Integrand size = 156, antiderivative size = 16 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=\left (2-243 e^{-\frac {2+x}{x}}\right )^8 \] Output:
(2-exp(5*ln(3)-(2+x)/x))^8
Time = 0.07 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.62 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=e^{-\frac {8 (2+x)}{x}} \left (243-2 e^{1+\frac {2}{x}}\right )^8 \] Input:
Integrate[(-2048*E^((-2 - x + 5*x*Log[3])/x) + 7168*E^((2*(-2 - x + 5*x*Lo g[3]))/x) - 10752*E^((3*(-2 - x + 5*x*Log[3]))/x) + 8960*E^((4*(-2 - x + 5 *x*Log[3]))/x) - 4480*E^((5*(-2 - x + 5*x*Log[3]))/x) + 1344*E^((6*(-2 - x + 5*x*Log[3]))/x) - 224*E^((7*(-2 - x + 5*x*Log[3]))/x) + 16*E^((8*(-2 - x + 5*x*Log[3]))/x))/x^2,x]
Output:
(243 - 2*E^(1 + 2/x))^8/E^((8*(2 + x))/x)
Leaf count is larger than twice the leaf count of optimal. \(89\) vs. \(2(16)=32\).
Time = 0.37 (sec) , antiderivative size = 89, normalized size of antiderivative = 5.56, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {2010, 2009}
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.
| \(\displaystyle \int \frac {-2048 e^{\frac {-x+5 x \log (3)-2}{x}}+7168 e^{\frac {2 (-x+5 x \log (3)-2)}{x}}-10752 e^{\frac {3 (-x+5 x \log (3)-2)}{x}}+8960 e^{\frac {4 (-x+5 x \log (3)-2)}{x}}-4480 e^{\frac {5 (-x+5 x \log (3)-2)}{x}}+1344 e^{\frac {6 (-x+5 x \log (3)-2)}{x}}-224 e^{\frac {7 (-x+5 x \log (3)-2)}{x}}+16 e^{\frac {8 (-x+5 x \log (3)-2)}{x}}}{x^2} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (\frac {194522647344910860816 e^{-\frac {16}{x}-8}}{x^2}-\frac {11207066102175934368 e^{-\frac {14}{x}-7}}{x^2}+\frac {276717681535208256 e^{-\frac {12}{x}-6}}{x^2}-\frac {3795852970304640 e^{-\frac {10}{x}-5}}{x^2}+\frac {31241588232960 e^{-\frac {8}{x}-4}}{x^2}-\frac {154279448064 e^{-\frac {6}{x}-3}}{x^2}+\frac {423263232 e^{-\frac {4}{x}-2}}{x^2}-\frac {497664 e^{-\frac {2}{x}-1}}{x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 12157665459056928801 e^{-\frac {16}{x}-8}-800504721583995312 e^{-\frac {14}{x}-7}+23059806794600688 e^{-\frac {12}{x}-6}-379585297030464 e^{-\frac {10}{x}-5}+3905198529120 e^{-\frac {8}{x}-4}-25713241344 e^{-\frac {6}{x}-3}+105815808 e^{-\frac {4}{x}-2}-248832 e^{-\frac {2}{x}-1}\) |
Input:
Int[(-2048*E^((-2 - x + 5*x*Log[3])/x) + 7168*E^((2*(-2 - x + 5*x*Log[3])) /x) - 10752*E^((3*(-2 - x + 5*x*Log[3]))/x) + 8960*E^((4*(-2 - x + 5*x*Log [3]))/x) - 4480*E^((5*(-2 - x + 5*x*Log[3]))/x) + 1344*E^((6*(-2 - x + 5*x *Log[3]))/x) - 224*E^((7*(-2 - x + 5*x*Log[3]))/x) + 16*E^((8*(-2 - x + 5* x*Log[3]))/x))/x^2,x]
Output:
12157665459056928801*E^(-8 - 16/x) - 800504721583995312*E^(-7 - 14/x) + 23 059806794600688*E^(-6 - 12/x) - 379585297030464*E^(-5 - 10/x) + 3905198529 120*E^(-4 - 8/x) - 25713241344*E^(-3 - 6/x) + 105815808*E^(-2 - 4/x) - 248 832*E^(-1 - 2/x)
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Time = 1.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.25
| method | result | size |
| derivativedivides | \(\left ({\mathrm e}^{\frac {5 x \ln \left (3\right )-x -2}{x}}-2\right )^{8}\) | \(20\) |
| default | \(\left ({\mathrm e}^{\frac {5 x \ln \left (3\right )-x -2}{x}}-2\right )^{8}\) | \(20\) |
| risch | \(12157665459056928801 \,{\mathrm e}^{-\frac {8 \left (2+x \right )}{x}}-800504721583995312 \,{\mathrm e}^{-\frac {7 \left (2+x \right )}{x}}+23059806794600688 \,{\mathrm e}^{-\frac {6 \left (2+x \right )}{x}}-379585297030464 \,{\mathrm e}^{-\frac {5 \left (2+x \right )}{x}}+3905198529120 \,{\mathrm e}^{-\frac {4 \left (2+x \right )}{x}}-25713241344 \,{\mathrm e}^{-\frac {3 \left (2+x \right )}{x}}+105815808 \,{\mathrm e}^{-\frac {2 \left (2+x \right )}{x}}-248832 \,{\mathrm e}^{-\frac {2+x}{x}}\) | \(90\) |
| parts | \({\mathrm e}^{\frac {40 x \ln \left (3\right )-8 x -16}{x}}-16 \,{\mathrm e}^{\frac {35 x \ln \left (3\right )-7 x -14}{x}}+112 \,{\mathrm e}^{\frac {30 x \ln \left (3\right )-6 x -12}{x}}-448 \,{\mathrm e}^{\frac {25 x \ln \left (3\right )-5 x -10}{x}}+1120 \,{\mathrm e}^{\frac {20 x \ln \left (3\right )-4 x -8}{x}}-1792 \,{\mathrm e}^{\frac {15 x \ln \left (3\right )-3 x -6}{x}}+1792 \,{\mathrm e}^{\frac {10 x \ln \left (3\right )-2 x -4}{x}}-1024 \,{\mathrm e}^{\frac {5 x \ln \left (3\right )-x -2}{x}}\) | \(150\) |
| norman | \(\frac {x \,{\mathrm e}^{\frac {40 x \ln \left (3\right )-8 x -16}{x}}+1792 x \,{\mathrm e}^{\frac {10 x \ln \left (3\right )-2 x -4}{x}}-1792 x \,{\mathrm e}^{\frac {15 x \ln \left (3\right )-3 x -6}{x}}+1120 x \,{\mathrm e}^{\frac {20 x \ln \left (3\right )-4 x -8}{x}}-448 x \,{\mathrm e}^{\frac {25 x \ln \left (3\right )-5 x -10}{x}}+112 x \,{\mathrm e}^{\frac {30 x \ln \left (3\right )-6 x -12}{x}}-16 x \,{\mathrm e}^{\frac {35 x \ln \left (3\right )-7 x -14}{x}}-1024 \,{\mathrm e}^{\frac {5 x \ln \left (3\right )-x -2}{x}} x}{x}\) | \(163\) |
| orering | \(\text {Expression too large to display}\) | \(55738\) |
Input:
int((16*exp((5*x*ln(3)-x-2)/x)^8-224*exp((5*x*ln(3)-x-2)/x)^7+1344*exp((5* x*ln(3)-x-2)/x)^6-4480*exp((5*x*ln(3)-x-2)/x)^5+8960*exp((5*x*ln(3)-x-2)/x )^4-10752*exp((5*x*ln(3)-x-2)/x)^3+7168*exp((5*x*ln(3)-x-2)/x)^2-2048*exp( (5*x*ln(3)-x-2)/x))/x^2,x,method=_RETURNVERBOSE)
Output:
(exp((5*x*ln(3)-x-2)/x)-2)^8
Leaf count of result is larger than twice the leaf count of optimal. 142 vs. \(2 (18) = 36\).
Time = 0.11 (sec) , antiderivative size = 142, normalized size of antiderivative = 8.88 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=e^{\left (\frac {8 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} - 16 \, e^{\left (\frac {7 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} + 112 \, e^{\left (\frac {6 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} - 448 \, e^{\left (\frac {5 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} + 1120 \, e^{\left (\frac {4 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} - 1792 \, e^{\left (\frac {3 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} + 1792 \, e^{\left (\frac {2 \, {\left (5 \, x \log \left (3\right ) - x - 2\right )}}{x}\right )} - 1024 \, e^{\left (\frac {5 \, x \log \left (3\right ) - x - 2}{x}\right )} \] Input:
integrate((16*exp((5*x*log(3)-x-2)/x)^8-224*exp((5*x*log(3)-x-2)/x)^7+1344 *exp((5*x*log(3)-x-2)/x)^6-4480*exp((5*x*log(3)-x-2)/x)^5+8960*exp((5*x*lo g(3)-x-2)/x)^4-10752*exp((5*x*log(3)-x-2)/x)^3+7168*exp((5*x*log(3)-x-2)/x )^2-2048*exp((5*x*log(3)-x-2)/x))/x^2,x, algorithm="fricas")
Output:
e^(8*(5*x*log(3) - x - 2)/x) - 16*e^(7*(5*x*log(3) - x - 2)/x) + 112*e^(6* (5*x*log(3) - x - 2)/x) - 448*e^(5*(5*x*log(3) - x - 2)/x) + 1120*e^(4*(5* x*log(3) - x - 2)/x) - 1792*e^(3*(5*x*log(3) - x - 2)/x) + 1792*e^(2*(5*x* log(3) - x - 2)/x) - 1024*e^((5*x*log(3) - x - 2)/x)
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (10) = 20\).
Time = 0.12 (sec) , antiderivative size = 131, normalized size of antiderivative = 8.19 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=e^{\frac {8 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} - 16 e^{\frac {7 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} + 112 e^{\frac {6 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} - 448 e^{\frac {5 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} + 1120 e^{\frac {4 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} - 1792 e^{\frac {3 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} + 1792 e^{\frac {2 \left (- x + 5 x \log {\left (3 \right )} - 2\right )}{x}} - 1024 e^{\frac {- x + 5 x \log {\left (3 \right )} - 2}{x}} \] Input:
integrate((16*exp((5*x*ln(3)-x-2)/x)**8-224*exp((5*x*ln(3)-x-2)/x)**7+1344 *exp((5*x*ln(3)-x-2)/x)**6-4480*exp((5*x*ln(3)-x-2)/x)**5+8960*exp((5*x*ln (3)-x-2)/x)**4-10752*exp((5*x*ln(3)-x-2)/x)**3+7168*exp((5*x*ln(3)-x-2)/x) **2-2048*exp((5*x*ln(3)-x-2)/x))/x**2,x)
Output:
exp(8*(-x + 5*x*log(3) - 2)/x) - 16*exp(7*(-x + 5*x*log(3) - 2)/x) + 112*e xp(6*(-x + 5*x*log(3) - 2)/x) - 448*exp(5*(-x + 5*x*log(3) - 2)/x) + 1120* exp(4*(-x + 5*x*log(3) - 2)/x) - 1792*exp(3*(-x + 5*x*log(3) - 2)/x) + 179 2*exp(2*(-x + 5*x*log(3) - 2)/x) - 1024*exp((-x + 5*x*log(3) - 2)/x)
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (18) = 36\).
Time = 0.04 (sec) , antiderivative size = 81, normalized size of antiderivative = 5.06 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=-248832 \, e^{\left (-\frac {2}{x} - 1\right )} + 105815808 \, e^{\left (-\frac {4}{x} - 2\right )} - 25713241344 \, e^{\left (-\frac {6}{x} - 3\right )} + 3905198529120 \, e^{\left (-\frac {8}{x} - 4\right )} - 379585297030464 \, e^{\left (-\frac {10}{x} - 5\right )} + 23059806794600688 \, e^{\left (-\frac {12}{x} - 6\right )} - 800504721583995312 \, e^{\left (-\frac {14}{x} - 7\right )} + 12157665459056928801 \, e^{\left (-\frac {16}{x} - 8\right )} \] Input:
integrate((16*exp((5*x*log(3)-x-2)/x)^8-224*exp((5*x*log(3)-x-2)/x)^7+1344 *exp((5*x*log(3)-x-2)/x)^6-4480*exp((5*x*log(3)-x-2)/x)^5+8960*exp((5*x*lo g(3)-x-2)/x)^4-10752*exp((5*x*log(3)-x-2)/x)^3+7168*exp((5*x*log(3)-x-2)/x )^2-2048*exp((5*x*log(3)-x-2)/x))/x^2,x, algorithm="maxima")
Output:
-248832*e^(-2/x - 1) + 105815808*e^(-4/x - 2) - 25713241344*e^(-6/x - 3) + 3905198529120*e^(-8/x - 4) - 379585297030464*e^(-10/x - 5) + 230598067946 00688*e^(-12/x - 6) - 800504721583995312*e^(-14/x - 7) + 12157665459056928 801*e^(-16/x - 8)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (18) = 36\).
Time = 0.12 (sec) , antiderivative size = 85, normalized size of antiderivative = 5.31 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=243 \, {\left (50031545098999707 \, e^{28} - 1024 \, e^{\left (\frac {14}{x} + 35\right )} + 435456 \, e^{\left (\frac {12}{x} + 34\right )} - 105815808 \, e^{\left (\frac {10}{x} + 33\right )} + 16070775840 \, e^{\left (\frac {8}{x} + 32\right )} - 1562079411648 \, e^{\left (\frac {6}{x} + 31\right )} + 94896324257616 \, e^{\left (\frac {4}{x} + 30\right )} - 3294258113514384 \, e^{\left (\frac {2}{x} + 29\right )}\right )} e^{\left (-\frac {16}{x} - 36\right )} \] Input:
integrate((16*exp((5*x*log(3)-x-2)/x)^8-224*exp((5*x*log(3)-x-2)/x)^7+1344 *exp((5*x*log(3)-x-2)/x)^6-4480*exp((5*x*log(3)-x-2)/x)^5+8960*exp((5*x*lo g(3)-x-2)/x)^4-10752*exp((5*x*log(3)-x-2)/x)^3+7168*exp((5*x*log(3)-x-2)/x )^2-2048*exp((5*x*log(3)-x-2)/x))/x^2,x, algorithm="giac")
Output:
243*(50031545098999707*e^28 - 1024*e^(14/x + 35) + 435456*e^(12/x + 34) - 105815808*e^(10/x + 33) + 16070775840*e^(8/x + 32) - 1562079411648*e^(6/x + 31) + 94896324257616*e^(4/x + 30) - 3294258113514384*e^(2/x + 29))*e^(-1 6/x - 36)
Time = 2.92 (sec) , antiderivative size = 81, normalized size of antiderivative = 5.06 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=105815808\,{\mathrm {e}}^{-\frac {4}{x}-2}-248832\,{\mathrm {e}}^{-\frac {2}{x}-1}-25713241344\,{\mathrm {e}}^{-\frac {6}{x}-3}+3905198529120\,{\mathrm {e}}^{-\frac {8}{x}-4}-379585297030464\,{\mathrm {e}}^{-\frac {10}{x}-5}+23059806794600688\,{\mathrm {e}}^{-\frac {12}{x}-6}-800504721583995312\,{\mathrm {e}}^{-\frac {14}{x}-7}+12157665459056928801\,{\mathrm {e}}^{-\frac {16}{x}-8} \] Input:
int(-(2048*exp(-(x - 5*x*log(3) + 2)/x) - 7168*exp(-(2*(x - 5*x*log(3) + 2 ))/x) + 10752*exp(-(3*(x - 5*x*log(3) + 2))/x) - 8960*exp(-(4*(x - 5*x*log (3) + 2))/x) + 4480*exp(-(5*(x - 5*x*log(3) + 2))/x) - 1344*exp(-(6*(x - 5 *x*log(3) + 2))/x) + 224*exp(-(7*(x - 5*x*log(3) + 2))/x) - 16*exp(-(8*(x - 5*x*log(3) + 2))/x))/x^2,x)
Output:
105815808*exp(- 4/x - 2) - 248832*exp(- 2/x - 1) - 25713241344*exp(- 6/x - 3) + 3905198529120*exp(- 8/x - 4) - 379585297030464*exp(- 10/x - 5) + 230 59806794600688*exp(- 12/x - 6) - 800504721583995312*exp(- 14/x - 7) + 1215 7665459056928801*exp(- 16/x - 8)
Time = 0.17 (sec) , antiderivative size = 98, normalized size of antiderivative = 6.12 \[ \int \frac {-2048 e^{\frac {-2-x+5 x \log (3)}{x}}+7168 e^{\frac {2 (-2-x+5 x \log (3))}{x}}-10752 e^{\frac {3 (-2-x+5 x \log (3))}{x}}+8960 e^{\frac {4 (-2-x+5 x \log (3))}{x}}-4480 e^{\frac {5 (-2-x+5 x \log (3))}{x}}+1344 e^{\frac {6 (-2-x+5 x \log (3))}{x}}-224 e^{\frac {7 (-2-x+5 x \log (3))}{x}}+16 e^{\frac {8 (-2-x+5 x \log (3))}{x}}}{x^2} \, dx=\frac {-248832 e^{\frac {14}{x}} e^{7}+105815808 e^{\frac {12}{x}} e^{6}-25713241344 e^{\frac {10}{x}} e^{5}+3905198529120 e^{\frac {8}{x}} e^{4}-379585297030464 e^{\frac {6}{x}} e^{3}+23059806794600688 e^{\frac {4}{x}} e^{2}-800504721583995312 e^{\frac {2}{x}} e +12157665459056928801}{e^{\frac {16}{x}} e^{8}} \] Input:
int((16*exp((5*x*log(3)-x-2)/x)^8-224*exp((5*x*log(3)-x-2)/x)^7+1344*exp(( 5*x*log(3)-x-2)/x)^6-4480*exp((5*x*log(3)-x-2)/x)^5+8960*exp((5*x*log(3)-x -2)/x)^4-10752*exp((5*x*log(3)-x-2)/x)^3+7168*exp((5*x*log(3)-x-2)/x)^2-20 48*exp((5*x*log(3)-x-2)/x))/x^2,x)
Output:
(243*( - 1024*e**(14/x)*e**7 + 435456*e**(12/x)*e**6 - 105815808*e**(10/x) *e**5 + 16070775840*e**(8/x)*e**4 - 1562079411648*e**(6/x)*e**3 + 94896324 257616*e**(4/x)*e**2 - 3294258113514384*e**(2/x)*e + 50031545098999707))/( e**(16/x)*e**8)