Integrand size = 187, antiderivative size = 32 \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=e^{\frac {x}{(5-x) \left (-2+x^2+\frac {-x+\log (5)}{4+x^2}\right )}} \]
Time = 0.09 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=e^{-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}} \]
Integrate[(E^((-4*x - x^3)/(40 - 3*x - 11*x^2 + 2*x^3 - 5*x^4 + x^5 + (-5 + x)*Log[5]))*(-160 - 164*x^2 + 22*x^3 - 49*x^4 + 16*x^5 - 5*x^6 + 2*x^7 + (20 + 15*x^2 - 2*x^3)*Log[5]))/(1600 - 240*x - 871*x^2 + 226*x^3 - 291*x^ 4 + 66*x^5 + 108*x^6 - 42*x^7 + 29*x^8 - 10*x^9 + x^10 + (-400 + 110*x + 1 04*x^2 - 42*x^3 + 54*x^4 - 20*x^5 + 2*x^6)*Log[5] + (25 - 10*x + x^2)*Log[ 5]^2),x]
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.
| \(\displaystyle \int \frac {\left (2 x^7-5 x^6+16 x^5-49 x^4+22 x^3-164 x^2+\left (-2 x^3+15 x^2+20\right ) \log (5)-160\right ) \exp \left (\frac {-x^3-4 x}{x^5-5 x^4+2 x^3-11 x^2-3 x+(x-5) \log (5)+40}\right )}{x^{10}-10 x^9+29 x^8-42 x^7+108 x^6+66 x^5-291 x^4+226 x^3-871 x^2+\left (x^2-10 x+25\right ) \log ^2(5)+\left (2 x^6-20 x^5+54 x^4-42 x^3+104 x^2+110 x-400\right ) \log (5)-240 x+1600} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {\left (-1038 x^3-x^2 (4528-\log (5))-2 x (10703-5 \log (5))-88118+77 \log (5)\right ) \left (2 x^7-5 x^6+16 x^5-49 x^4+22 x^3-164 x^2+\left (-2 x^3+15 x^2+20\right ) \log (5)-160\right ) \exp \left (\frac {-x^3-4 x}{x^5-5 x^4+2 x^3-11 x^2-3 x+(x-5) \log (5)+40}\right )}{(662+\log (5))^3 \left (-x^4-2 x^2+x+8-\log (5)\right )}+\frac {\left (2 x^7-5 x^6+16 x^5-49 x^4+22 x^3-164 x^2+\left (-2 x^3+15 x^2+20\right ) \log (5)-160\right ) \exp \left (\frac {-x^3-4 x}{x^5-5 x^4+2 x^3-11 x^2-3 x+(x-5) \log (5)+40}\right )}{(x-5)^2 (662+\log (5))^2}+\frac {\left (519 x^3+x^2 (1933-\log (5))+x (7393-10 \log (5))+18572-77 \log (5)\right ) \left (2 x^7-5 x^6+16 x^5-49 x^4+22 x^3-164 x^2+\left (-2 x^3+15 x^2+20\right ) \log (5)-160\right ) \exp \left (\frac {-x^3-4 x}{x^5-5 x^4+2 x^3-11 x^2-3 x+(x-5) \log (5)+40}\right )}{(662+\log (5))^2 \left (-x^4-2 x^2+x+8-\log (5)\right )^2}-\frac {1038 \left (2 x^7-5 x^6+16 x^5-49 x^4+22 x^3-164 x^2+\left (-2 x^3+15 x^2+20\right ) \log (5)-160\right ) \exp \left (\frac {-x^3-4 x}{x^5-5 x^4+2 x^3-11 x^2-3 x+(x-5) \log (5)+40}\right )}{(x-5) (662+\log (5))^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^7-5 x^6+16 x^5-49 x^4-2 x^3 (\log (5)-11)+x^2 (15 \log (5)-164)+20 (\log (5)-8)\right ) \exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x-8+\log (5)\right )}\right )}{(5-x)^2 \left (-x^4-2 x^2+x+8-\log (5)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (145 x^2+2 x (63-\log (5))+5 (247-\log (125))\right ) \exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x-8+\log (5)\right )}\right )}{(662+\log (5)) \left (-x^4-2 x^2+x+8-\log (5)\right )}+\frac {145 \exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x-8+\log (5)\right )}\right )}{(x-5)^2 (662+\log (5))}+\frac {\left (-\left (x^3 (1111-112 \log (5))\right )-x^2 (3569-563 \log (5))-x \left (4179+4 \log ^2(5)-415 \log (5)\right )-14488-20 \log ^2(5)+1971 \log (5)\right ) \exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x-8+\log (5)\right )}\right )}{(662+\log (5)) \left (-x^4-2 x^2+x+8-\log (5)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {\left (4179+4 \log ^2(5)-415 \log (5)\right ) \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right ) x}{\left (x^4+2 x^2-x+\log (5)-8\right )^2}dx}{662+\log (5)}+\frac {145 \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right )}{(x-5)^2}dx}{662+\log (5)}-\frac {(1811-20 \log (5)) (8-\log (5)) \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right )}{\left (x^4+2 x^2-x+\log (5)-8\right )^2}dx}{662+\log (5)}-\frac {(3569-563 \log (5)) \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right ) x^2}{\left (x^4+2 x^2-x+\log (5)-8\right )^2}dx}{662+\log (5)}-\frac {5 (247-\log (125)) \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right )}{x^4+2 x^2-x+\log (5)-8}dx}{662+\log (5)}-\frac {2 (63-\log (5)) \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right ) x}{x^4+2 x^2-x+\log (5)-8}dx}{662+\log (5)}-\frac {145 \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right ) x^2}{x^4+2 x^2-x+\log (5)-8}dx}{662+\log (5)}-\frac {(1111-112 \log (5)) \int \frac {\exp \left (-\frac {x \left (x^2+4\right )}{(x-5) \left (x^4+2 x^2-x+\log (5)-8\right )}\right ) x^3}{\left (x^4+2 x^2-x+\log (5)-8\right )^2}dx}{662+\log (5)}\) |
Int[(E^((-4*x - x^3)/(40 - 3*x - 11*x^2 + 2*x^3 - 5*x^4 + x^5 + (-5 + x)*L og[5]))*(-160 - 164*x^2 + 22*x^3 - 49*x^4 + 16*x^5 - 5*x^6 + 2*x^7 + (20 + 15*x^2 - 2*x^3)*Log[5]))/(1600 - 240*x - 871*x^2 + 226*x^3 - 291*x^4 + 66 *x^5 + 108*x^6 - 42*x^7 + 29*x^8 - 10*x^9 + x^10 + (-400 + 110*x + 104*x^2 - 42*x^3 + 54*x^4 - 20*x^5 + 2*x^6)*Log[5] + (25 - 10*x + x^2)*Log[5]^2), x]
3.27.93.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 2.72 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00
| method | result | size |
| risch | \({\mathrm e}^{-\frac {x \left (x^{2}+4\right )}{\left (-5+x \right ) \left (x^{4}+2 x^{2}+\ln \left (5\right )-x -8\right )}}\) | \(32\) |
| gosper | \({\mathrm e}^{-\frac {x \left (x^{2}+4\right )}{x^{5}-5 x^{4}+2 x^{3}+x \ln \left (5\right )-11 x^{2}-5 \ln \left (5\right )-3 x +40}}\) | \(43\) |
| parallelrisch | \({\mathrm e}^{\frac {-x^{3}-4 x}{x^{5}-5 x^{4}+2 x^{3}+x \ln \left (5\right )-11 x^{2}-5 \ln \left (5\right )-3 x +40}}\) | \(45\) |
| norman | \(\frac {x^{5} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (-5+x \right ) \ln \left (5\right )+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}+\left (-5 \ln \left (5\right )+40\right ) {\mathrm e}^{\frac {-x^{3}-4 x}{\left (-5+x \right ) \ln \left (5\right )+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}+\left (\ln \left (5\right )-3\right ) x \,{\mathrm e}^{\frac {-x^{3}-4 x}{\left (-5+x \right ) \ln \left (5\right )+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}-11 x^{2} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (-5+x \right ) \ln \left (5\right )+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}+2 x^{3} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (-5+x \right ) \ln \left (5\right )+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}-5 x^{4} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (-5+x \right ) \ln \left (5\right )+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}}{\left (-5+x \right ) \left (x^{4}+2 x^{2}+\ln \left (5\right )-x -8\right )}\) | \(309\) |
int(((-2*x^3+15*x^2+20)*ln(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164*x^2-160 )*exp((-x^3-4*x)/((-5+x)*ln(5)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x^2-10*x+ 25)*ln(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*ln(5)+x^10-10*x ^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+1600),x,meth od=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.28 \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=e^{\left (-\frac {x^{3} + 4 \, x}{x^{5} - 5 \, x^{4} + 2 \, x^{3} - 11 \, x^{2} + {\left (x - 5\right )} \log \left (5\right ) - 3 \, x + 40}\right )} \]
integrate(((-2*x^3+15*x^2+20)*log(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164* x^2-160)*exp((-x^3-4*x)/((-5+x)*log(5)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x ^2-10*x+25)*log(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*log(5) +x^10-10*x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+16 00),x, algorithm=\
Time = 5.22 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.22 \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=e^{\frac {- x^{3} - 4 x}{x^{5} - 5 x^{4} + 2 x^{3} - 11 x^{2} - 3 x + \left (x - 5\right ) \log {\left (5 \right )} + 40}} \]
integrate(((-2*x**3+15*x**2+20)*ln(5)+2*x**7-5*x**6+16*x**5-49*x**4+22*x** 3-164*x**2-160)*exp((-x**3-4*x)/((-5+x)*ln(5)+x**5-5*x**4+2*x**3-11*x**2-3 *x+40))/((x**2-10*x+25)*ln(5)**2+(2*x**6-20*x**5+54*x**4-42*x**3+104*x**2+ 110*x-400)*ln(5)+x**10-10*x**9+29*x**8-42*x**7+108*x**6+66*x**5-291*x**4+2 26*x**3-871*x**2-240*x+1600),x)
Leaf count of result is larger than twice the leaf count of optimal. 301 vs. \(2 (31) = 62\).
Time = 2.23 (sec) , antiderivative size = 301, normalized size of antiderivative = 9.41 \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=e^{\left (\frac {145 \, x^{3}}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} - \frac {x^{2} \log \left (5\right )}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} + \frac {63 \, x^{2}}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} - \frac {5 \, x \log \left (5\right )}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} + \frac {605 \, x}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} - \frac {29 \, \log \left (5\right )}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} + \frac {232}{x^{4} {\left (\log \left (5\right ) + 662\right )} + 2 \, x^{2} {\left (\log \left (5\right ) + 662\right )} - x {\left (\log \left (5\right ) + 662\right )} + \log \left (5\right )^{2} + 654 \, \log \left (5\right ) - 5296} - \frac {145}{x {\left (\log \left (5\right ) + 662\right )} - 5 \, \log \left (5\right ) - 3310}\right )} \]
integrate(((-2*x^3+15*x^2+20)*log(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164* x^2-160)*exp((-x^3-4*x)/((-5+x)*log(5)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x ^2-10*x+25)*log(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*log(5) +x^10-10*x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+16 00),x, algorithm=\
e^(145*x^3/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - x^2*log(5)/(x^4*(log(5) + 662) + 2*x^2*(l og(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) + 63*x^2/( x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - 5*x*log(5)/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) + 605*x/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - 29*log(5)/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) + 232/(x^4*(log(5) + 662) + 2*x^2*(l og(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - 145/(x*( log(5) + 662) - 5*log(5) - 3310))
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (31) = 62\).
Time = 0.26 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.38 \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=e^{\left (-\frac {x^{3}}{x^{5} - 5 \, x^{4} + 2 \, x^{3} - 11 \, x^{2} + x \log \left (5\right ) - 3 \, x - 5 \, \log \left (5\right ) + 40} - \frac {4 \, x}{x^{5} - 5 \, x^{4} + 2 \, x^{3} - 11 \, x^{2} + x \log \left (5\right ) - 3 \, x - 5 \, \log \left (5\right ) + 40}\right )} \]
integrate(((-2*x^3+15*x^2+20)*log(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164* x^2-160)*exp((-x^3-4*x)/((-5+x)*log(5)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x ^2-10*x+25)*log(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*log(5) +x^10-10*x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+16 00),x, algorithm=\
e^(-x^3/(x^5 - 5*x^4 + 2*x^3 - 11*x^2 + x*log(5) - 3*x - 5*log(5) + 40) - 4*x/(x^5 - 5*x^4 + 2*x^3 - 11*x^2 + x*log(5) - 3*x - 5*log(5) + 40))
Timed out. \[ \int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx=\text {Hanged} \]
int((exp(-(4*x + x^3)/(log(5)*(x - 5) - 3*x - 11*x^2 + 2*x^3 - 5*x^4 + x^5 + 40))*(log(5)*(15*x^2 - 2*x^3 + 20) - 164*x^2 + 22*x^3 - 49*x^4 + 16*x^5 - 5*x^6 + 2*x^7 - 160))/(log(5)*(110*x + 104*x^2 - 42*x^3 + 54*x^4 - 20*x ^5 + 2*x^6 - 400) - 240*x + log(5)^2*(x^2 - 10*x + 25) - 871*x^2 + 226*x^3 - 291*x^4 + 66*x^5 + 108*x^6 - 42*x^7 + 29*x^8 - 10*x^9 + x^10 + 1600),x)