Integrand size = 427, antiderivative size = 32 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=e^{-1+e^{4 x} (-5+x)-\frac {1}{x^2 \left (3-(-1+x)^4 x^2\right )^2}} \] Output:
exp(exp(4*x)*(-5+x)-1/x^2/(3-(-1+x)^4*x^2)^2-1)
Leaf count is larger than twice the leaf count of optimal. \(217\) vs. \(2(32)=64\).
Time = 0.64 (sec) , antiderivative size = 217, normalized size of antiderivative = 6.78 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=e^{\frac {-1-9 \left (1+5 e^{4 x}\right ) x^2+9 e^{4 x} x^3+6 \left (1+5 e^{4 x}\right ) x^4-6 \left (4+21 e^{4 x}\right ) x^5+\left (35+199 e^{4 x}\right ) x^6-\left (16+115 e^{4 x}\right ) x^7-2 \left (11+47 e^{4 x}\right ) x^8+\left (56+302 e^{4 x}\right ) x^9-14 \left (5+29 e^{4 x}\right ) x^{10}+14 \left (4+25 e^{4 x}\right ) x^{11}-28 \left (1+7 e^{4 x}\right ) x^{12}+\left (8+68 e^{4 x}\right ) x^{13}-\left (1+13 e^{4 x}\right ) x^{14}+e^{4 x} x^{15}}{x^2 \left (-3+x^2-4 x^3+6 x^4-4 x^5+x^6\right )^2}} \] Input:
Integrate[(E^((-1 - 9*x^2 + 6*x^4 - 24*x^5 + 35*x^6 - 16*x^7 - 22*x^8 + 56 *x^9 - 70*x^10 + 56*x^11 - 28*x^12 + 8*x^13 - x^14 + E^(4*x)*(-45*x^2 + 9* x^3 + 30*x^4 - 126*x^5 + 199*x^6 - 115*x^7 - 94*x^8 + 302*x^9 - 406*x^10 + 350*x^11 - 196*x^12 + 68*x^13 - 13*x^14 + x^15))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*(-6 + 6*x^2 - 32*x^3 + 60*x^4 - 48*x^5 + 14*x^6 + E^(4*x)*(513*x ^3 - 108*x^4 - 513*x^5 + 2160*x^6 - 3339*x^7 + 1296*x^8 + 4112*x^9 - 10244 *x^10 + 12684*x^11 - 7652*x^12 - 3481*x^13 + 14652*x^14 - 20265*x^15 + 187 08*x^16 - 12573*x^17 + 6160*x^18 - 2134*x^19 + 492*x^20 - 67*x^21 + 4*x^22 )))/(-27*x^3 + 27*x^5 - 108*x^6 + 153*x^7 - 36*x^8 - 224*x^9 + 492*x^10 - 564*x^11 + 284*x^12 + 243*x^13 - 720*x^14 + 915*x^15 - 792*x^16 + 495*x^17 - 220*x^18 + 66*x^19 - 12*x^20 + x^21),x]
Output:
E^((-1 - 9*(1 + 5*E^(4*x))*x^2 + 9*E^(4*x)*x^3 + 6*(1 + 5*E^(4*x))*x^4 - 6 *(4 + 21*E^(4*x))*x^5 + (35 + 199*E^(4*x))*x^6 - (16 + 115*E^(4*x))*x^7 - 2*(11 + 47*E^(4*x))*x^8 + (56 + 302*E^(4*x))*x^9 - 14*(5 + 29*E^(4*x))*x^1 0 + 14*(4 + 25*E^(4*x))*x^11 - 28*(1 + 7*E^(4*x))*x^12 + (8 + 68*E^(4*x))* x^13 - (1 + 13*E^(4*x))*x^14 + E^(4*x)*x^15)/(x^2*(-3 + x^2 - 4*x^3 + 6*x^ 4 - 4*x^5 + x^6)^2))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (14 x^6-48 x^5+60 x^4-32 x^3+6 x^2+e^{4 x} \left (4 x^{22}-67 x^{21}+492 x^{20}-2134 x^{19}+6160 x^{18}-12573 x^{17}+18708 x^{16}-20265 x^{15}+14652 x^{14}-3481 x^{13}-7652 x^{12}+12684 x^{11}-10244 x^{10}+4112 x^9+1296 x^8-3339 x^7+2160 x^6-513 x^5-108 x^4+513 x^3\right )-6\right ) \exp \left (\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^{14}-8 x^{13}+28 x^{12}-56 x^{11}+70 x^{10}-56 x^9+22 x^8+16 x^7-35 x^6+24 x^5-6 x^4+9 x^2}\right )}{x^{21}-12 x^{20}+66 x^{19}-220 x^{18}+495 x^{17}-792 x^{16}+915 x^{15}-720 x^{14}+243 x^{13}+284 x^{12}-564 x^{11}+492 x^{10}-224 x^9-36 x^8+153 x^7-108 x^6+27 x^5-27 x^3} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (14 x^6-48 x^5+60 x^4-32 x^3+6 x^2+e^{4 x} \left (4 x^{22}-67 x^{21}+492 x^{20}-2134 x^{19}+6160 x^{18}-12573 x^{17}+18708 x^{16}-20265 x^{15}+14652 x^{14}-3481 x^{13}-7652 x^{12}+12684 x^{11}-10244 x^{10}+4112 x^9+1296 x^8-3339 x^7+2160 x^6-513 x^5-108 x^4+513 x^3\right )-6\right ) \exp \left (\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^{14}-8 x^{13}+28 x^{12}-56 x^{11}+70 x^{10}-56 x^9+22 x^8+16 x^7-35 x^6+24 x^5-6 x^4+9 x^2}\right )}{x^3 \left (x^{18}-12 x^{17}+66 x^{16}-220 x^{15}+495 x^{14}-792 x^{13}+915 x^{12}-720 x^{11}+243 x^{10}+284 x^9-564 x^8+492 x^7-224 x^6-36 x^5+153 x^4-108 x^3+27 x^2-27\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {\left (14 x^6-48 x^5+60 x^4-32 x^3+6 x^2+e^{4 x} \left (4 x^{22}-67 x^{21}+492 x^{20}-2134 x^{19}+6160 x^{18}-12573 x^{17}+18708 x^{16}-20265 x^{15}+14652 x^{14}-3481 x^{13}-7652 x^{12}+12684 x^{11}-10244 x^{10}+4112 x^9+1296 x^8-3339 x^7+2160 x^6-513 x^5-108 x^4+513 x^3\right )-6\right ) \exp \left (\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^{14}-8 x^{13}+28 x^{12}-56 x^{11}+70 x^{10}-56 x^9+22 x^8+16 x^7-35 x^6+24 x^5-6 x^4+9 x^2}\right )}{x^3 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-14 x^6+48 x^5-60 x^4+32 x^3-6 x^2-e^{4 x} \left (4 x^{22}-67 x^{21}+492 x^{20}-2134 x^{19}+6160 x^{18}-12573 x^{17}+18708 x^{16}-20265 x^{15}+14652 x^{14}-3481 x^{13}-7652 x^{12}+12684 x^{11}-10244 x^{10}+4112 x^9+1296 x^8-3339 x^7+2160 x^6-513 x^5-108 x^4+513 x^3\right )+6\right ) \exp \left (\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}+56 x^9-22 x^8-16 x^7+35 x^6-24 x^5+6 x^4-9 x^2+e^{4 x} \left (x^{15}-13 x^{14}+68 x^{13}-196 x^{12}+350 x^{11}-406 x^{10}+302 x^9-94 x^8-115 x^7+199 x^6-126 x^5+30 x^4+9 x^3-45 x^2\right )-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-4 e^{4 x} x^{22}+67 e^{4 x} x^{21}-492 e^{4 x} x^{20}+2134 e^{4 x} x^{19}-6160 e^{4 x} x^{18}+12573 e^{4 x} x^{17}-18708 e^{4 x} x^{16}+20265 e^{4 x} x^{15}-14652 e^{4 x} x^{14}+3481 e^{4 x} x^{13}+7652 e^{4 x} x^{12}-12684 e^{4 x} x^{11}+10244 e^{4 x} x^{10}-4112 e^{4 x} x^9-1296 e^{4 x} x^8+3339 e^{4 x} x^7-2 \left (1080 e^{4 x}+7\right ) x^6+3 \left (171 e^{4 x}+16\right ) x^5+12 \left (9 e^{4 x}-5\right ) x^4-\left (513 e^{4 x}-32\right ) x^3-6 x^2+6\right ) \exp \left (\frac {e^{4 x} x^{15}-\left (13 e^{4 x}+1\right ) x^{14}+\left (68 e^{4 x}+8\right ) x^{13}-28 \left (7 e^{4 x}+1\right ) x^{12}+14 \left (25 e^{4 x}+4\right ) x^{11}-14 \left (29 e^{4 x}+5\right ) x^{10}+\left (302 e^{4 x}+56\right ) x^9-2 \left (47 e^{4 x}+11\right ) x^8-\left (115 e^{4 x}+16\right ) x^7+\left (199 e^{4 x}+35\right ) x^6-6 \left (21 e^{4 x}+4\right ) x^5+6 \left (5 e^{4 x}+1\right ) x^4+9 e^{4 x} x^3-9 \left (5 e^{4 x}+1\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}\right )}{x^3 \left (-x^6+4 x^5-6 x^4+4 x^3-x^2+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {14 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^3}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}-\frac {48 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x^2}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {60 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}} x}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+e^{4 x+\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2 x^2}} (4 x-19)-\frac {32 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3}+\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x}-\frac {6 e^{\frac {e^{4 x} x^{15}-\left (1+13 e^{4 x}\right ) x^{14}+\left (8+68 e^{4 x}\right ) x^{13}-28 \left (1+7 e^{4 x}\right ) x^{12}+14 \left (4+25 e^{4 x}\right ) x^{11}-14 \left (5+29 e^{4 x}\right ) x^{10}+\left (56+302 e^{4 x}\right ) x^9-2 \left (11+47 e^{4 x}\right ) x^8-\left (16+115 e^{4 x}\right ) x^7+\left (35+199 e^{4 x}\right ) x^6-6 \left (4+21 e^{4 x}\right ) x^5+6 \left (1+5 e^{4 x}\right ) x^4+9 e^{4 x} x^3-9 \left (1+5 e^{4 x}\right ) x^2-1}{x^2 \left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^2}}}{\left (x^6-4 x^5+6 x^4-4 x^3+x^2-3\right )^3 x^3}\right )dx\) |
Input:
Int[(E^((-1 - 9*x^2 + 6*x^4 - 24*x^5 + 35*x^6 - 16*x^7 - 22*x^8 + 56*x^9 - 70*x^10 + 56*x^11 - 28*x^12 + 8*x^13 - x^14 + E^(4*x)*(-45*x^2 + 9*x^3 + 30*x^4 - 126*x^5 + 199*x^6 - 115*x^7 - 94*x^8 + 302*x^9 - 406*x^10 + 350*x ^11 - 196*x^12 + 68*x^13 - 13*x^14 + x^15))/(9*x^2 - 6*x^4 + 24*x^5 - 35*x ^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^1 4))*(-6 + 6*x^2 - 32*x^3 + 60*x^4 - 48*x^5 + 14*x^6 + E^(4*x)*(513*x^3 - 1 08*x^4 - 513*x^5 + 2160*x^6 - 3339*x^7 + 1296*x^8 + 4112*x^9 - 10244*x^10 + 12684*x^11 - 7652*x^12 - 3481*x^13 + 14652*x^14 - 20265*x^15 + 18708*x^1 6 - 12573*x^17 + 6160*x^18 - 2134*x^19 + 492*x^20 - 67*x^21 + 4*x^22)))/(- 27*x^3 + 27*x^5 - 108*x^6 + 153*x^7 - 36*x^8 - 224*x^9 + 492*x^10 - 564*x^ 11 + 284*x^12 + 243*x^13 - 720*x^14 + 915*x^15 - 792*x^16 + 495*x^17 - 220 *x^18 + 66*x^19 - 12*x^20 + x^21),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(217\) vs. \(2(30)=60\).
Time = 0.53 (sec) , antiderivative size = 218, normalized size of antiderivative = 6.81
\[{\mathrm e}^{\frac {-1-45 x^{2} {\mathrm e}^{4 x}+{\mathrm e}^{4 x} x^{15}-13 \,{\mathrm e}^{4 x} x^{14}+68 \,{\mathrm e}^{4 x} x^{13}-196 \,{\mathrm e}^{4 x} x^{12}+350 \,{\mathrm e}^{4 x} x^{11}-406 \,{\mathrm e}^{4 x} x^{10}+302 \,{\mathrm e}^{4 x} x^{9}-94 \,{\mathrm e}^{4 x} x^{8}-115 \,{\mathrm e}^{4 x} x^{7}+199 \,{\mathrm e}^{4 x} x^{6}-126 \,{\mathrm e}^{4 x} x^{5}+30 \,{\mathrm e}^{4 x} x^{4}+9 \,{\mathrm e}^{4 x} x^{3}-x^{14}+8 x^{13}-28 x^{12}+56 x^{11}-70 x^{10}-22 x^{8}+56 x^{9}+35 x^{6}-16 x^{7}-9 x^{2}+6 x^{4}-24 x^{5}}{x^{2} \left (x^{6}-4 x^{5}+6 x^{4}-4 x^{3}+x^{2}-3\right )^{2}}}\]
Input:
int(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x^16-20 265*x^15+14652*x^14-3481*x^13-7652*x^12+12684*x^11-10244*x^10+4112*x^9+129 6*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-48*x^5+60 *x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-406*x^10 +302*x^9-94*x^8-115*x^7+199*x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x)-x^14 +8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x^5+6*x^4-9 *x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35*x^6+2 4*x^5-6*x^4+9*x^2))/(x^21-12*x^20+66*x^19-220*x^18+495*x^17-792*x^16+915*x ^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^8+153*x^7-10 8*x^6+27*x^5-27*x^3),x)
Output:
exp((-1-45*x^2*exp(4*x)+exp(4*x)*x^15-13*exp(4*x)*x^14+68*exp(4*x)*x^13-19 6*exp(4*x)*x^12+350*exp(4*x)*x^11-406*exp(4*x)*x^10+302*exp(4*x)*x^9-94*ex p(4*x)*x^8-115*exp(4*x)*x^7+199*exp(4*x)*x^6-126*exp(4*x)*x^5+30*exp(4*x)* x^4+9*exp(4*x)*x^3-x^14+8*x^13-28*x^12+56*x^11-70*x^10-22*x^8+56*x^9+35*x^ 6-16*x^7-9*x^2+6*x^4-24*x^5)/x^2/(x^6-4*x^5+6*x^4-4*x^3+x^2-3)^2)
Leaf count of result is larger than twice the leaf count of optimal. 199 vs. \(2 (29) = 58\).
Time = 0.10 (sec) , antiderivative size = 199, normalized size of antiderivative = 6.22 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=e^{\left (-\frac {x^{14} - 8 \, x^{13} + 28 \, x^{12} - 56 \, x^{11} + 70 \, x^{10} - 56 \, x^{9} + 22 \, x^{8} + 16 \, x^{7} - 35 \, x^{6} + 24 \, x^{5} - 6 \, x^{4} + 9 \, x^{2} - {\left (x^{15} - 13 \, x^{14} + 68 \, x^{13} - 196 \, x^{12} + 350 \, x^{11} - 406 \, x^{10} + 302 \, x^{9} - 94 \, x^{8} - 115 \, x^{7} + 199 \, x^{6} - 126 \, x^{5} + 30 \, x^{4} + 9 \, x^{3} - 45 \, x^{2}\right )} e^{\left (4 \, x\right )} + 1}{x^{14} - 8 \, x^{13} + 28 \, x^{12} - 56 \, x^{11} + 70 \, x^{10} - 56 \, x^{9} + 22 \, x^{8} + 16 \, x^{7} - 35 \, x^{6} + 24 \, x^{5} - 6 \, x^{4} + 9 \, x^{2}}\right )} \] Input:
integrate(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x ^16-20265*x^15+14652*x^14-3481*x^13-7652*x^12+12684*x^11-10244*x^10+4112*x ^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-48* x^5+60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-40 6*x^10+302*x^9-94*x^8-115*x^7+199*x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x )-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x^5+6 *x^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35 *x^6+24*x^5-6*x^4+9*x^2))/(x^21-12*x^20+66*x^19-220*x^18+495*x^17-792*x^16 +915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^8+153* x^7-108*x^6+27*x^5-27*x^3),x, algorithm="fricas")
Output:
e^(-(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^ 7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2 - (x^15 - 13*x^14 + 68*x^13 - 196*x^12 + 350*x^11 - 406*x^10 + 302*x^9 - 94*x^8 - 115*x^7 + 199*x^6 - 126*x^5 + 30*x^4 + 9*x^3 - 45*x^2)*e^(4*x) + 1)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2))
Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (27) = 54\).
Time = 3.28 (sec) , antiderivative size = 196, normalized size of antiderivative = 6.12 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=e^{\frac {- x^{14} + 8 x^{13} - 28 x^{12} + 56 x^{11} - 70 x^{10} + 56 x^{9} - 22 x^{8} - 16 x^{7} + 35 x^{6} - 24 x^{5} + 6 x^{4} - 9 x^{2} + \left (x^{15} - 13 x^{14} + 68 x^{13} - 196 x^{12} + 350 x^{11} - 406 x^{10} + 302 x^{9} - 94 x^{8} - 115 x^{7} + 199 x^{6} - 126 x^{5} + 30 x^{4} + 9 x^{3} - 45 x^{2}\right ) e^{4 x} - 1}{x^{14} - 8 x^{13} + 28 x^{12} - 56 x^{11} + 70 x^{10} - 56 x^{9} + 22 x^{8} + 16 x^{7} - 35 x^{6} + 24 x^{5} - 6 x^{4} + 9 x^{2}}} \] Input:
integrate(((4*x**22-67*x**21+492*x**20-2134*x**19+6160*x**18-12573*x**17+1 8708*x**16-20265*x**15+14652*x**14-3481*x**13-7652*x**12+12684*x**11-10244 *x**10+4112*x**9+1296*x**8-3339*x**7+2160*x**6-513*x**5-108*x**4+513*x**3) *exp(4*x)+14*x**6-48*x**5+60*x**4-32*x**3+6*x**2-6)*exp(((x**15-13*x**14+6 8*x**13-196*x**12+350*x**11-406*x**10+302*x**9-94*x**8-115*x**7+199*x**6-1 26*x**5+30*x**4+9*x**3-45*x**2)*exp(4*x)-x**14+8*x**13-28*x**12+56*x**11-7 0*x**10+56*x**9-22*x**8-16*x**7+35*x**6-24*x**5+6*x**4-9*x**2-1)/(x**14-8* x**13+28*x**12-56*x**11+70*x**10-56*x**9+22*x**8+16*x**7-35*x**6+24*x**5-6 *x**4+9*x**2))/(x**21-12*x**20+66*x**19-220*x**18+495*x**17-792*x**16+915* x**15-720*x**14+243*x**13+284*x**12-564*x**11+492*x**10-224*x**9-36*x**8+1 53*x**7-108*x**6+27*x**5-27*x**3),x)
Output:
exp((-x**14 + 8*x**13 - 28*x**12 + 56*x**11 - 70*x**10 + 56*x**9 - 22*x**8 - 16*x**7 + 35*x**6 - 24*x**5 + 6*x**4 - 9*x**2 + (x**15 - 13*x**14 + 68* x**13 - 196*x**12 + 350*x**11 - 406*x**10 + 302*x**9 - 94*x**8 - 115*x**7 + 199*x**6 - 126*x**5 + 30*x**4 + 9*x**3 - 45*x**2)*exp(4*x) - 1)/(x**14 - 8*x**13 + 28*x**12 - 56*x**11 + 70*x**10 - 56*x**9 + 22*x**8 + 16*x**7 - 35*x**6 + 24*x**5 - 6*x**4 + 9*x**2))
Leaf count of result is larger than twice the leaf count of optimal. 470 vs. \(2 (29) = 58\).
Time = 8.23 (sec) , antiderivative size = 470, normalized size of antiderivative = 14.69 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=e^{\left (-\frac {x^{4}}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} + \frac {x^{4}}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} + \frac {4 \, x^{3}}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} - \frac {4 \, x^{3}}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} + x e^{\left (4 \, x\right )} - \frac {2 \, x^{2}}{x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9} + \frac {2 \, x^{2}}{3 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} + \frac {4 \, x}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} - \frac {4 \, x}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} - \frac {1}{3 \, {\left (x^{12} - 8 \, x^{11} + 28 \, x^{10} - 56 \, x^{9} + 70 \, x^{8} - 56 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 35 \, x^{4} + 24 \, x^{3} - 6 \, x^{2} + 9\right )}} + \frac {1}{9 \, {\left (x^{6} - 4 \, x^{5} + 6 \, x^{4} - 4 \, x^{3} + x^{2} - 3\right )}} - \frac {1}{9 \, x^{2}} - 5 \, e^{\left (4 \, x\right )} - 1\right )} \] Input:
integrate(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x ^16-20265*x^15+14652*x^14-3481*x^13-7652*x^12+12684*x^11-10244*x^10+4112*x ^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-48* x^5+60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-40 6*x^10+302*x^9-94*x^8-115*x^7+199*x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x )-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x^5+6 *x^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35 *x^6+24*x^5-6*x^4+9*x^2))/(x^21-12*x^20+66*x^19-220*x^18+495*x^17-792*x^16 +915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^8+153* x^7-108*x^6+27*x^5-27*x^3),x, algorithm="maxima")
Output:
e^(-1/3*x^4/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) + 1/9*x^4/(x^6 - 4*x^5 + 6*x^4 - 4* x^3 + x^2 - 3) + 4/3*x^3/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x ^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) - 4/9*x^3/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) + x*e^(4*x) - 2*x^2/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) + 2/3*x^2/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) + 4/3*x/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 24*x^3 - 6*x^2 + 9) - 4/9*x/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) - 1/3/(x^12 - 8*x^11 + 28*x^10 - 56*x^9 + 70*x^8 - 56*x^7 + 22*x^6 + 16*x^5 - 35*x^4 + 2 4*x^3 - 6*x^2 + 9) + 1/9/(x^6 - 4*x^5 + 6*x^4 - 4*x^3 + x^2 - 3) - 1/9/x^2 - 5*e^(4*x) - 1)
Leaf count of result is larger than twice the leaf count of optimal. 1836 vs. \(2 (29) = 58\).
Time = 5.06 (sec) , antiderivative size = 1836, normalized size of antiderivative = 57.38 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=\text {Too large to display} \] Input:
integrate(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x ^16-20265*x^15+14652*x^14-3481*x^13-7652*x^12+12684*x^11-10244*x^10+4112*x ^9+1296*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-48* x^5+60*x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-40 6*x^10+302*x^9-94*x^8-115*x^7+199*x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x )-x^14+8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x^5+6 *x^4-9*x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35 *x^6+24*x^5-6*x^4+9*x^2))/(x^21-12*x^20+66*x^19-220*x^18+495*x^17-792*x^16 +915*x^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^8+153* x^7-108*x^6+27*x^5-27*x^3),x, algorithm="giac")
Output:
e^(x^15*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22 *x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 13*x^14*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - x^14/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x ^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 68*x^1 3*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 8*x^13/(x^14 - 8*x^13 + 28*x^ 12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^ 4 + 9*x^2) - 196*x^12*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 28*x^12/( x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 3 5*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 350*x^11*e^(4*x)/(x^14 - 8*x^13 + 28*x^1 2 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 56*x^11/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 406*x^10*e^(4*x)/(x ^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35 *x^6 + 24*x^5 - 6*x^4 + 9*x^2) - 70*x^10/(x^14 - 8*x^13 + 28*x^12 - 56*x^1 1 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 302*x^9*e^(4*x)/(x^14 - 8*x^13 + 28*x^12 - 56*x^11 + 70*x^10 - 56*x^9 + 22*x^8 + 16*x^7 - 35*x^6 + 24*x^5 - 6*x^4 + 9*x^2) + 56*x^9/(x^14 - 8*x...
Time = 4.50 (sec) , antiderivative size = 1862, normalized size of antiderivative = 58.19 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=\text {Too large to display} \] Input:
int(-(exp(-(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 7 0*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14 + exp(4*x)*(45*x^2 - 9*x^3 - 30 *x^4 + 126*x^5 - 199*x^6 + 115*x^7 + 94*x^8 - 302*x^9 + 406*x^10 - 350*x^1 1 + 196*x^12 - 68*x^13 + 13*x^14 - x^15) + 1)/(9*x^2 - 6*x^4 + 24*x^5 - 35 *x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x ^14))*(exp(4*x)*(513*x^3 - 108*x^4 - 513*x^5 + 2160*x^6 - 3339*x^7 + 1296* x^8 + 4112*x^9 - 10244*x^10 + 12684*x^11 - 7652*x^12 - 3481*x^13 + 14652*x ^14 - 20265*x^15 + 18708*x^16 - 12573*x^17 + 6160*x^18 - 2134*x^19 + 492*x ^20 - 67*x^21 + 4*x^22) + 6*x^2 - 32*x^3 + 60*x^4 - 48*x^5 + 14*x^6 - 6))/ (27*x^3 - 27*x^5 + 108*x^6 - 153*x^7 + 36*x^8 + 224*x^9 - 492*x^10 + 564*x ^11 - 284*x^12 - 243*x^13 + 720*x^14 - 915*x^15 + 792*x^16 - 495*x^17 + 22 0*x^18 - 66*x^19 + 12*x^20 - x^21),x)
Output:
exp((6*x^4)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(9*x^2)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-x^14/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 2 2*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((8*x^13 )/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(16*x^7)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(24*x^5)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(22*x^8)/(9 *x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x ^11 + 28*x^12 - 8*x^13 + x^14))*exp(-(28*x^12)/(9*x^2 - 6*x^4 + 24*x^5 - 3 5*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((35*x^6)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 5 6*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((56*x^9)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp((56*x^11)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14)) *exp(-(70*x^10)/(9*x^2 - 6*x^4 + 24*x^5 - 35*x^6 + 16*x^7 + 22*x^8 - 56*x^ 9 + 70*x^10 - 56*x^11 + 28*x^12 - 8*x^13 + x^14))*exp(-1/(9*x^2 - 6*x^4...
Time = 0.21 (sec) , antiderivative size = 201, normalized size of antiderivative = 6.28 \[ \int \frac {e^{\frac {-1-9 x^2+6 x^4-24 x^5+35 x^6-16 x^7-22 x^8+56 x^9-70 x^{10}+56 x^{11}-28 x^{12}+8 x^{13}-x^{14}+e^{4 x} \left (-45 x^2+9 x^3+30 x^4-126 x^5+199 x^6-115 x^7-94 x^8+302 x^9-406 x^{10}+350 x^{11}-196 x^{12}+68 x^{13}-13 x^{14}+x^{15}\right )}{9 x^2-6 x^4+24 x^5-35 x^6+16 x^7+22 x^8-56 x^9+70 x^{10}-56 x^{11}+28 x^{12}-8 x^{13}+x^{14}}} \left (-6+6 x^2-32 x^3+60 x^4-48 x^5+14 x^6+e^{4 x} \left (513 x^3-108 x^4-513 x^5+2160 x^6-3339 x^7+1296 x^8+4112 x^9-10244 x^{10}+12684 x^{11}-7652 x^{12}-3481 x^{13}+14652 x^{14}-20265 x^{15}+18708 x^{16}-12573 x^{17}+6160 x^{18}-2134 x^{19}+492 x^{20}-67 x^{21}+4 x^{22}\right )\right )}{-27 x^3+27 x^5-108 x^6+153 x^7-36 x^8-224 x^9+492 x^{10}-564 x^{11}+284 x^{12}+243 x^{13}-720 x^{14}+915 x^{15}-792 x^{16}+495 x^{17}-220 x^{18}+66 x^{19}-12 x^{20}+x^{21}} \, dx=\frac {e^{e^{4 x} x}}{e^{\frac {5 e^{4 x} x^{14}-40 e^{4 x} x^{13}+140 e^{4 x} x^{12}-280 e^{4 x} x^{11}+350 e^{4 x} x^{10}-280 e^{4 x} x^{9}+110 e^{4 x} x^{8}+80 e^{4 x} x^{7}-175 e^{4 x} x^{6}+120 e^{4 x} x^{5}-30 e^{4 x} x^{4}+45 e^{4 x} x^{2}+1}{x^{14}-8 x^{13}+28 x^{12}-56 x^{11}+70 x^{10}-56 x^{9}+22 x^{8}+16 x^{7}-35 x^{6}+24 x^{5}-6 x^{4}+9 x^{2}}} e} \] Input:
int(((4*x^22-67*x^21+492*x^20-2134*x^19+6160*x^18-12573*x^17+18708*x^16-20 265*x^15+14652*x^14-3481*x^13-7652*x^12+12684*x^11-10244*x^10+4112*x^9+129 6*x^8-3339*x^7+2160*x^6-513*x^5-108*x^4+513*x^3)*exp(4*x)+14*x^6-48*x^5+60 *x^4-32*x^3+6*x^2-6)*exp(((x^15-13*x^14+68*x^13-196*x^12+350*x^11-406*x^10 +302*x^9-94*x^8-115*x^7+199*x^6-126*x^5+30*x^4+9*x^3-45*x^2)*exp(4*x)-x^14 +8*x^13-28*x^12+56*x^11-70*x^10+56*x^9-22*x^8-16*x^7+35*x^6-24*x^5+6*x^4-9 *x^2-1)/(x^14-8*x^13+28*x^12-56*x^11+70*x^10-56*x^9+22*x^8+16*x^7-35*x^6+2 4*x^5-6*x^4+9*x^2))/(x^21-12*x^20+66*x^19-220*x^18+495*x^17-792*x^16+915*x ^15-720*x^14+243*x^13+284*x^12-564*x^11+492*x^10-224*x^9-36*x^8+153*x^7-10 8*x^6+27*x^5-27*x^3),x)
Output:
e**(e**(4*x)*x)/(e**((5*e**(4*x)*x**14 - 40*e**(4*x)*x**13 + 140*e**(4*x)* x**12 - 280*e**(4*x)*x**11 + 350*e**(4*x)*x**10 - 280*e**(4*x)*x**9 + 110* e**(4*x)*x**8 + 80*e**(4*x)*x**7 - 175*e**(4*x)*x**6 + 120*e**(4*x)*x**5 - 30*e**(4*x)*x**4 + 45*e**(4*x)*x**2 + 1)/(x**14 - 8*x**13 + 28*x**12 - 56 *x**11 + 70*x**10 - 56*x**9 + 22*x**8 + 16*x**7 - 35*x**6 + 24*x**5 - 6*x* *4 + 9*x**2))*e)