Integrand size = 211, antiderivative size = 35 \[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=e^{-\frac {x}{3 \left (-e^x+x \left (-4-\frac {1}{x}+x\right )\right )}} \left (2+\frac {x}{\log (\log (4))}\right ) \] Output:
exp(ln(2+x/ln(2*ln(2)))-x/(3*(x-1/x-4)*x-3*exp(x)))
Time = 0.05 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.14 \[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=\frac {e^{\frac {x}{3 \left (1+e^x+4 x-x^2\right )}} (3 x+6 \log (\log (4)))}{3 \log (\log (4))} \] Input:
Integrate[(E^((x + (3 + 3*E^x + 12*x - 3*x^2)*Log[(x + 2*Log[Log[4]])/Log[ Log[4]]])/(3 + 3*E^x + 12*x - 3*x^2))*(3 + 3*E^(2*x) + 25*x + 42*x^2 - 23* x^3 + 3*x^4 + E^x*(6 + 25*x - 7*x^2) + (2 + E^x*(2 - 2*x) + 2*x^2)*Log[Log [4]]))/(3*x + 3*E^(2*x)*x + 24*x^2 + 42*x^3 - 24*x^4 + 3*x^5 + E^x*(6*x + 24*x^2 - 6*x^3) + (6 + 6*E^(2*x) + 48*x + 84*x^2 - 48*x^3 + 6*x^4 + E^x*(1 2 + 48*x - 12*x^2))*Log[Log[4]]),x]
Output:
(E^(x/(3*(1 + E^x + 4*x - x^2)))*(3*x + 6*Log[Log[4]]))/(3*Log[Log[4]])
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.
| \(\displaystyle \int \frac {\left (3 x^4-23 x^3+42 x^2+e^x \left (-7 x^2+25 x+6\right )+\left (2 x^2+e^x (2-2 x)+2\right ) \log (\log (4))+25 x+3 e^{2 x}+3\right ) \exp \left (\frac {\left (-3 x^2+12 x+3 e^x+3\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )+x}{-3 x^2+12 x+3 e^x+3}\right )}{3 x^5-24 x^4+42 x^3+24 x^2+e^x \left (-6 x^3+24 x^2+6 x\right )+\left (6 x^4-48 x^3+84 x^2+e^x \left (-12 x^2+48 x+12\right )+48 x+6 e^{2 x}+6\right ) \log (\log (4))+3 e^{2 x} x+3 x} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} \left (3 x^4-23 x^3+2 x^2 (21+\log (\log (4)))+e^x \left (-7 x^2+25 x-2 x \log (\log (4))+6+2 \log (\log (4))\right )+25 x+3 e^{2 x}+3 \left (1+\frac {2}{3} \log (\log (4))\right )\right )}{3 \left (-x^2+4 x+e^x+1\right )^2 \log (\log (4))}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} \left (3 x^4-23 x^3+2 (21+\log (\log (4))) x^2+25 x+3 e^{2 x}+e^x \left (-7 x^2-2 \log (\log (4)) x+25 x+2 (3+\log (\log (4)))\right )+2 \log (\log (4))+3\right )}{\left (-x^2+4 x+e^x+1\right )^2}dx}{3 \log (\log (4))}\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \frac {\int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} \left (3 x^4-23 x^3+2 (21+\log (\log (4))) x^2+25 x+3 e^{2 x}+e^x \left (-7 x^2-2 \log (\log (4)) x+25 x+2 (3+\log (\log (4)))\right )+3 \left (1+\frac {2}{3} \log (\log (4))\right )\right )}{\left (-x^2+4 x+e^x+1\right )^2}dx}{3 \log (\log (4))}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {\int \left (\frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} (x-1) (x+2 \log (\log (4)))}{x^2-4 x-e^x-1}-\frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x \left (x^2-6 x+3\right ) (x+2 \log (\log (4)))}{\left (x^2-4 x-e^x-1\right )^2}+3 e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}}\right )dx}{3 \log (\log (4))}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {3 \int e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}}dx+\int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x^2}{x^2-4 x-e^x-1}dx+2 \log (\log (4)) \int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}}}{-x^2+4 x+e^x+1}dx-6 \log (\log (4)) \int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x}{\left (x^2-4 x-e^x-1\right )^2}dx-3 (1-4 \log (\log (4))) \int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x^2}{\left (x^2-4 x-e^x-1\right )^2}dx-(1-2 \log (\log (4))) \int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x}{x^2-4 x-e^x-1}dx-\int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x^4}{\left (x^2-4 x-e^x-1\right )^2}dx+2 (3-\log (\log (4))) \int \frac {e^{\frac {x}{3 \left (-x^2+4 x+e^x+1\right )}} x^3}{\left (x^2-4 x-e^x-1\right )^2}dx}{3 \log (\log (4))}\) |
Input:
Int[(E^((x + (3 + 3*E^x + 12*x - 3*x^2)*Log[(x + 2*Log[Log[4]])/Log[Log[4] ]])/(3 + 3*E^x + 12*x - 3*x^2))*(3 + 3*E^(2*x) + 25*x + 42*x^2 - 23*x^3 + 3*x^4 + E^x*(6 + 25*x - 7*x^2) + (2 + E^x*(2 - 2*x) + 2*x^2)*Log[Log[4]])) /(3*x + 3*E^(2*x)*x + 24*x^2 + 42*x^3 - 24*x^4 + 3*x^5 + E^x*(6*x + 24*x^2 - 6*x^3) + (6 + 6*E^(2*x) + 48*x + 84*x^2 - 48*x^3 + 6*x^4 + E^x*(12 + 48 *x - 12*x^2))*Log[Log[4]]),x]
Output:
$Aborted
Time = 91.43 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left (3 \,{\mathrm e}^{x}-3 x^{2}+12 x +3\right ) \ln \left (\frac {2 \ln \left (2 \ln \left (2\right )\right )+x}{\ln \left (2 \ln \left (2\right )\right )}\right )+x}{3 \,{\mathrm e}^{x}-3 x^{2}+12 x +3}}\) | \(53\) |
| risch | \({\mathrm e}^{\frac {-3 \ln \left (\frac {2 \ln \left (2\right )+2 \ln \left (\ln \left (2\right )\right )+x}{\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )}\right ) x^{2}+3 \,{\mathrm e}^{x} \ln \left (\frac {2 \ln \left (2\right )+2 \ln \left (\ln \left (2\right )\right )+x}{\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )}\right )+12 \ln \left (\frac {2 \ln \left (2\right )+2 \ln \left (\ln \left (2\right )\right )+x}{\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )}\right ) x +3 \ln \left (\frac {2 \ln \left (2\right )+2 \ln \left (\ln \left (2\right )\right )+x}{\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )}\right )+x}{3 \,{\mathrm e}^{x}-3 x^{2}+12 x +3}}\) | \(118\) |
Input:
int((((2-2*x)*exp(x)+2*x^2+2)*ln(2*ln(2))+3*exp(x)^2+(-7*x^2+25*x+6)*exp(x )+3*x^4-23*x^3+42*x^2+25*x+3)*exp(((3*exp(x)-3*x^2+12*x+3)*ln((2*ln(2*ln(2 ))+x)/ln(2*ln(2)))+x)/(3*exp(x)-3*x^2+12*x+3))/((6*exp(x)^2+(-12*x^2+48*x+ 12)*exp(x)+6*x^4-48*x^3+84*x^2+48*x+6)*ln(2*ln(2))+3*x*exp(x)^2+(-6*x^3+24 *x^2+6*x)*exp(x)+3*x^5-24*x^4+42*x^3+24*x^2+3*x),x,method=_RETURNVERBOSE)
Output:
exp(1/3/(-x^2+exp(x)+4*x+1)*((3*exp(x)-3*x^2+12*x+3)*ln((2*ln(2*ln(2))+x)/ ln(2*ln(2)))+x))
Time = 0.10 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51 \[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=e^{\left (\frac {3 \, {\left (x^{2} - 4 \, x - e^{x} - 1\right )} \log \left (\frac {x + 2 \, \log \left (2 \, \log \left (2\right )\right )}{\log \left (2 \, \log \left (2\right )\right )}\right ) - x}{3 \, {\left (x^{2} - 4 \, x - e^{x} - 1\right )}}\right )} \] Input:
integrate((((2-2*x)*exp(x)+2*x^2+2)*log(2*log(2))+3*exp(x)^2+(-7*x^2+25*x+ 6)*exp(x)+3*x^4-23*x^3+42*x^2+25*x+3)*exp(((3*exp(x)-3*x^2+12*x+3)*log((2* log(2*log(2))+x)/log(2*log(2)))+x)/(3*exp(x)-3*x^2+12*x+3))/((6*exp(x)^2+( -12*x^2+48*x+12)*exp(x)+6*x^4-48*x^3+84*x^2+48*x+6)*log(2*log(2))+3*x*exp( x)^2+(-6*x^3+24*x^2+6*x)*exp(x)+3*x^5-24*x^4+42*x^3+24*x^2+3*x),x, algorit hm="fricas")
Output:
e^(1/3*(3*(x^2 - 4*x - e^x - 1)*log((x + 2*log(2*log(2)))/log(2*log(2))) - x)/(x^2 - 4*x - e^x - 1))
Time = 3.53 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.46 \[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=e^{\frac {x + \left (- 3 x^{2} + 12 x + 3 e^{x} + 3\right ) \log {\left (\frac {x + 2 \log {\left (2 \log {\left (2 \right )} \right )}}{\log {\left (2 \log {\left (2 \right )} \right )}} \right )}}{- 3 x^{2} + 12 x + 3 e^{x} + 3}} \] Input:
integrate((((2-2*x)*exp(x)+2*x**2+2)*ln(2*ln(2))+3*exp(x)**2+(-7*x**2+25*x +6)*exp(x)+3*x**4-23*x**3+42*x**2+25*x+3)*exp(((3*exp(x)-3*x**2+12*x+3)*ln ((2*ln(2*ln(2))+x)/ln(2*ln(2)))+x)/(3*exp(x)-3*x**2+12*x+3))/((6*exp(x)**2 +(-12*x**2+48*x+12)*exp(x)+6*x**4-48*x**3+84*x**2+48*x+6)*ln(2*ln(2))+3*x* exp(x)**2+(-6*x**3+24*x**2+6*x)*exp(x)+3*x**5-24*x**4+42*x**3+24*x**2+3*x) ,x)
Output:
exp((x + (-3*x**2 + 12*x + 3*exp(x) + 3)*log((x + 2*log(2*log(2)))/log(2*l og(2))))/(-3*x**2 + 12*x + 3*exp(x) + 3))
Time = 0.60 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.09 \[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=\frac {{\left (x + 2 \, \log \left (2\right ) + 2 \, \log \left (\log \left (2\right )\right )\right )} e^{\left (-\frac {x}{3 \, {\left (x^{2} - 4 \, x - e^{x} - 1\right )}}\right )}}{\log \left (2\right ) + \log \left (\log \left (2\right )\right )} \] Input:
integrate((((2-2*x)*exp(x)+2*x^2+2)*log(2*log(2))+3*exp(x)^2+(-7*x^2+25*x+ 6)*exp(x)+3*x^4-23*x^3+42*x^2+25*x+3)*exp(((3*exp(x)-3*x^2+12*x+3)*log((2* log(2*log(2))+x)/log(2*log(2)))+x)/(3*exp(x)-3*x^2+12*x+3))/((6*exp(x)^2+( -12*x^2+48*x+12)*exp(x)+6*x^4-48*x^3+84*x^2+48*x+6)*log(2*log(2))+3*x*exp( x)^2+(-6*x^3+24*x^2+6*x)*exp(x)+3*x^5-24*x^4+42*x^3+24*x^2+3*x),x, algorit hm="maxima")
Output:
(x + 2*log(2) + 2*log(log(2)))*e^(-1/3*x/(x^2 - 4*x - e^x - 1))/(log(2) + log(log(2)))
\[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=\int { \frac {{\left (3 \, x^{4} - 23 \, x^{3} + 42 \, x^{2} - {\left (7 \, x^{2} - 25 \, x - 6\right )} e^{x} + 2 \, {\left (x^{2} - {\left (x - 1\right )} e^{x} + 1\right )} \log \left (2 \, \log \left (2\right )\right ) + 25 \, x + 3 \, e^{\left (2 \, x\right )} + 3\right )} e^{\left (\frac {3 \, {\left (x^{2} - 4 \, x - e^{x} - 1\right )} \log \left (\frac {x + 2 \, \log \left (2 \, \log \left (2\right )\right )}{\log \left (2 \, \log \left (2\right )\right )}\right ) - x}{3 \, {\left (x^{2} - 4 \, x - e^{x} - 1\right )}}\right )}}{3 \, {\left (x^{5} - 8 \, x^{4} + 14 \, x^{3} + 8 \, x^{2} + x e^{\left (2 \, x\right )} - 2 \, {\left (x^{3} - 4 \, x^{2} - x\right )} e^{x} + 2 \, {\left (x^{4} - 8 \, x^{3} + 14 \, x^{2} - 2 \, {\left (x^{2} - 4 \, x - 1\right )} e^{x} + 8 \, x + e^{\left (2 \, x\right )} + 1\right )} \log \left (2 \, \log \left (2\right )\right ) + x\right )}} \,d x } \] Input:
integrate((((2-2*x)*exp(x)+2*x^2+2)*log(2*log(2))+3*exp(x)^2+(-7*x^2+25*x+ 6)*exp(x)+3*x^4-23*x^3+42*x^2+25*x+3)*exp(((3*exp(x)-3*x^2+12*x+3)*log((2* log(2*log(2))+x)/log(2*log(2)))+x)/(3*exp(x)-3*x^2+12*x+3))/((6*exp(x)^2+( -12*x^2+48*x+12)*exp(x)+6*x^4-48*x^3+84*x^2+48*x+6)*log(2*log(2))+3*x*exp( x)^2+(-6*x^3+24*x^2+6*x)*exp(x)+3*x^5-24*x^4+42*x^3+24*x^2+3*x),x, algorit hm="giac")
Output:
undef
Timed out. \[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=\int \frac {{\mathrm {e}}^{\frac {x+\ln \left (\frac {x+2\,\ln \left (2\,\ln \left (2\right )\right )}{\ln \left (2\,\ln \left (2\right )\right )}\right )\,\left (12\,x+3\,{\mathrm {e}}^x-3\,x^2+3\right )}{12\,x+3\,{\mathrm {e}}^x-3\,x^2+3}}\,\left (25\,x+3\,{\mathrm {e}}^{2\,x}+\ln \left (2\,\ln \left (2\right )\right )\,\left (2\,x^2-{\mathrm {e}}^x\,\left (2\,x-2\right )+2\right )+{\mathrm {e}}^x\,\left (-7\,x^2+25\,x+6\right )+42\,x^2-23\,x^3+3\,x^4+3\right )}{3\,x+3\,x\,{\mathrm {e}}^{2\,x}+\ln \left (2\,\ln \left (2\right )\right )\,\left (48\,x+6\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (-12\,x^2+48\,x+12\right )+84\,x^2-48\,x^3+6\,x^4+6\right )+24\,x^2+42\,x^3-24\,x^4+3\,x^5+{\mathrm {e}}^x\,\left (-6\,x^3+24\,x^2+6\,x\right )} \,d x \] Input:
int((exp((x + log((x + 2*log(2*log(2)))/log(2*log(2)))*(12*x + 3*exp(x) - 3*x^2 + 3))/(12*x + 3*exp(x) - 3*x^2 + 3))*(25*x + 3*exp(2*x) + log(2*log( 2))*(2*x^2 - exp(x)*(2*x - 2) + 2) + exp(x)*(25*x - 7*x^2 + 6) + 42*x^2 - 23*x^3 + 3*x^4 + 3))/(3*x + 3*x*exp(2*x) + log(2*log(2))*(48*x + 6*exp(2*x ) + exp(x)*(48*x - 12*x^2 + 12) + 84*x^2 - 48*x^3 + 6*x^4 + 6) + 24*x^2 + 42*x^3 - 24*x^4 + 3*x^5 + exp(x)*(6*x + 24*x^2 - 6*x^3)),x)
Output:
int((exp((x + log((x + 2*log(2*log(2)))/log(2*log(2)))*(12*x + 3*exp(x) - 3*x^2 + 3))/(12*x + 3*exp(x) - 3*x^2 + 3))*(25*x + 3*exp(2*x) + log(2*log( 2))*(2*x^2 - exp(x)*(2*x - 2) + 2) + exp(x)*(25*x - 7*x^2 + 6) + 42*x^2 - 23*x^3 + 3*x^4 + 3))/(3*x + 3*x*exp(2*x) + log(2*log(2))*(48*x + 6*exp(2*x ) + exp(x)*(48*x - 12*x^2 + 12) + 84*x^2 - 48*x^3 + 6*x^4 + 6) + 24*x^2 + 42*x^3 - 24*x^4 + 3*x^5 + exp(x)*(6*x + 24*x^2 - 6*x^3)), x)
\[ \int \frac {e^{\frac {x+\left (3+3 e^x+12 x-3 x^2\right ) \log \left (\frac {x+2 \log (\log (4))}{\log (\log (4))}\right )}{3+3 e^x+12 x-3 x^2}} \left (3+3 e^{2 x}+25 x+42 x^2-23 x^3+3 x^4+e^x \left (6+25 x-7 x^2\right )+\left (2+e^x (2-2 x)+2 x^2\right ) \log (\log (4))\right )}{3 x+3 e^{2 x} x+24 x^2+42 x^3-24 x^4+3 x^5+e^x \left (6 x+24 x^2-6 x^3\right )+\left (6+6 e^{2 x}+48 x+84 x^2-48 x^3+6 x^4+e^x \left (12+48 x-12 x^2\right )\right ) \log (\log (4))} \, dx=\text {too large to display} \] Input:
int((((2-2*x)*exp(x)+2*x^2+2)*log(2*log(2))+3*exp(x)^2+(-7*x^2+25*x+6)*exp (x)+3*x^4-23*x^3+42*x^2+25*x+3)*exp(((3*exp(x)-3*x^2+12*x+3)*log((2*log(2* log(2))+x)/log(2*log(2)))+x)/(3*exp(x)-3*x^2+12*x+3))/((6*exp(x)^2+(-12*x^ 2+48*x+12)*exp(x)+6*x^4-48*x^3+84*x^2+48*x+6)*log(2*log(2))+3*x*exp(x)^2+( -6*x^3+24*x^2+6*x)*exp(x)+3*x^5-24*x^4+42*x^3+24*x^2+3*x),x)
Output:
(54*e**((3*e**x*x - 3*x**3 + 12*x**2 + 4*x)/(3*e**x - 3*x**2 + 12*x + 3))* log(2*log(2)) + 81*e**((3*e**x*x - 3*x**3 + 12*x**2 + 4*x)/(3*e**x - 3*x** 2 + 12*x + 3)) - 54*e**(x/(3*e**x - 3*x**2 + 12*x + 3))*log(2*log(2))*x**2 + 198*e**(x/(3*e**x - 3*x**2 + 12*x + 3))*log(2*log(2))*x + 48*e**(x/(3*e **x - 3*x**2 + 12*x + 3))*log(2*log(2)) - 81*e**(x/(3*e**x - 3*x**2 + 12*x + 3))*x**2 + 297*e**(x/(3*e**x - 3*x**2 + 12*x + 3))*x + 72*e**(x/(3*e**x - 3*x**2 + 12*x + 3)) - 6*e**x*int(e**((6*e**x*x - 6*x**3 + 24*x**2 + 7*x )/(3*e**x - 3*x**2 + 12*x + 3))/(e**(3*x) - 3*e**(2*x)*x**2 + 12*e**(2*x)* x + 3*e**(2*x) + 3*e**x*x**4 - 24*e**x*x**3 + 42*e**x*x**2 + 24*e**x*x + 3 *e**x - x**6 + 12*x**5 - 45*x**4 + 40*x**3 + 45*x**2 + 12*x + 1),x)*log(2* log(2)) - 9*e**x*int(e**((6*e**x*x - 6*x**3 + 24*x**2 + 7*x)/(3*e**x - 3*x **2 + 12*x + 3))/(e**(3*x) - 3*e**(2*x)*x**2 + 12*e**(2*x)*x + 3*e**(2*x) + 3*e**x*x**4 - 24*e**x*x**3 + 42*e**x*x**2 + 24*e**x*x + 3*e**x - x**6 + 12*x**5 - 45*x**4 + 40*x**3 + 45*x**2 + 12*x + 1),x) + 42*e**x*int(e**((6* e**x*x - 6*x**3 + 24*x**2 + 7*x)/(3*e**x - 3*x**2 + 12*x + 3))/(e**(2*x) - 2*e**x*x**2 + 8*e**x*x + 2*e**x + x**4 - 8*x**3 + 14*x**2 + 8*x + 1),x) + 28*e**x*int(e**((3*e**x*x - 3*x**3 + 12*x**2 + 4*x)/(3*e**x - 3*x**2 + 12 *x + 3))/(e**(2*x) - 2*e**x*x**2 + 8*e**x*x + 2*e**x + x**4 - 8*x**3 + 14* x**2 + 8*x + 1),x)*log(2*log(2)) + 84*e**x*int(e**((3*e**x*x - 3*x**3 + 12 *x**2 + 4*x)/(3*e**x - 3*x**2 + 12*x + 3))/(e**(2*x) - 2*e**x*x**2 + 8*...