \right )\right )^{2}}\) | \(241\) |
| default | \(\frac {169 \ln \left (2-x \right )^{2} \left (2-x \right )^{2}-104 \ln \left (2-x \right ) \left (2-x \right )^{3}+16 \left (2-x \right )^{4}-1092 \ln \left (2-x \right )^{2} \left (2-x \right )+752 \ln \left (2-x \right ) \left (2-x \right )^{2}-128 \left (2-x \right )^{3}+1764 \ln \left (2-x \right )^{2}-1760 \ln \left (2-x \right ) \left (2-x \right )+384 \left (2-x \right )^{2}+1344 \ln \left (2-x \right )-768+512 x}{\left (-{\mathrm e}^{8+2 \ln \left (2-x \right )}+3 \ln \left (2-x \right ) {\mathrm e}^{8+\ln \left (2-x \right )}+\left (2-x \right )^{3}-3 \ln \left (2-x \right ) \left (2-x \right )^{2}+4 \,{\mathrm e}^{8+\ln \left (2-x \right )}-10 \,{\mathrm e}^{8} \ln \left (2-x \right )-6 \left (2-x \right )^{2}+16 \ln \left (2-x \right ) \left (2-x \right )-4 \,{\mathrm e}^{8}+16-12 x -20 \ln \left (2-x \right )\right )^{2}}\) | \(241\) |
| parallelrisch | \(-\frac {\left (73728 \ln \left (2-x \right ) x^{4}+147456 \ln \left (2-x \right )^{2} x^{2}+18432 \,{\mathrm e}^{8} x^{5}+442368 \,{\mathrm e}^{8} \ln \left (2-x \right )^{2} x^{2}-18432 \,{\mathrm e}^{16} \ln \left (2-x \right )^{2} x +9216 x^{6}+221184 x^{3} \ln \left (2-x \right )^{2}+82944 x^{4} \ln \left (2-x \right )^{2}+55296 x^{5} \ln \left (2-x \right )+294912 \ln \left (2-x \right )^{2} {\mathrm e}^{8} x -14400 \ln \left (2-x \right )^{2} {\mathrm e}^{16} x^{2}-4608 \ln \left (2-x \right ) {\mathrm e}^{16} x^{3}+165888 \ln \left (2-x \right )^{2} {\mathrm e}^{8} x^{3}+110592 \ln \left (2-x \right ) {\mathrm e}^{8} x^{4}+147456 \ln \left (2-x \right ) {\mathrm e}^{8} x^{3}\right ) {\mathrm e}^{-16}}{576 \left ({\mathrm e}^{16} x^{4}+6 \ln \left (2-x \right ) {\mathrm e}^{16} x^{3}+9 \ln \left (2-x \right )^{2} {\mathrm e}^{16} x^{2}+8 \,{\mathrm e}^{16} x^{2} \ln \left (2-x \right )+24 \,{\mathrm e}^{16} \ln \left (2-x \right )^{2} x +2 \,{\mathrm e}^{8} x^{5}+12 \ln \left (2-x \right ) {\mathrm e}^{8} x^{4}+18 \ln \left (2-x \right )^{2} {\mathrm e}^{8} x^{3}+16 \,{\mathrm e}^{16} \ln \left (2-x \right )^{2}+16 \ln \left (2-x \right ) {\mathrm e}^{8} x^{3}+48 \,{\mathrm e}^{8} \ln \left (2-x \right )^{2} x^{2}+x^{6}+6 x^{5} \ln \left (2-x \right )+9 x^{4} \ln \left (2-x \right )^{2}+32 \ln \left (2-x \right )^{2} {\mathrm e}^{8} x +8 \ln \left (2-x \right ) x^{4}+24 x^{3} \ln \left (2-x \right )^{2}+16 \ln \left (2-x \right )^{2} x^{2}\right )}\) | \(448\) |
Input:
int((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+4096)* ln(2-x)^3+((-26*x^4+52*x^3)*exp(4)^2-988*x^5-456*x^4+3328*x^3+3072*x^2)*ln (2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4)*ln(2-x)+ 8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)*exp(4)^6+ (81*x^5+162*x^4-216*x^3-672*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-216*x^4-67 2*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)*ln(2-x)^3+(( 27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288*x^3)*exp( 4)^4+(81*x^7+54*x^6-288*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x^6-96*x^5) *ln(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-72*x^5)*exp(4)^4+ (27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*ln(2-x)+(x^7-2*x^6)*ex p(4)^6+(3*x^8-6*x^7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^9),x,method= _RETURNVERBOSE)
Output:
(169*x^2+416*x+256)/(9*x^2*exp(16)+24*x*exp(16)+18*exp(8)*x^3+16*exp(16)+4 8*exp(8)*x^2+9*x^4+32*x*exp(8)+24*x^3+16*x^2)-(25*x^3+78*ln(2-x)*x^2+32*x^ 2+200*x*ln(2-x)+128*ln(2-x))*x^3/(x+exp(8))^2/(x^2+3*x*ln(2-x)+4*ln(2-x))^ 2/(9*x^2+24*x+16)
Leaf count of result is larger than twice the leaf count of optimal. 168 vs. \(2 (32) = 64\).
Time = 0.10 (sec) , antiderivative size = 168, normalized size of antiderivative = 5.09 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\frac {16 \, x^{4} + {\left (169 \, x^{2} + 416 \, x + 256\right )} \log \left (-x + 2\right )^{2} + 8 \, {\left (13 \, x^{3} + 16 \, x^{2}\right )} \log \left (-x + 2\right )}{x^{6} + 2 \, x^{5} e^{8} + x^{4} e^{16} + {\left (9 \, x^{4} + 24 \, x^{3} + 16 \, x^{2} + {\left (9 \, x^{2} + 24 \, x + 16\right )} e^{16} + 2 \, {\left (9 \, x^{3} + 24 \, x^{2} + 16 \, x\right )} e^{8}\right )} \log \left (-x + 2\right )^{2} + 2 \, {\left (3 \, x^{5} + 4 \, x^{4} + {\left (3 \, x^{3} + 4 \, x^{2}\right )} e^{16} + 2 \, {\left (3 \, x^{4} + 4 \, x^{3}\right )} e^{8}\right )} \log \left (-x + 2\right )} \] Input:
integrate((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+ 4096)*log(2-x)^3+((-26*x^4+52*x^3)*exp(4)^2-988*x^5-456*x^4+3328*x^3+3072* x^2)*log(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4)* log(2-x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)* exp(4)^6+(81*x^5+162*x^4-216*x^3-672*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-2 16*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)*log (2-x)^3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288 *x^3)*exp(4)^4+(81*x^7+54*x^6-288*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x ^6-96*x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-72*x^5 )*exp(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x ^7-2*x^6)*exp(4)^6+(3*x^8-6*x^7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^ 9),x, algorithm="fricas")
Output:
(16*x^4 + (169*x^2 + 416*x + 256)*log(-x + 2)^2 + 8*(13*x^3 + 16*x^2)*log( -x + 2))/(x^6 + 2*x^5*e^8 + x^4*e^16 + (9*x^4 + 24*x^3 + 16*x^2 + (9*x^2 + 24*x + 16)*e^16 + 2*(9*x^3 + 24*x^2 + 16*x)*e^8)*log(-x + 2)^2 + 2*(3*x^5 + 4*x^4 + (3*x^3 + 4*x^2)*e^16 + 2*(3*x^4 + 4*x^3)*e^8)*log(-x + 2))
Leaf count of result is larger than twice the leaf count of optimal. 360 vs. \(2 (24) = 48\).
Time = 2.21 (sec) , antiderivative size = 360, normalized size of antiderivative = 10.91 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=- \frac {- 169 x^{2} - 416 x - 256}{9 x^{4} + x^{3} \cdot \left (24 + 18 e^{8}\right ) + x^{2} \cdot \left (16 + 48 e^{8} + 9 e^{16}\right ) + x \left (32 e^{8} + 24 e^{16}\right ) + 16 e^{16}} + \frac {- 25 x^{6} - 32 x^{5} + \left (- 78 x^{5} - 200 x^{4} - 128 x^{3}\right ) \log {\left (2 - x \right )}}{9 x^{8} + 24 x^{7} + 18 x^{7} e^{8} + 16 x^{6} + 48 x^{6} e^{8} + 9 x^{6} e^{16} + 32 x^{5} e^{8} + 24 x^{5} e^{16} + 16 x^{4} e^{16} + \left (54 x^{7} + 216 x^{6} + 108 x^{6} e^{8} + 288 x^{5} + 432 x^{5} e^{8} + 54 x^{5} e^{16} + 128 x^{4} + 576 x^{4} e^{8} + 216 x^{4} e^{16} + 256 x^{3} e^{8} + 288 x^{3} e^{16} + 128 x^{2} e^{16}\right ) \log {\left (2 - x \right )} + \left (81 x^{6} + 432 x^{5} + 162 x^{5} e^{8} + 864 x^{4} + 864 x^{4} e^{8} + 81 x^{4} e^{16} + 768 x^{3} + 1728 x^{3} e^{8} + 432 x^{3} e^{16} + 256 x^{2} + 1536 x^{2} e^{8} + 864 x^{2} e^{16} + 512 x e^{8} + 768 x e^{16} + 256 e^{16}\right ) \log {\left (2 - x \right )}^{2}} \] Input:
integrate((((104*x**2-80*x-256)*exp(4)**2-1014*x**4-1716*x**3+2752*x**2+74 24*x+4096)*ln(2-x)**3+((-26*x**4+52*x**3)*exp(4)**2-988*x**5-456*x**4+3328 *x**3+3072*x**2)*ln(2-x)**2+((-8*x**5+42*x**4+32*x**3)*exp(4)**2-312*x**6+ 266*x**5+800*x**4)*ln(2-x)+8*x**5*exp(4)**2-32*x**7+72*x**6)/(((27*x**4+54 *x**3-72*x**2-224*x-128)*exp(4)**6+(81*x**5+162*x**4-216*x**3-672*x**2-384 *x)*exp(4)**4+(81*x**6+162*x**5-216*x**4-672*x**3-384*x**2)*exp(4)**2+27*x **7+54*x**6-72*x**5-224*x**4-128*x**3)*ln(2-x)**3+((27*x**5+18*x**4-96*x** 3-96*x**2)*exp(4)**6+(81*x**6+54*x**5-288*x**4-288*x**3)*exp(4)**4+(81*x** 7+54*x**6-288*x**5-288*x**4)*exp(4)**2+27*x**8+18*x**7-96*x**6-96*x**5)*ln (2-x)**2+((9*x**6-6*x**5-24*x**4)*exp(4)**6+(27*x**7-18*x**6-72*x**5)*exp( 4)**4+(27*x**8-18*x**7-72*x**6)*exp(4)**2+9*x**9-6*x**8-24*x**7)*ln(2-x)+( x**7-2*x**6)*exp(4)**6+(3*x**8-6*x**7)*exp(4)**4+(3*x**9-6*x**8)*exp(4)**2 +x**10-2*x**9),x)
Output:
-(-169*x**2 - 416*x - 256)/(9*x**4 + x**3*(24 + 18*exp(8)) + x**2*(16 + 48 *exp(8) + 9*exp(16)) + x*(32*exp(8) + 24*exp(16)) + 16*exp(16)) + (-25*x** 6 - 32*x**5 + (-78*x**5 - 200*x**4 - 128*x**3)*log(2 - x))/(9*x**8 + 24*x* *7 + 18*x**7*exp(8) + 16*x**6 + 48*x**6*exp(8) + 9*x**6*exp(16) + 32*x**5* exp(8) + 24*x**5*exp(16) + 16*x**4*exp(16) + (54*x**7 + 216*x**6 + 108*x** 6*exp(8) + 288*x**5 + 432*x**5*exp(8) + 54*x**5*exp(16) + 128*x**4 + 576*x **4*exp(8) + 216*x**4*exp(16) + 256*x**3*exp(8) + 288*x**3*exp(16) + 128*x **2*exp(16))*log(2 - x) + (81*x**6 + 432*x**5 + 162*x**5*exp(8) + 864*x**4 + 864*x**4*exp(8) + 81*x**4*exp(16) + 768*x**3 + 1728*x**3*exp(8) + 432*x **3*exp(16) + 256*x**2 + 1536*x**2*exp(8) + 864*x**2*exp(16) + 512*x*exp(8 ) + 768*x*exp(16) + 256*exp(16))*log(2 - x)**2)
Leaf count of result is larger than twice the leaf count of optimal. 165 vs. \(2 (32) = 64\).
Time = 0.34 (sec) , antiderivative size = 165, normalized size of antiderivative = 5.00 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\frac {16 \, x^{4} + {\left (169 \, x^{2} + 416 \, x + 256\right )} \log \left (-x + 2\right )^{2} + 8 \, {\left (13 \, x^{3} + 16 \, x^{2}\right )} \log \left (-x + 2\right )}{x^{6} + 2 \, x^{5} e^{8} + x^{4} e^{16} + {\left (9 \, x^{4} + 6 \, x^{3} {\left (3 \, e^{8} + 4\right )} + x^{2} {\left (9 \, e^{16} + 48 \, e^{8} + 16\right )} + 8 \, x {\left (3 \, e^{16} + 4 \, e^{8}\right )} + 16 \, e^{16}\right )} \log \left (-x + 2\right )^{2} + 2 \, {\left (3 \, x^{5} + 2 \, x^{4} {\left (3 \, e^{8} + 2\right )} + x^{3} {\left (3 \, e^{16} + 8 \, e^{8}\right )} + 4 \, x^{2} e^{16}\right )} \log \left (-x + 2\right )} \] Input:
integrate((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+ 4096)*log(2-x)^3+((-26*x^4+52*x^3)*exp(4)^2-988*x^5-456*x^4+3328*x^3+3072* x^2)*log(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4)* log(2-x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)* exp(4)^6+(81*x^5+162*x^4-216*x^3-672*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-2 16*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)*log (2-x)^3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288 *x^3)*exp(4)^4+(81*x^7+54*x^6-288*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x ^6-96*x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-72*x^5 )*exp(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x ^7-2*x^6)*exp(4)^6+(3*x^8-6*x^7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^ 9),x, algorithm="maxima")
Output:
(16*x^4 + (169*x^2 + 416*x + 256)*log(-x + 2)^2 + 8*(13*x^3 + 16*x^2)*log( -x + 2))/(x^6 + 2*x^5*e^8 + x^4*e^16 + (9*x^4 + 6*x^3*(3*e^8 + 4) + x^2*(9 *e^16 + 48*e^8 + 16) + 8*x*(3*e^16 + 4*e^8) + 16*e^16)*log(-x + 2)^2 + 2*( 3*x^5 + 2*x^4*(3*e^8 + 2) + x^3*(3*e^16 + 8*e^8) + 4*x^2*e^16)*log(-x + 2) )
Leaf count of result is larger than twice the leaf count of optimal. 4600 vs. \(2 (32) = 64\).
Time = 0.81 (sec) , antiderivative size = 4600, normalized size of antiderivative = 139.39 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\text {Too large to display} \] Input:
integrate((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+ 4096)*log(2-x)^3+((-26*x^4+52*x^3)*exp(4)^2-988*x^5-456*x^4+3328*x^3+3072* x^2)*log(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4)* log(2-x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)* exp(4)^6+(81*x^5+162*x^4-216*x^3-672*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-2 16*x^4-672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)*log (2-x)^3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288 *x^3)*exp(4)^4+(81*x^7+54*x^6-288*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x ^6-96*x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-72*x^5 )*exp(4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x ^7-2*x^6)*exp(4)^6+(3*x^8-6*x^7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^ 9),x, algorithm="giac")
Output:
-(2808*(x - 2)^6*e^16*log(3*x + 4) - 3168*(x - 2)^6*e^8*log(3*x + 4) + 168 48*(x - 2)^5*e^16*log(3*x + 4)*log(-x + 2) - 19008*(x - 2)^5*e^8*log(3*x + 4)*log(-x + 2) + 25272*(x - 2)^4*e^16*log(3*x + 4)*log(-x + 2)^2 - 28512* (x - 2)^4*e^8*log(3*x + 4)*log(-x + 2)^2 - 2808*(x - 2)^6*e^16*log(-3*x - 4) + 3168*(x - 2)^6*e^8*log(-3*x - 4) - 16848*(x - 2)^5*e^16*log(-x + 2)*l og(-3*x - 4) + 19008*(x - 2)^5*e^8*log(-x + 2)*log(-3*x - 4) - 25272*(x - 2)^4*e^16*log(-x + 2)^2*log(-3*x - 4) + 28512*(x - 2)^4*e^8*log(-x + 2)^2* log(-3*x - 4) + 5616*(x - 2)^5*e^24*log(3*x + 4) + 27360*(x - 2)^5*e^16*lo g(3*x + 4) - 38016*(x - 2)^5*e^8*log(3*x + 4) + 33696*(x - 2)^4*e^24*log(3 *x + 4)*log(-x + 2) + 152928*(x - 2)^4*e^16*log(3*x + 4)*log(-x + 2) - 215 424*(x - 2)^4*e^8*log(3*x + 4)*log(-x + 2) + 50544*(x - 2)^3*e^24*log(3*x + 4)*log(-x + 2)^2 + 212544*(x - 2)^3*e^16*log(3*x + 4)*log(-x + 2)^2 - 30 4128*(x - 2)^3*e^8*log(3*x + 4)*log(-x + 2)^2 - 5616*(x - 2)^5*e^24*log(-3 *x - 4) - 27360*(x - 2)^5*e^16*log(-3*x - 4) + 38016*(x - 2)^5*e^8*log(-3* x - 4) - 33696*(x - 2)^4*e^24*log(-x + 2)*log(-3*x - 4) - 152928*(x - 2)^4 *e^16*log(-x + 2)*log(-3*x - 4) + 215424*(x - 2)^4*e^8*log(-x + 2)*log(-3* x - 4) - 50544*(x - 2)^3*e^24*log(-x + 2)^2*log(-3*x - 4) - 212544*(x - 2) ^3*e^16*log(-x + 2)^2*log(-3*x - 4) + 304128*(x - 2)^3*e^8*log(-x + 2)^2*l og(-3*x - 4) + 2808*(x - 2)^4*e^32*log(3*x + 4) + 52992*(x - 2)^4*e^24*log (3*x + 4) + 105120*(x - 2)^4*e^16*log(3*x + 4) - 190080*(x - 2)^4*e^8*l...
Time = 3.39 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.67 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\frac {{\left (16\,\ln \left (2-x\right )+13\,x\,\ln \left (2-x\right )+4\,x^2\right )}^2}{{\left (x+{\mathrm {e}}^8\right )}^2\,{\left (4\,\ln \left (2-x\right )+3\,x\,\ln \left (2-x\right )+x^2\right )}^2} \] Input:
int(-(log(2 - x)^2*(exp(8)*(52*x^3 - 26*x^4) + 3072*x^2 + 3328*x^3 - 456*x ^4 - 988*x^5) + log(2 - x)^3*(7424*x - exp(8)*(80*x - 104*x^2 + 256) + 275 2*x^2 - 1716*x^3 - 1014*x^4 + 4096) + 8*x^5*exp(8) + log(2 - x)*(exp(8)*(3 2*x^3 + 42*x^4 - 8*x^5) + 800*x^4 + 266*x^5 - 312*x^6) + 72*x^6 - 32*x^7)/ (log(2 - x)*(exp(24)*(24*x^4 + 6*x^5 - 9*x^6) + exp(8)*(72*x^6 + 18*x^7 - 27*x^8) + exp(16)*(72*x^5 + 18*x^6 - 27*x^7) + 24*x^7 + 6*x^8 - 9*x^9) + l og(2 - x)^3*(exp(8)*(384*x^2 + 672*x^3 + 216*x^4 - 162*x^5 - 81*x^6) + exp (24)*(224*x + 72*x^2 - 54*x^3 - 27*x^4 + 128) + exp(16)*(384*x + 672*x^2 + 216*x^3 - 162*x^4 - 81*x^5) + 128*x^3 + 224*x^4 + 72*x^5 - 54*x^6 - 27*x^ 7) + exp(8)*(6*x^8 - 3*x^9) + exp(16)*(6*x^7 - 3*x^8) + exp(24)*(2*x^6 - x ^7) + log(2 - x)^2*(96*x^5 + 96*x^6 - 18*x^7 - 27*x^8 + exp(24)*(96*x^2 + 96*x^3 - 18*x^4 - 27*x^5) + exp(8)*(288*x^4 + 288*x^5 - 54*x^6 - 81*x^7) + exp(16)*(288*x^3 + 288*x^4 - 54*x^5 - 81*x^6)) + 2*x^9 - x^10),x)
Output:
(16*log(2 - x) + 13*x*log(2 - x) + 4*x^2)^2/((x + exp(8))^2*(4*log(2 - x) + 3*x*log(2 - x) + x^2)^2)
Time = 0.74 (sec) , antiderivative size = 290, normalized size of antiderivative = 8.79 \[ \int \frac {8 e^8 x^5+72 x^6-32 x^7+\left (800 x^4+266 x^5-312 x^6+e^8 \left (32 x^3+42 x^4-8 x^5\right )\right ) \log (2-x)+\left (3072 x^2+3328 x^3-456 x^4-988 x^5+e^8 \left (52 x^3-26 x^4\right )\right ) \log ^2(2-x)+\left (4096+7424 x+2752 x^2-1716 x^3-1014 x^4+e^8 \left (-256-80 x+104 x^2\right )\right ) \log ^3(2-x)}{-2 x^9+x^{10}+e^{24} \left (-2 x^6+x^7\right )+e^{16} \left (-6 x^7+3 x^8\right )+e^8 \left (-6 x^8+3 x^9\right )+\left (-24 x^7-6 x^8+9 x^9+e^{24} \left (-24 x^4-6 x^5+9 x^6\right )+e^{16} \left (-72 x^5-18 x^6+27 x^7\right )+e^8 \left (-72 x^6-18 x^7+27 x^8\right )\right ) \log (2-x)+\left (-96 x^5-96 x^6+18 x^7+27 x^8+e^{24} \left (-96 x^2-96 x^3+18 x^4+27 x^5\right )+e^{16} \left (-288 x^3-288 x^4+54 x^5+81 x^6\right )+e^8 \left (-288 x^4-288 x^5+54 x^6+81 x^7\right )\right ) \log ^2(2-x)+\left (-128 x^3-224 x^4-72 x^5+54 x^6+27 x^7+e^{24} \left (-128-224 x-72 x^2+54 x^3+27 x^4\right )+e^{16} \left (-384 x-672 x^2-216 x^3+162 x^4+81 x^5\right )+e^8 \left (-384 x^2-672 x^3-216 x^4+162 x^5+81 x^6\right )\right ) \log ^3(2-x)} \, dx=\frac {169 \mathrm {log}\left (-x +2\right )^{2} x^{2}+416 \mathrm {log}\left (-x +2\right )^{2} x +256 \mathrm {log}\left (-x +2\right )^{2}+104 \,\mathrm {log}\left (-x +2\right ) x^{3}+128 \,\mathrm {log}\left (-x +2\right ) x^{2}+16 x^{4}}{9 \mathrm {log}\left (-x +2\right )^{2} e^{16} x^{2}+24 \mathrm {log}\left (-x +2\right )^{2} e^{16} x +16 \mathrm {log}\left (-x +2\right )^{2} e^{16}+18 \mathrm {log}\left (-x +2\right )^{2} e^{8} x^{3}+48 \mathrm {log}\left (-x +2\right )^{2} e^{8} x^{2}+32 \mathrm {log}\left (-x +2\right )^{2} e^{8} x +9 \mathrm {log}\left (-x +2\right )^{2} x^{4}+24 \mathrm {log}\left (-x +2\right )^{2} x^{3}+16 \mathrm {log}\left (-x +2\right )^{2} x^{2}+6 \,\mathrm {log}\left (-x +2\right ) e^{16} x^{3}+8 \,\mathrm {log}\left (-x +2\right ) e^{16} x^{2}+12 \,\mathrm {log}\left (-x +2\right ) e^{8} x^{4}+16 \,\mathrm {log}\left (-x +2\right ) e^{8} x^{3}+6 \,\mathrm {log}\left (-x +2\right ) x^{5}+8 \,\mathrm {log}\left (-x +2\right ) x^{4}+e^{16} x^{4}+2 e^{8} x^{5}+x^{6}} \] Input:
int((((104*x^2-80*x-256)*exp(4)^2-1014*x^4-1716*x^3+2752*x^2+7424*x+4096)* log(2-x)^3+((-26*x^4+52*x^3)*exp(4)^2-988*x^5-456*x^4+3328*x^3+3072*x^2)*l og(2-x)^2+((-8*x^5+42*x^4+32*x^3)*exp(4)^2-312*x^6+266*x^5+800*x^4)*log(2- x)+8*x^5*exp(4)^2-32*x^7+72*x^6)/(((27*x^4+54*x^3-72*x^2-224*x-128)*exp(4) ^6+(81*x^5+162*x^4-216*x^3-672*x^2-384*x)*exp(4)^4+(81*x^6+162*x^5-216*x^4 -672*x^3-384*x^2)*exp(4)^2+27*x^7+54*x^6-72*x^5-224*x^4-128*x^3)*log(2-x)^ 3+((27*x^5+18*x^4-96*x^3-96*x^2)*exp(4)^6+(81*x^6+54*x^5-288*x^4-288*x^3)* exp(4)^4+(81*x^7+54*x^6-288*x^5-288*x^4)*exp(4)^2+27*x^8+18*x^7-96*x^6-96* x^5)*log(2-x)^2+((9*x^6-6*x^5-24*x^4)*exp(4)^6+(27*x^7-18*x^6-72*x^5)*exp( 4)^4+(27*x^8-18*x^7-72*x^6)*exp(4)^2+9*x^9-6*x^8-24*x^7)*log(2-x)+(x^7-2*x ^6)*exp(4)^6+(3*x^8-6*x^7)*exp(4)^4+(3*x^9-6*x^8)*exp(4)^2+x^10-2*x^9),x)
Output:
(169*log( - x + 2)**2*x**2 + 416*log( - x + 2)**2*x + 256*log( - x + 2)**2 + 104*log( - x + 2)*x**3 + 128*log( - x + 2)*x**2 + 16*x**4)/(9*log( - x + 2)**2*e**16*x**2 + 24*log( - x + 2)**2*e**16*x + 16*log( - x + 2)**2*e** 16 + 18*log( - x + 2)**2*e**8*x**3 + 48*log( - x + 2)**2*e**8*x**2 + 32*lo g( - x + 2)**2*e**8*x + 9*log( - x + 2)**2*x**4 + 24*log( - x + 2)**2*x**3 + 16*log( - x + 2)**2*x**2 + 6*log( - x + 2)*e**16*x**3 + 8*log( - x + 2) *e**16*x**2 + 12*log( - x + 2)*e**8*x**4 + 16*log( - x + 2)*e**8*x**3 + 6* log( - x + 2)*x**5 + 8*log( - x + 2)*x**4 + e**16*x**4 + 2*e**8*x**5 + x** 6)