Integrand size = 177, antiderivative size = 24 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=e^{-3+x+\frac {1}{x-\frac {4 \left (5+\frac {3}{x}+x\right )}{x}+\log (5)}} \]
Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(24)=48\).
Time = 0.19 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.29 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=5^{-\frac {x^2 \log (5)}{-12-20 x+x^3+x^2 (-4+\log (5))}} e^{\frac {36+48 x+x^4+x^3 (-7+\log (5))+x^2 \left (-7-3 \log (5)+\log ^2(5)\right )}{-12-20 x+x^3+x^2 (-4+\log (5))}} \]
Integrate[(E^((36 + 48*x - 7*x^2 - 7*x^3 + x^4 + (-3*x^2 + x^3)*Log[5])/(- 12 - 20*x - 4*x^2 + x^3 + x^2*Log[5]))*(144 + 456*x + 476*x^2 + 136*x^3 - 25*x^4 - 8*x^5 + x^6 + (-24*x^2 - 40*x^3 - 8*x^4 + 2*x^5)*Log[5] + x^4*Log [5]^2))/(144 + 480*x + 496*x^2 + 136*x^3 - 24*x^4 - 8*x^5 + x^6 + (-24*x^2 - 40*x^3 - 8*x^4 + 2*x^5)*Log[5] + x^4*Log[5]^2),x]
E^((36 + 48*x + x^4 + x^3*(-7 + Log[5]) + x^2*(-7 - 3*Log[5] + Log[5]^2))/ (-12 - 20*x + x^3 + x^2*(-4 + Log[5])))/5^((x^2*Log[5])/(-12 - 20*x + x^3 + x^2*(-4 + Log[5])))
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.
| \(\displaystyle \int \frac {\left (x^6-8 x^5-25 x^4+x^4 \log ^2(5)+136 x^3+476 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+456 x+144\right ) \exp \left (\frac {x^4-7 x^3-7 x^2+\left (x^3-3 x^2\right ) \log (5)+48 x+36}{x^3-4 x^2+x^2 \log (5)-20 x-12}\right )}{x^6-8 x^5-24 x^4+x^4 \log ^2(5)+136 x^3+496 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+480 x+144} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x^6-8 x^5+x^4 \left (\log ^2(5)-25\right )+136 x^3+476 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+456 x+144\right ) \exp \left (\frac {x^4-7 x^3-7 x^2+\left (x^3-3 x^2\right ) \log (5)+48 x+36}{x^3-4 x^2+x^2 \log (5)-20 x-12}\right )}{x^6-8 x^5-24 x^4+x^4 \log ^2(5)+136 x^3+496 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+480 x+144}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x^6-8 x^5+x^4 \left (\log ^2(5)-25\right )+136 x^3+476 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+456 x+144\right ) \exp \left (\frac {x^4-7 x^3-7 x^2+\left (x^3-3 x^2\right ) \log (5)+48 x+36}{x^3-4 x^2+x^2 \log (5)-20 x-12}\right )}{x^6-8 x^5+x^4 \left (\log ^2(5)-24\right )+136 x^3+496 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+480 x+144}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {\left (x^6-8 x^5+x^4 \left (\log ^2(5)-25\right )+136 x^3+476 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+456 x+144\right ) \exp \left (\frac {x^4-7 x^3-7 x^2+\left (x^3-3 x^2\right ) \log (5)+48 x+36}{x^3-4 x^2+x^2 \log (5)-20 x-12}\right )}{\left (x^3-4 x^2+x^2 \log (5)-20 x-12\right )^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x^6-8 x^5+x^4 \left (\log ^2(5)-25\right )+136 x^3+476 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+456 x+144\right ) \exp \left (\frac {x^4-7 x^3-7 x^2+\left (x^3-3 x^2\right ) \log (5)+48 x+36}{x^3-4 x^2+x^2 \log (5)-20 x-12}\right )}{\left (x^3+x^2 (\log (5)-4)-20 x-12\right )^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (x^6-8 x^5+x^4 \left (\log ^2(5)-25\right )+136 x^3+476 x^2+\left (2 x^5-8 x^4-40 x^3-24 x^2\right ) \log (5)+456 x+144\right ) \exp \left (\frac {x^4-x^3 (7-\log (5))-x^2 (7+\log (125))+48 x+36}{x^3-x^2 (4-\log (5))-20 x-12}\right )}{\left (-x^3+x^2 (4-\log (5))+20 x+12\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (-\left (x^2 \left (56+\log ^2(5)-8 \log (5)\right )\right )-4 x (29-5 \log (5))-12 (4-\log (5))\right ) \exp \left (\frac {x^4-x^3 (7-\log (5))-x^2 (7+\log (125))+48 x+36}{x^3-x^2 (4-\log (5))-20 x-12}\right )}{\left (-x^3+x^2 (4-\log (5))+20 x+12\right )^2}+\frac {(x+4-\log (5)) \exp \left (\frac {x^4-x^3 (7-\log (5))-x^2 (7+\log (125))+48 x+36}{x^3-x^2 (4-\log (5))-20 x-12}\right )}{-x^3+x^2 (4-\log (5))+20 x+12}+\exp \left (\frac {x^4-x^3 (7-\log (5))-x^2 (7+\log (125))+48 x+36}{x^3-x^2 (4-\log (5))-20 x-12}\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\left (56+\log ^2(5)-8 \log (5)\right ) \int \frac {\exp \left (\frac {x^4-(7-\log (5)) x^3-(7+\log (125)) x^2+48 x+36}{x^3-(4-\log (5)) x^2-20 x-12}\right ) x^2}{\left (-x^3+(4-\log (5)) x^2+20 x+12\right )^2}dx+\int \exp \left (\frac {x^4-(7-\log (5)) x^3-(7+\log (125)) x^2+48 x+36}{x^3-(4-\log (5)) x^2-20 x-12}\right )dx-12 (4-\log (5)) \int \frac {\exp \left (\frac {x^4-(7-\log (5)) x^3-(7+\log (125)) x^2+48 x+36}{x^3-(4-\log (5)) x^2-20 x-12}\right )}{\left (-x^3+(4-\log (5)) x^2+20 x+12\right )^2}dx-4 (29-5 \log (5)) \int \frac {\exp \left (\frac {x^4-(7-\log (5)) x^3-(7+\log (125)) x^2+48 x+36}{x^3-(4-\log (5)) x^2-20 x-12}\right ) x}{\left (-x^3+(4-\log (5)) x^2+20 x+12\right )^2}dx+(4-\log (5)) \int \frac {\exp \left (\frac {x^4-(7-\log (5)) x^3-(7+\log (125)) x^2+48 x+36}{x^3-(4-\log (5)) x^2-20 x-12}\right )}{-x^3+(4-\log (5)) x^2+20 x+12}dx+\int \frac {\exp \left (\frac {x^4-(7-\log (5)) x^3-(7+\log (125)) x^2+48 x+36}{x^3-(4-\log (5)) x^2-20 x-12}\right ) x}{-x^3+(4-\log (5)) x^2+20 x+12}dx\) |
Int[(E^((36 + 48*x - 7*x^2 - 7*x^3 + x^4 + (-3*x^2 + x^3)*Log[5])/(-12 - 2 0*x - 4*x^2 + x^3 + x^2*Log[5]))*(144 + 456*x + 476*x^2 + 136*x^3 - 25*x^4 - 8*x^5 + x^6 + (-24*x^2 - 40*x^3 - 8*x^4 + 2*x^5)*Log[5] + x^4*Log[5]^2) )/(144 + 480*x + 496*x^2 + 136*x^3 - 24*x^4 - 8*x^5 + x^6 + (-24*x^2 - 40* x^3 - 8*x^4 + 2*x^5)*Log[5] + x^4*Log[5]^2),x]
3.12.54.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
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]
Leaf count of result is larger than twice the leaf count of optimal. \(53\) vs. \(2(23)=46\).
Time = 1.00 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.25
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left (x^{3}-3 x^{2}\right ) \ln \left (5\right )+x^{4}-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}\) | \(54\) |
| gosper | \({\mathrm e}^{\frac {x^{3} \ln \left (5\right )+x^{4}-3 x^{2} \ln \left (5\right )-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}\) | \(55\) |
| risch | \({\mathrm e}^{\frac {x^{3} \ln \left (5\right )+x^{4}-3 x^{2} \ln \left (5\right )-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}\) | \(55\) |
| norman | \(\frac {x^{3} {\mathrm e}^{\frac {\left (x^{3}-3 x^{2}\right ) \ln \left (5\right )+x^{4}-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}+\left (\ln \left (5\right )-4\right ) x^{2} {\mathrm e}^{\frac {\left (x^{3}-3 x^{2}\right ) \ln \left (5\right )+x^{4}-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}-20 x \,{\mathrm e}^{\frac {\left (x^{3}-3 x^{2}\right ) \ln \left (5\right )+x^{4}-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}-12 \,{\mathrm e}^{\frac {\left (x^{3}-3 x^{2}\right ) \ln \left (5\right )+x^{4}-7 x^{3}-7 x^{2}+48 x +36}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}}}{x^{2} \ln \left (5\right )+x^{3}-4 x^{2}-20 x -12}\) | \(253\) |
int((x^4*ln(5)^2+(2*x^5-8*x^4-40*x^3-24*x^2)*ln(5)+x^6-8*x^5-25*x^4+136*x^ 3+476*x^2+456*x+144)*exp(((x^3-3*x^2)*ln(5)+x^4-7*x^3-7*x^2+48*x+36)/(x^2* ln(5)+x^3-4*x^2-20*x-12))/(x^4*ln(5)^2+(2*x^5-8*x^4-40*x^3-24*x^2)*ln(5)+x ^6-8*x^5-24*x^4+136*x^3+496*x^2+480*x+144),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (23) = 46\).
Time = 0.29 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.21 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=e^{\left (\frac {x^{4} - 7 \, x^{3} - 7 \, x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} \log \left (5\right ) + 48 \, x + 36}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12}\right )} \]
integrate((x^4*log(5)^2+(2*x^5-8*x^4-40*x^3-24*x^2)*log(5)+x^6-8*x^5-25*x^ 4+136*x^3+476*x^2+456*x+144)*exp(((x^3-3*x^2)*log(5)+x^4-7*x^3-7*x^2+48*x+ 36)/(x^2*log(5)+x^3-4*x^2-20*x-12))/(x^4*log(5)^2+(2*x^5-8*x^4-40*x^3-24*x ^2)*log(5)+x^6-8*x^5-24*x^4+136*x^3+496*x^2+480*x+144),x, algorithm=\
e^((x^4 - 7*x^3 - 7*x^2 + (x^3 - 3*x^2)*log(5) + 48*x + 36)/(x^3 + x^2*log (5) - 4*x^2 - 20*x - 12))
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (20) = 40\).
Time = 1.02 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=e^{\frac {x^{4} - 7 x^{3} - 7 x^{2} + 48 x + \left (x^{3} - 3 x^{2}\right ) \log {\left (5 \right )} + 36}{x^{3} - 4 x^{2} + x^{2} \log {\left (5 \right )} - 20 x - 12}} \]
integrate((x**4*ln(5)**2+(2*x**5-8*x**4-40*x**3-24*x**2)*ln(5)+x**6-8*x**5 -25*x**4+136*x**3+476*x**2+456*x+144)*exp(((x**3-3*x**2)*ln(5)+x**4-7*x**3 -7*x**2+48*x+36)/(x**2*ln(5)+x**3-4*x**2-20*x-12))/(x**4*ln(5)**2+(2*x**5- 8*x**4-40*x**3-24*x**2)*ln(5)+x**6-8*x**5-24*x**4+136*x**3+496*x**2+480*x+ 144),x)
exp((x**4 - 7*x**3 - 7*x**2 + 48*x + (x**3 - 3*x**2)*log(5) + 36)/(x**3 - 4*x**2 + x**2*log(5) - 20*x - 12))
Time = 0.53 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=e^{\left (x + \frac {x^{2}}{x^{3} + x^{2} {\left (\log \left (5\right ) - 4\right )} - 20 \, x - 12} - 3\right )} \]
integrate((x^4*log(5)^2+(2*x^5-8*x^4-40*x^3-24*x^2)*log(5)+x^6-8*x^5-25*x^ 4+136*x^3+476*x^2+456*x+144)*exp(((x^3-3*x^2)*log(5)+x^4-7*x^3-7*x^2+48*x+ 36)/(x^2*log(5)+x^3-4*x^2-20*x-12))/(x^4*log(5)^2+(2*x^5-8*x^4-40*x^3-24*x ^2)*log(5)+x^6-8*x^5-24*x^4+136*x^3+496*x^2+480*x+144),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 181 vs. \(2 (23) = 46\).
Time = 0.32 (sec) , antiderivative size = 181, normalized size of antiderivative = 7.54 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=e^{\left (\frac {x^{4}}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12} + \frac {x^{3} \log \left (5\right )}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12} - \frac {7 \, x^{3}}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12} - \frac {3 \, x^{2} \log \left (5\right )}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12} - \frac {7 \, x^{2}}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12} + \frac {48 \, x}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12} + \frac {36}{x^{3} + x^{2} \log \left (5\right ) - 4 \, x^{2} - 20 \, x - 12}\right )} \]
integrate((x^4*log(5)^2+(2*x^5-8*x^4-40*x^3-24*x^2)*log(5)+x^6-8*x^5-25*x^ 4+136*x^3+476*x^2+456*x+144)*exp(((x^3-3*x^2)*log(5)+x^4-7*x^3-7*x^2+48*x+ 36)/(x^2*log(5)+x^3-4*x^2-20*x-12))/(x^4*log(5)^2+(2*x^5-8*x^4-40*x^3-24*x ^2)*log(5)+x^6-8*x^5-24*x^4+136*x^3+496*x^2+480*x+144),x, algorithm=\
e^(x^4/(x^3 + x^2*log(5) - 4*x^2 - 20*x - 12) + x^3*log(5)/(x^3 + x^2*log( 5) - 4*x^2 - 20*x - 12) - 7*x^3/(x^3 + x^2*log(5) - 4*x^2 - 20*x - 12) - 3 *x^2*log(5)/(x^3 + x^2*log(5) - 4*x^2 - 20*x - 12) - 7*x^2/(x^3 + x^2*log( 5) - 4*x^2 - 20*x - 12) + 48*x/(x^3 + x^2*log(5) - 4*x^2 - 20*x - 12) + 36 /(x^3 + x^2*log(5) - 4*x^2 - 20*x - 12))
Time = 13.62 (sec) , antiderivative size = 184, normalized size of antiderivative = 7.67 \[ \int \frac {e^{\frac {36+48 x-7 x^2-7 x^3+x^4+\left (-3 x^2+x^3\right ) \log (5)}{-12-20 x-4 x^2+x^3+x^2 \log (5)}} \left (144+456 x+476 x^2+136 x^3-25 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)\right )}{144+480 x+496 x^2+136 x^3-24 x^4-8 x^5+x^6+\left (-24 x^2-40 x^3-8 x^4+2 x^5\right ) \log (5)+x^4 \log ^2(5)} \, dx=5^{\frac {3\,x^2-x^3}{20\,x-x^2\,\ln \left (5\right )+4\,x^2-x^3+12}}\,{\mathrm {e}}^{-\frac {x^4}{20\,x-x^2\,\ln \left (5\right )+4\,x^2-x^3+12}}\,{\mathrm {e}}^{\frac {7\,x^2}{20\,x-x^2\,\ln \left (5\right )+4\,x^2-x^3+12}}\,{\mathrm {e}}^{\frac {7\,x^3}{20\,x-x^2\,\ln \left (5\right )+4\,x^2-x^3+12}}\,{\mathrm {e}}^{-\frac {36}{20\,x-x^2\,\ln \left (5\right )+4\,x^2-x^3+12}}\,{\mathrm {e}}^{-\frac {48\,x}{20\,x-x^2\,\ln \left (5\right )+4\,x^2-x^3+12}} \]
int((exp(-(48*x - log(5)*(3*x^2 - x^3) - 7*x^2 - 7*x^3 + x^4 + 36)/(20*x - x^2*log(5) + 4*x^2 - x^3 + 12))*(456*x + x^4*log(5)^2 - log(5)*(24*x^2 + 40*x^3 + 8*x^4 - 2*x^5) + 476*x^2 + 136*x^3 - 25*x^4 - 8*x^5 + x^6 + 144)) /(480*x + x^4*log(5)^2 - log(5)*(24*x^2 + 40*x^3 + 8*x^4 - 2*x^5) + 496*x^ 2 + 136*x^3 - 24*x^4 - 8*x^5 + x^6 + 144),x)
5^((3*x^2 - x^3)/(20*x - x^2*log(5) + 4*x^2 - x^3 + 12))*exp(-x^4/(20*x - x^2*log(5) + 4*x^2 - x^3 + 12))*exp((7*x^2)/(20*x - x^2*log(5) + 4*x^2 - x ^3 + 12))*exp((7*x^3)/(20*x - x^2*log(5) + 4*x^2 - x^3 + 12))*exp(-36/(20* x - x^2*log(5) + 4*x^2 - x^3 + 12))*exp(-(48*x)/(20*x - x^2*log(5) + 4*x^2 - x^3 + 12))