Integrand size = 193, antiderivative size = 25 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=e^{e^{2 x}} \left (2+\frac {x}{-3+3 \log \left (\log \left (9+x^2\right )\right )}\right ) \] Output:
exp(exp(2*x))*(2+x/(3*ln(ln(x^2+9))-3))
Time = 0.07 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\frac {1}{3} e^{e^{2 x}} \left (6+\frac {x}{-1+\log \left (\log \left (9+x^2\right )\right )}\right ) \] Input:
Integrate[(E^E^(2*x)*(-2*x^2 + (-9 - x^2 + E^(2*x)*(108 - 18*x + 12*x^2 - 2*x^3))*Log[9 + x^2]) + E^E^(2*x)*(9 + x^2 + E^(2*x)*(-216 + 18*x - 24*x^2 + 2*x^3))*Log[9 + x^2]*Log[Log[9 + x^2]] + E^(E^(2*x) + 2*x)*(108 + 12*x^ 2)*Log[9 + x^2]*Log[Log[9 + x^2]]^2)/((27 + 3*x^2)*Log[9 + x^2] + (-54 - 6 *x^2)*Log[9 + x^2]*Log[Log[9 + x^2]] + (27 + 3*x^2)*Log[9 + x^2]*Log[Log[9 + x^2]]^2),x]
Output:
(E^E^(2*x)*(6 + x/(-1 + Log[Log[9 + x^2]])))/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.
| \(\displaystyle \int \frac {e^{2 x+e^{2 x}} \left (12 x^2+108\right ) \log \left (x^2+9\right ) \log ^2\left (\log \left (x^2+9\right )\right )+e^{e^{2 x}} \left (x^2+e^{2 x} \left (2 x^3-24 x^2+18 x-216\right )+9\right ) \log \left (x^2+9\right ) \log \left (\log \left (x^2+9\right )\right )+e^{e^{2 x}} \left (\left (-x^2+e^{2 x} \left (-2 x^3+12 x^2-18 x+108\right )-9\right ) \log \left (x^2+9\right )-2 x^2\right )}{\left (3 x^2+27\right ) \log \left (x^2+9\right ) \log ^2\left (\log \left (x^2+9\right )\right )+\left (-6 x^2-54\right ) \log \left (x^2+9\right ) \log \left (\log \left (x^2+9\right )\right )+\left (3 x^2+27\right ) \log \left (x^2+9\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{e^{2 x}} \left (\left (x^2+9\right ) \log \left (x^2+9\right ) \left (\log \left (\log \left (x^2+9\right )\right )-1\right ) \left (12 e^{2 x} \log \left (\log \left (x^2+9\right )\right )+2 e^{2 x} (x-6)+1\right )-2 x^2\right )}{3 \left (x^2+9\right ) \log \left (x^2+9\right ) \left (1-\log \left (\log \left (x^2+9\right )\right )\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int -\frac {e^{e^{2 x}} \left (2 x^2+\left (x^2+9\right ) \log \left (x^2+9\right ) \left (1-\log \left (\log \left (x^2+9\right )\right )\right ) \left (-2 e^{2 x} (6-x)+12 e^{2 x} \log \left (\log \left (x^2+9\right )\right )+1\right )\right )}{\left (x^2+9\right ) \log \left (x^2+9\right ) \left (1-\log \left (\log \left (x^2+9\right )\right )\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{3} \int \frac {e^{e^{2 x}} \left (2 x^2+\left (x^2+9\right ) \log \left (x^2+9\right ) \left (1-\log \left (\log \left (x^2+9\right )\right )\right ) \left (-2 e^{2 x} (6-x)+12 e^{2 x} \log \left (\log \left (x^2+9\right )\right )+1\right )\right )}{\left (x^2+9\right ) \log \left (x^2+9\right ) \left (1-\log \left (\log \left (x^2+9\right )\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7276 |
| \(\displaystyle -\frac {1}{3} \int \left (\frac {e^{e^{2 x}} \left (\log \left (x^2+9\right ) x^2-\log \left (x^2+9\right ) \log \left (\log \left (x^2+9\right )\right ) x^2+2 x^2+9 \log \left (x^2+9\right )-9 \log \left (x^2+9\right ) \log \left (\log \left (x^2+9\right )\right )\right )}{\left (x^2+9\right ) \log \left (x^2+9\right ) \left (\log \left (\log \left (x^2+9\right )\right )-1\right )^2}-\frac {2 e^{2 x+e^{2 x}} \left (x+6 \log \left (\log \left (x^2+9\right )\right )-6\right )}{\log \left (\log \left (x^2+9\right )\right )-1}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{3} \left (-\int \frac {e^{e^{2 x}}}{1-\log \left (\log \left (x^2+9\right )\right )}dx-2 \int \frac {e^{e^{2 x}}}{\log \left (x^2+9\right ) \left (\log \left (\log \left (x^2+9\right )\right )-1\right )^2}dx+3 i \int \frac {e^{e^{2 x}}}{(3 i-x) \log \left (x^2+9\right ) \left (\log \left (\log \left (x^2+9\right )\right )-1\right )^2}dx+3 i \int \frac {e^{e^{2 x}}}{(x+3 i) \log \left (x^2+9\right ) \left (\log \left (\log \left (x^2+9\right )\right )-1\right )^2}dx+2 \int \frac {e^{2 x+e^{2 x}} x}{\log \left (\log \left (x^2+9\right )\right )-1}dx+6 e^{e^{2 x}}\right )\) |
Input:
Int[(E^E^(2*x)*(-2*x^2 + (-9 - x^2 + E^(2*x)*(108 - 18*x + 12*x^2 - 2*x^3) )*Log[9 + x^2]) + E^E^(2*x)*(9 + x^2 + E^(2*x)*(-216 + 18*x - 24*x^2 + 2*x ^3))*Log[9 + x^2]*Log[Log[9 + x^2]] + E^(E^(2*x) + 2*x)*(108 + 12*x^2)*Log [9 + x^2]*Log[Log[9 + x^2]]^2)/((27 + 3*x^2)*Log[9 + x^2] + (-54 - 6*x^2)* Log[9 + x^2]*Log[Log[9 + x^2]] + (27 + 3*x^2)*Log[9 + x^2]*Log[Log[9 + x^2 ]]^2),x]
Output:
$Aborted
Time = 147.61 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12
| method | result | size |
| risch | \(2 \,{\mathrm e}^{{\mathrm e}^{2 x}}+\frac {x \,{\mathrm e}^{{\mathrm e}^{2 x}}}{3 \ln \left (\ln \left (x^{2}+9\right )\right )-3}\) | \(28\) |
| parallelrisch | \(\frac {18 x \,{\mathrm e}^{{\mathrm e}^{2 x}}+108 \ln \left (\ln \left (x^{2}+9\right )\right ) {\mathrm e}^{{\mathrm e}^{2 x}}-108 \,{\mathrm e}^{{\mathrm e}^{2 x}}}{54 \ln \left (\ln \left (x^{2}+9\right )\right )-54}\) | \(44\) |
Input:
int(((12*x^2+108)*exp(2*x)*ln(x^2+9)*exp(exp(2*x))*ln(ln(x^2+9))^2+((2*x^3 -24*x^2+18*x-216)*exp(2*x)+x^2+9)*ln(x^2+9)*exp(exp(2*x))*ln(ln(x^2+9))+(( (-2*x^3+12*x^2-18*x+108)*exp(2*x)-x^2-9)*ln(x^2+9)-2*x^2)*exp(exp(2*x)))/( (3*x^2+27)*ln(x^2+9)*ln(ln(x^2+9))^2+(-6*x^2-54)*ln(x^2+9)*ln(ln(x^2+9))+( 3*x^2+27)*ln(x^2+9)),x,method=_RETURNVERBOSE)
Output:
2*exp(exp(2*x))+1/3*x*exp(exp(2*x))/(ln(ln(x^2+9))-1)
Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (22) = 44\).
Time = 0.09 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.20 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\frac {{\left (x - 6\right )} e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )} + 6 \, e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )} \log \left (\log \left (x^{2} + 9\right )\right )}{3 \, {\left (e^{\left (2 \, x\right )} \log \left (\log \left (x^{2} + 9\right )\right ) - e^{\left (2 \, x\right )}\right )}} \] Input:
integrate(((12*x^2+108)*exp(2*x)*log(x^2+9)*exp(exp(2*x))*log(log(x^2+9))^ 2+((2*x^3-24*x^2+18*x-216)*exp(2*x)+x^2+9)*log(x^2+9)*exp(exp(2*x))*log(lo g(x^2+9))+(((-2*x^3+12*x^2-18*x+108)*exp(2*x)-x^2-9)*log(x^2+9)-2*x^2)*exp (exp(2*x)))/((3*x^2+27)*log(x^2+9)*log(log(x^2+9))^2+(-6*x^2-54)*log(x^2+9 )*log(log(x^2+9))+(3*x^2+27)*log(x^2+9)),x, algorithm="fricas")
Output:
1/3*((x - 6)*e^(2*x + e^(2*x)) + 6*e^(2*x + e^(2*x))*log(log(x^2 + 9)))/(e ^(2*x)*log(log(x^2 + 9)) - e^(2*x))
Time = 0.51 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\frac {\left (x + 6 \log {\left (\log {\left (x^{2} + 9 \right )} \right )} - 6\right ) e^{e^{2 x}}}{3 \log {\left (\log {\left (x^{2} + 9 \right )} \right )} - 3} \] Input:
integrate(((12*x**2+108)*exp(2*x)*ln(x**2+9)*exp(exp(2*x))*ln(ln(x**2+9))* *2+((2*x**3-24*x**2+18*x-216)*exp(2*x)+x**2+9)*ln(x**2+9)*exp(exp(2*x))*ln (ln(x**2+9))+(((-2*x**3+12*x**2-18*x+108)*exp(2*x)-x**2-9)*ln(x**2+9)-2*x* *2)*exp(exp(2*x)))/((3*x**2+27)*ln(x**2+9)*ln(ln(x**2+9))**2+(-6*x**2-54)* ln(x**2+9)*ln(ln(x**2+9))+(3*x**2+27)*ln(x**2+9)),x)
Output:
(x + 6*log(log(x**2 + 9)) - 6)*exp(exp(2*x))/(3*log(log(x**2 + 9)) - 3)
Time = 0.11 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.48 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\frac {{\left (x - 6\right )} e^{\left (e^{\left (2 \, x\right )}\right )} + 6 \, e^{\left (e^{\left (2 \, x\right )}\right )} \log \left (\log \left (x^{2} + 9\right )\right )}{3 \, {\left (\log \left (\log \left (x^{2} + 9\right )\right ) - 1\right )}} \] Input:
integrate(((12*x^2+108)*exp(2*x)*log(x^2+9)*exp(exp(2*x))*log(log(x^2+9))^ 2+((2*x^3-24*x^2+18*x-216)*exp(2*x)+x^2+9)*log(x^2+9)*exp(exp(2*x))*log(lo g(x^2+9))+(((-2*x^3+12*x^2-18*x+108)*exp(2*x)-x^2-9)*log(x^2+9)-2*x^2)*exp (exp(2*x)))/((3*x^2+27)*log(x^2+9)*log(log(x^2+9))^2+(-6*x^2-54)*log(x^2+9 )*log(log(x^2+9))+(3*x^2+27)*log(x^2+9)),x, algorithm="maxima")
Output:
1/3*((x - 6)*e^(e^(2*x)) + 6*e^(e^(2*x))*log(log(x^2 + 9)))/(log(log(x^2 + 9)) - 1)
Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (22) = 44\).
Time = 0.16 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.56 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\frac {x e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )} + 6 \, e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )} \log \left (\log \left (x^{2} + 9\right )\right ) - 6 \, e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )}}{3 \, {\left (e^{\left (2 \, x\right )} \log \left (\log \left (x^{2} + 9\right )\right ) - e^{\left (2 \, x\right )}\right )}} \] Input:
integrate(((12*x^2+108)*exp(2*x)*log(x^2+9)*exp(exp(2*x))*log(log(x^2+9))^ 2+((2*x^3-24*x^2+18*x-216)*exp(2*x)+x^2+9)*log(x^2+9)*exp(exp(2*x))*log(lo g(x^2+9))+(((-2*x^3+12*x^2-18*x+108)*exp(2*x)-x^2-9)*log(x^2+9)-2*x^2)*exp (exp(2*x)))/((3*x^2+27)*log(x^2+9)*log(log(x^2+9))^2+(-6*x^2-54)*log(x^2+9 )*log(log(x^2+9))+(3*x^2+27)*log(x^2+9)),x, algorithm="giac")
Output:
1/3*(x*e^(2*x + e^(2*x)) + 6*e^(2*x + e^(2*x))*log(log(x^2 + 9)) - 6*e^(2* x + e^(2*x)))/(e^(2*x)*log(log(x^2 + 9)) - e^(2*x))
Timed out. \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{2\,x+{\mathrm {e}}^{2\,x}}\,\ln \left (x^2+9\right )\,\left (12\,x^2+108\right )\,{\ln \left (\ln \left (x^2+9\right )\right )}^2+{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\ln \left (x^2+9\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (2\,x^3-24\,x^2+18\,x-216\right )+x^2+9\right )\,\ln \left (\ln \left (x^2+9\right )\right )-{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\left (\ln \left (x^2+9\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (2\,x^3-12\,x^2+18\,x-108\right )+x^2+9\right )+2\,x^2\right )}{\ln \left (x^2+9\right )\,\left (3\,x^2+27\right )\,{\ln \left (\ln \left (x^2+9\right )\right )}^2-\ln \left (x^2+9\right )\,\left (6\,x^2+54\right )\,\ln \left (\ln \left (x^2+9\right )\right )+\ln \left (x^2+9\right )\,\left (3\,x^2+27\right )} \,d x \] Input:
int((log(log(x^2 + 9))*exp(exp(2*x))*log(x^2 + 9)*(exp(2*x)*(18*x - 24*x^2 + 2*x^3 - 216) + x^2 + 9) - exp(exp(2*x))*(log(x^2 + 9)*(exp(2*x)*(18*x - 12*x^2 + 2*x^3 - 108) + x^2 + 9) + 2*x^2) + log(log(x^2 + 9))^2*exp(2*x)* exp(exp(2*x))*log(x^2 + 9)*(12*x^2 + 108))/(log(x^2 + 9)*(3*x^2 + 27) + lo g(log(x^2 + 9))^2*log(x^2 + 9)*(3*x^2 + 27) - log(log(x^2 + 9))*log(x^2 + 9)*(6*x^2 + 54)),x)
Output:
int((log(log(x^2 + 9))*exp(exp(2*x))*log(x^2 + 9)*(exp(2*x)*(18*x - 24*x^2 + 2*x^3 - 216) + x^2 + 9) - exp(exp(2*x))*(log(x^2 + 9)*(exp(2*x)*(18*x - 12*x^2 + 2*x^3 - 108) + x^2 + 9) + 2*x^2) + log(log(x^2 + 9))^2*exp(2*x + exp(2*x))*log(x^2 + 9)*(12*x^2 + 108))/(log(x^2 + 9)*(3*x^2 + 27) + log(l og(x^2 + 9))^2*log(x^2 + 9)*(3*x^2 + 27) - log(log(x^2 + 9))*log(x^2 + 9)* (6*x^2 + 54)), x)
Time = 0.21 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.32 \[ \int \frac {e^{e^{2 x}} \left (-2 x^2+\left (-9-x^2+e^{2 x} \left (108-18 x+12 x^2-2 x^3\right )\right ) \log \left (9+x^2\right )\right )+e^{e^{2 x}} \left (9+x^2+e^{2 x} \left (-216+18 x-24 x^2+2 x^3\right )\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+e^{e^{2 x}+2 x} \left (108+12 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )}{\left (27+3 x^2\right ) \log \left (9+x^2\right )+\left (-54-6 x^2\right ) \log \left (9+x^2\right ) \log \left (\log \left (9+x^2\right )\right )+\left (27+3 x^2\right ) \log \left (9+x^2\right ) \log ^2\left (\log \left (9+x^2\right )\right )} \, dx=\frac {e^{e^{2 x}} \left (6 \,\mathrm {log}\left (\mathrm {log}\left (x^{2}+9\right )\right )+x -6\right )}{3 \,\mathrm {log}\left (\mathrm {log}\left (x^{2}+9\right )\right )-3} \] Input:
int(((12*x^2+108)*exp(2*x)*log(x^2+9)*exp(exp(2*x))*log(log(x^2+9))^2+((2* x^3-24*x^2+18*x-216)*exp(2*x)+x^2+9)*log(x^2+9)*exp(exp(2*x))*log(log(x^2+ 9))+(((-2*x^3+12*x^2-18*x+108)*exp(2*x)-x^2-9)*log(x^2+9)-2*x^2)*exp(exp(2 *x)))/((3*x^2+27)*log(x^2+9)*log(log(x^2+9))^2+(-6*x^2-54)*log(x^2+9)*log( log(x^2+9))+(3*x^2+27)*log(x^2+9)),x)
Output:
(e**(e**(2*x))*(6*log(log(x**2 + 9)) + x - 6))/(3*(log(log(x**2 + 9)) - 1) )