Integrand size = 153, antiderivative size = 31 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=e^{e^{(x-\log (5))^2}-\frac {1}{3} x^2 \left (-e^{e^3}+x\right )^4} \] Output:
exp(exp((-ln(5)+x)^2)-1/3*x^2*(x-exp(exp(3)))^4)
Leaf count is larger than twice the leaf count of optimal. \(75\) vs. \(2(31)=62\).
Time = 0.15 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.42 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=e^{\frac {1}{3} \left (3\ 5^{-2 x} e^{x^2+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \] Input:
Integrate[(E^((3*E^(x^2 - 2*x*Log[5] + Log[5]^2) - E^(4*E^3)*x^2 + 4*E^(3* E^3)*x^3 - 6*E^(2*E^3)*x^4 + 4*E^E^3*x^5 - x^6)/3)*(-2*E^(4*E^3)*x + 12*E^ (3*E^3)*x^2 - 24*E^(2*E^3)*x^3 + 20*E^E^3*x^4 - 6*x^5 + E^(x^2 - 2*x*Log[5 ] + Log[5]^2)*(6*x - 6*Log[5])))/3,x]
Output:
E^(((3*E^(x^2 + Log[5]^2))/5^(2*x) - E^(4*E^3)*x^2 + 4*E^(3*E^3)*x^3 - 6*E ^(2*E^3)*x^4 + 4*E^E^3*x^5 - x^6)/3)
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.
| \(\displaystyle \int \frac {1}{3} \left (-6 x^5+20 e^{e^3} x^4-24 e^{2 e^3} x^3+12 e^{3 e^3} x^2+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))-2 e^{4 e^3} x\right ) \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3 e^{x^2-2 x \log (5)+\log ^2(5)}\right )\right ) \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int -2 \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )\right ) \left (3 x^5-10 e^{e^3} x^4+12 e^{2 e^3} x^3-6 e^{3 e^3} x^2+e^{4 e^3} x-3\ 5^{-2 x} e^{x^2+\log ^2(5)} (x-\log (5))\right )dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {2}{3} \int \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )\right ) \left (3 x^5-10 e^{e^3} x^4+12 e^{2 e^3} x^3-6 e^{3 e^3} x^2+e^{4 e^3} x-3\ 5^{-2 x} e^{x^2+\log ^2(5)} (x-\log (5))\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {2}{3} \int \left (3 \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )\right ) x^5-10 \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+e^3\right ) x^4+12 \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+2 e^3\right ) x^3-6 \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+3 e^3\right ) x^2+\exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+4 e^3\right ) x-3\ 5^{-2 x} \exp \left (x^2+\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+\log ^2(5)\right ) (x-\log (5))\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2}{3} \left (3 \log (5) \int 5^{-2 x} \exp \left (x^2+\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+\log ^2(5)\right )dx+\int \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+4 e^3\right ) xdx-3 \int 5^{-2 x} \exp \left (x^2+\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+\log ^2(5)\right ) xdx-6 \int \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+3 e^3\right ) x^2dx+12 \int \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+2 e^3\right ) x^3dx-10 \int \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )+e^3\right ) x^4dx+3 \int \exp \left (\frac {1}{3} \left (-x^6+4 e^{e^3} x^5-6 e^{2 e^3} x^4+4 e^{3 e^3} x^3-e^{4 e^3} x^2+3\ 5^{-2 x} e^{x^2+\log ^2(5)}\right )\right ) x^5dx\right )\) |
Input:
Int[(E^((3*E^(x^2 - 2*x*Log[5] + Log[5]^2) - E^(4*E^3)*x^2 + 4*E^(3*E^3)*x ^3 - 6*E^(2*E^3)*x^4 + 4*E^E^3*x^5 - x^6)/3)*(-2*E^(4*E^3)*x + 12*E^(3*E^3 )*x^2 - 24*E^(2*E^3)*x^3 + 20*E^E^3*x^4 - 6*x^5 + E^(x^2 - 2*x*Log[5] + Lo g[5]^2)*(6*x - 6*Log[5])))/3,x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(25)=50\).
Time = 2.11 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.90
| method | result | size |
| risch | \({\mathrm e}^{\left (\frac {1}{25}\right )^{x} {\mathrm e}^{\ln \left (5\right )^{2}+x^{2}}-\frac {x^{2} {\mathrm e}^{4 \,{\mathrm e}^{3}}}{3}+\frac {4 x^{3} {\mathrm e}^{3 \,{\mathrm e}^{3}}}{3}-2 x^{4} {\mathrm e}^{2 \,{\mathrm e}^{3}}+\frac {4 x^{5} {\mathrm e}^{{\mathrm e}^{3}}}{3}-\frac {x^{6}}{3}}\) | \(59\) |
| norman | \({\mathrm e}^{{\mathrm e}^{\ln \left (5\right )^{2}-2 x \ln \left (5\right )+x^{2}}-\frac {x^{2} {\mathrm e}^{4 \,{\mathrm e}^{3}}}{3}+\frac {4 x^{3} {\mathrm e}^{3 \,{\mathrm e}^{3}}}{3}-2 x^{4} {\mathrm e}^{2 \,{\mathrm e}^{3}}+\frac {4 x^{5} {\mathrm e}^{{\mathrm e}^{3}}}{3}-\frac {x^{6}}{3}}\) | \(60\) |
| parallelrisch | \({\mathrm e}^{{\mathrm e}^{\ln \left (5\right )^{2}-2 x \ln \left (5\right )+x^{2}}-\frac {x^{2} {\mathrm e}^{4 \,{\mathrm e}^{3}}}{3}+\frac {4 x^{3} {\mathrm e}^{3 \,{\mathrm e}^{3}}}{3}-2 x^{4} {\mathrm e}^{2 \,{\mathrm e}^{3}}+\frac {4 x^{5} {\mathrm e}^{{\mathrm e}^{3}}}{3}-\frac {x^{6}}{3}}\) | \(60\) |
Input:
int(1/3*((-6*ln(5)+6*x)*exp(ln(5)^2-2*x*ln(5)+x^2)-2*x*exp(exp(3))^4+12*x^ 2*exp(exp(3))^3-24*x^3*exp(exp(3))^2+20*x^4*exp(exp(3))-6*x^5)*exp(exp(ln( 5)^2-2*x*ln(5)+x^2)-1/3*x^2*exp(exp(3))^4+4/3*x^3*exp(exp(3))^3-2*x^4*exp( exp(3))^2+4/3*x^5*exp(exp(3))-1/3*x^6),x,method=_RETURNVERBOSE)
Output:
exp((1/25)^x*exp(ln(5)^2+x^2)-1/3*x^2*exp(4*exp(3))+4/3*x^3*exp(3*exp(3))- 2*x^4*exp(2*exp(3))+4/3*x^5*exp(exp(3))-1/3*x^6)
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (25) = 50\).
Time = 0.07 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.90 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=e^{\left (-\frac {1}{3} \, x^{6} + \frac {4}{3} \, x^{5} e^{\left (e^{3}\right )} - 2 \, x^{4} e^{\left (2 \, e^{3}\right )} + \frac {4}{3} \, x^{3} e^{\left (3 \, e^{3}\right )} - \frac {1}{3} \, x^{2} e^{\left (4 \, e^{3}\right )} + e^{\left (x^{2} - 2 \, x \log \left (5\right ) + \log \left (5\right )^{2}\right )}\right )} \] Input:
integrate(1/3*((-6*log(5)+6*x)*exp(log(5)^2-2*x*log(5)+x^2)-2*x*exp(exp(3) )^4+12*x^2*exp(exp(3))^3-24*x^3*exp(exp(3))^2+20*x^4*exp(exp(3))-6*x^5)*ex p(exp(log(5)^2-2*x*log(5)+x^2)-1/3*x^2*exp(exp(3))^4+4/3*x^3*exp(exp(3))^3 -2*x^4*exp(exp(3))^2+4/3*x^5*exp(exp(3))-1/3*x^6),x, algorithm="fricas")
Output:
e^(-1/3*x^6 + 4/3*x^5*e^(e^3) - 2*x^4*e^(2*e^3) + 4/3*x^3*e^(3*e^3) - 1/3* x^2*e^(4*e^3) + e^(x^2 - 2*x*log(5) + log(5)^2))
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (22) = 44\).
Time = 0.21 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.29 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=e^{- \frac {x^{6}}{3} + \frac {4 x^{5} e^{e^{3}}}{3} - 2 x^{4} e^{2 e^{3}} + \frac {4 x^{3} e^{3 e^{3}}}{3} - \frac {x^{2} e^{4 e^{3}}}{3} + e^{x^{2} - 2 x \log {\left (5 \right )} + \log {\left (5 \right )}^{2}}} \] Input:
integrate(1/3*((-6*ln(5)+6*x)*exp(ln(5)**2-2*x*ln(5)+x**2)-2*x*exp(exp(3)) **4+12*x**2*exp(exp(3))**3-24*x**3*exp(exp(3))**2+20*x**4*exp(exp(3))-6*x* *5)*exp(exp(ln(5)**2-2*x*ln(5)+x**2)-1/3*x**2*exp(exp(3))**4+4/3*x**3*exp( exp(3))**3-2*x**4*exp(exp(3))**2+4/3*x**5*exp(exp(3))-1/3*x**6),x)
Output:
exp(-x**6/3 + 4*x**5*exp(exp(3))/3 - 2*x**4*exp(2*exp(3)) + 4*x**3*exp(3*e xp(3))/3 - x**2*exp(4*exp(3))/3 + exp(x**2 - 2*x*log(5) + log(5)**2))
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (25) = 50\).
Time = 0.55 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.90 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=e^{\left (-\frac {1}{3} \, x^{6} + \frac {4}{3} \, x^{5} e^{\left (e^{3}\right )} - 2 \, x^{4} e^{\left (2 \, e^{3}\right )} + \frac {4}{3} \, x^{3} e^{\left (3 \, e^{3}\right )} - \frac {1}{3} \, x^{2} e^{\left (4 \, e^{3}\right )} + e^{\left (x^{2} - 2 \, x \log \left (5\right ) + \log \left (5\right )^{2}\right )}\right )} \] Input:
integrate(1/3*((-6*log(5)+6*x)*exp(log(5)^2-2*x*log(5)+x^2)-2*x*exp(exp(3) )^4+12*x^2*exp(exp(3))^3-24*x^3*exp(exp(3))^2+20*x^4*exp(exp(3))-6*x^5)*ex p(exp(log(5)^2-2*x*log(5)+x^2)-1/3*x^2*exp(exp(3))^4+4/3*x^3*exp(exp(3))^3 -2*x^4*exp(exp(3))^2+4/3*x^5*exp(exp(3))-1/3*x^6),x, algorithm="maxima")
Output:
e^(-1/3*x^6 + 4/3*x^5*e^(e^3) - 2*x^4*e^(2*e^3) + 4/3*x^3*e^(3*e^3) - 1/3* x^2*e^(4*e^3) + e^(x^2 - 2*x*log(5) + log(5)^2))
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (25) = 50\).
Time = 0.22 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.90 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=e^{\left (-\frac {1}{3} \, x^{6} + \frac {4}{3} \, x^{5} e^{\left (e^{3}\right )} - 2 \, x^{4} e^{\left (2 \, e^{3}\right )} + \frac {4}{3} \, x^{3} e^{\left (3 \, e^{3}\right )} - \frac {1}{3} \, x^{2} e^{\left (4 \, e^{3}\right )} + e^{\left (x^{2} - 2 \, x \log \left (5\right ) + \log \left (5\right )^{2}\right )}\right )} \] Input:
integrate(1/3*((-6*log(5)+6*x)*exp(log(5)^2-2*x*log(5)+x^2)-2*x*exp(exp(3) )^4+12*x^2*exp(exp(3))^3-24*x^3*exp(exp(3))^2+20*x^4*exp(exp(3))-6*x^5)*ex p(exp(log(5)^2-2*x*log(5)+x^2)-1/3*x^2*exp(exp(3))^4+4/3*x^3*exp(exp(3))^3 -2*x^4*exp(exp(3))^2+4/3*x^5*exp(exp(3))-1/3*x^6),x, algorithm="giac")
Output:
e^(-1/3*x^6 + 4/3*x^5*e^(e^3) - 2*x^4*e^(2*e^3) + 4/3*x^3*e^(3*e^3) - 1/3* x^2*e^(4*e^3) + e^(x^2 - 2*x*log(5) + log(5)^2))
Time = 2.69 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.03 \[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx={\mathrm {e}}^{{\left (\frac {1}{25}\right )}^x\,{\mathrm {e}}^{{\ln \left (5\right )}^2}\,{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^{\frac {4\,x^5\,{\mathrm {e}}^{{\mathrm {e}}^3}}{3}}\,{\mathrm {e}}^{-\frac {x^6}{3}}\,{\mathrm {e}}^{-2\,x^4\,{\mathrm {e}}^{2\,{\mathrm {e}}^3}}\,{\mathrm {e}}^{-\frac {x^2\,{\mathrm {e}}^{4\,{\mathrm {e}}^3}}{3}}\,{\mathrm {e}}^{\frac {4\,x^3\,{\mathrm {e}}^{3\,{\mathrm {e}}^3}}{3}} \] Input:
int(-(exp(exp(log(5)^2 - 2*x*log(5) + x^2) + (4*x^5*exp(exp(3)))/3 - (x^2* exp(4*exp(3)))/3 + (4*x^3*exp(3*exp(3)))/3 - 2*x^4*exp(2*exp(3)) - x^6/3)* (2*x*exp(4*exp(3)) - 20*x^4*exp(exp(3)) - exp(log(5)^2 - 2*x*log(5) + x^2) *(6*x - 6*log(5)) - 12*x^2*exp(3*exp(3)) + 24*x^3*exp(2*exp(3)) + 6*x^5))/ 3,x)
Output:
exp((1/25)^x*exp(log(5)^2)*exp(x^2))*exp((4*x^5*exp(exp(3)))/3)*exp(-x^6/3 )*exp(-2*x^4*exp(2*exp(3)))*exp(-(x^2*exp(4*exp(3)))/3)*exp((4*x^3*exp(3*e xp(3)))/3)
\[ \int \frac {1}{3} e^{\frac {1}{3} \left (3 e^{x^2-2 x \log (5)+\log ^2(5)}-e^{4 e^3} x^2+4 e^{3 e^3} x^3-6 e^{2 e^3} x^4+4 e^{e^3} x^5-x^6\right )} \left (-2 e^{4 e^3} x+12 e^{3 e^3} x^2-24 e^{2 e^3} x^3+20 e^{e^3} x^4-6 x^5+e^{x^2-2 x \log (5)+\log ^2(5)} (6 x-6 \log (5))\right ) \, dx=-2 e^{\mathrm {log}\left (5\right )^{2}} \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}+3 \,5^{2 x} x^{2}}{3 \,5^{2 x}}}}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}} 5^{2 x}}d x \right ) \mathrm {log}\left (5\right )+2 e^{\mathrm {log}\left (5\right )^{2}} \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}+3 \,5^{2 x} x^{2}}{3 \,5^{2 x}}} x}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}} 5^{2 x}}d x \right )-\frac {2 e^{4 e^{3}} \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}}{3 \,5^{2 x}}} x}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}}}d x \right )}{3}+4 e^{3 e^{3}} \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}}{3 \,5^{2 x}}} x^{2}}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}}}d x \right )-8 e^{2 e^{3}} \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}}{3 \,5^{2 x}}} x^{3}}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}}}d x \right )+\frac {20 e^{e^{3}} \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}}{3 \,5^{2 x}}} x^{4}}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}}}d x \right )}{3}-2 \left (\int \frac {e^{\frac {3 e^{\mathrm {log}\left (5\right )^{2}+x^{2}}+4 e^{3 e^{3}} 5^{2 x} x^{3}+4 e^{e^{3}} 5^{2 x} x^{5}}{3 \,5^{2 x}}} x^{5}}{e^{\frac {e^{4 e^{3}} x^{2}}{3}+2 e^{2 e^{3}} x^{4}+\frac {x^{6}}{3}}}d x \right ) \] Input:
int(1/3*((-6*log(5)+6*x)*exp(log(5)^2-2*x*log(5)+x^2)-2*x*exp(exp(3))^4+12 *x^2*exp(exp(3))^3-24*x^3*exp(exp(3))^2+20*x^4*exp(exp(3))-6*x^5)*exp(exp( log(5)^2-2*x*log(5)+x^2)-1/3*x^2*exp(exp(3))^4+4/3*x^3*exp(exp(3))^3-2*x^4 *exp(exp(3))^2+4/3*x^5*exp(exp(3))-1/3*x^6),x)
Output:
(2*( - 3*e**(log(5)**2)*int(e**((3*e**(log(5)**2 + x**2) + 4*e**(3*e**3)*5 **(2*x)*x**3 + 4*e**(e**3)*5**(2*x)*x**5 + 3*5**(2*x)*x**2)/(3*5**(2*x)))/ (e**((e**(4*e**3)*x**2 + 6*e**(2*e**3)*x**4 + x**6)/3)*5**(2*x)),x)*log(5) + 3*e**(log(5)**2)*int((e**((3*e**(log(5)**2 + x**2) + 4*e**(3*e**3)*5**( 2*x)*x**3 + 4*e**(e**3)*5**(2*x)*x**5 + 3*5**(2*x)*x**2)/(3*5**(2*x)))*x)/ (e**((e**(4*e**3)*x**2 + 6*e**(2*e**3)*x**4 + x**6)/3)*5**(2*x)),x) - e**( 4*e**3)*int((e**((3*e**(log(5)**2 + x**2) + 4*e**(3*e**3)*5**(2*x)*x**3 + 4*e**(e**3)*5**(2*x)*x**5)/(3*5**(2*x)))*x)/e**((e**(4*e**3)*x**2 + 6*e**( 2*e**3)*x**4 + x**6)/3),x) + 6*e**(3*e**3)*int((e**((3*e**(log(5)**2 + x** 2) + 4*e**(3*e**3)*5**(2*x)*x**3 + 4*e**(e**3)*5**(2*x)*x**5)/(3*5**(2*x)) )*x**2)/e**((e**(4*e**3)*x**2 + 6*e**(2*e**3)*x**4 + x**6)/3),x) - 12*e**( 2*e**3)*int((e**((3*e**(log(5)**2 + x**2) + 4*e**(3*e**3)*5**(2*x)*x**3 + 4*e**(e**3)*5**(2*x)*x**5)/(3*5**(2*x)))*x**3)/e**((e**(4*e**3)*x**2 + 6*e **(2*e**3)*x**4 + x**6)/3),x) + 10*e**(e**3)*int((e**((3*e**(log(5)**2 + x **2) + 4*e**(3*e**3)*5**(2*x)*x**3 + 4*e**(e**3)*5**(2*x)*x**5)/(3*5**(2*x )))*x**4)/e**((e**(4*e**3)*x**2 + 6*e**(2*e**3)*x**4 + x**6)/3),x) - 3*int ((e**((3*e**(log(5)**2 + x**2) + 4*e**(3*e**3)*5**(2*x)*x**3 + 4*e**(e**3) *5**(2*x)*x**5)/(3*5**(2*x)))*x**5)/e**((e**(4*e**3)*x**2 + 6*e**(2*e**3)* x**4 + x**6)/3),x)))/3