Integrand size = 79, antiderivative size = 30 \[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=-2-2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \] Output:
-2-exp(ln(2*exp(exp(exp(3)*exp(exp(6+x)))))/(-2+x))
\[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=\int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx \] Input:
Integrate[(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)*(E^(9 + E ^(3 + E^(6 + x)) + E^(6 + x) + x)*(2 - x) + Log[2*E^E^E^(3 + E^(6 + x))])) /(4 - 4*x + x^2),x]
Output:
Integrate[(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)*(E^(9 + E ^(3 + E^(6 + x)) + E^(6 + x) + x)*(2 - x) + Log[2*E^E^E^(3 + E^(6 + x))])) /(4 - 4*x + x^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.
\(\displaystyle \int \frac {2^{\frac {1}{x-2}} \left (e^{e^{e^{e^{x+6}+3}}}\right )^{\frac {1}{x-2}} \left (e^{x+e^{e^{x+6}+3}+e^{x+6}+9} (2-x)+\log \left (2 e^{e^{e^{e^{x+6}+3}}}\right )\right )}{x^2-4 x+4} \, dx\) |
\(\Big \downarrow \) 7277 |
\(\displaystyle 4 \int \frac {2^{\frac {1}{x-2}-2} \left (e^{e^{e^{3+e^{x+6}}}}\right )^{\frac {1}{x-2}} \left (e^{x+e^{3+e^{x+6}}+e^{x+6}+9} (2-x)+\log \left (2 e^{e^{e^{3+e^{x+6}}}}\right )\right )}{(2-x)^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle 4 \int \left (\frac {2^{\frac {1}{x-2}-2} \left (e^{e^{e^{3+e^{x+6}}}}\right )^{\frac {1}{x-2}} \log \left (2 e^{e^{e^{3+e^{x+6}}}}\right )}{(x-2)^2}-\frac {2^{\frac {1}{x-2}-2} e^{x+e^{3+e^{x+6}}+e^{x+6}+9} \left (e^{e^{e^{3+e^{x+6}}}}\right )^{\frac {1}{x-2}}}{x-2}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle 4 \left (-\int \frac {2^{\frac {1}{x-2}-2} e^{x+e^{3+e^{x+6}}+e^{x+6}+9} \left (e^{e^{e^{3+e^{x+6}}}}\right )^{\frac {1}{x-2}}}{x-2}dx-\int e^{x+e^{3+e^{x+6}}+e^{x+6}+9} \int \frac {2^{\frac {1}{x-2}-2} \left (e^{e^{e^{3+e^{x+6}}}}\right )^{\frac {1}{x-2}}}{(x-2)^2}dxdx+\log \left (2 e^{e^{e^{e^{x+6}+3}}}\right ) \int \frac {2^{\frac {1}{x-2}-2} \left (e^{e^{e^{3+e^{x+6}}}}\right )^{\frac {1}{x-2}}}{(x-2)^2}dx\right )\) |
Input:
Int[(2^(-2 + x)^(-1)*(E^E^E^(3 + E^(6 + x)))^(-2 + x)^(-1)*(E^(9 + E^(3 + E^(6 + x)) + E^(6 + x) + x)*(2 - x) + Log[2*E^E^E^(3 + E^(6 + x))]))/(4 - 4*x + x^2),x]
Output:
$Aborted
Time = 0.23 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83
\[-2^{\frac {1}{-2+x}} \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{3+{\mathrm e}^{6+x}}}}\right )^{\frac {1}{-2+x}}\]
Input:
int((ln(2*exp(exp(exp(3)*exp(exp(6+x)))))+(2-x)*exp(3)*exp(6+x)*exp(exp(6+ x))*exp(exp(3)*exp(exp(6+x))))*exp(ln(2*exp(exp(exp(3)*exp(exp(6+x)))))/(- 2+x))/(x^2-4*x+4),x)
Output:
-2^(1/(-2+x))*exp(exp(exp(3+exp(6+x))))^(1/(-2+x))
Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (21) = 42\).
Time = 0.09 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.60 \[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=-e^{\left (\frac {{\left (e^{\left (x + e^{\left (x + 6\right )} + 9\right )} \log \left (2\right ) + e^{\left (x + e^{\left (x + 6\right )} + e^{\left (e^{\left (x + 6\right )} + 3\right )} + 9\right )}\right )} e^{\left (-x - e^{\left (x + 6\right )} - 9\right )}}{x - 2}\right )} \] Input:
integrate((log(2*exp(exp(exp(3)*exp(exp(6+x)))))+(2-x)*exp(3)*exp(6+x)*exp (exp(6+x))*exp(exp(3)*exp(exp(6+x))))*exp(log(2*exp(exp(exp(3)*exp(exp(6+x )))))/(-2+x))/(x^2-4*x+4),x, algorithm="fricas")
Output:
-e^((e^(x + e^(x + 6) + 9)*log(2) + e^(x + e^(x + 6) + e^(e^(x + 6) + 3) + 9))*e^(-x - e^(x + 6) - 9)/(x - 2))
Timed out. \[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=\text {Timed out} \] Input:
integrate((ln(2*exp(exp(exp(3)*exp(exp(6+x)))))+(2-x)*exp(3)*exp(6+x)*exp( exp(6+x))*exp(exp(3)*exp(exp(6+x))))*exp(ln(2*exp(exp(exp(3)*exp(exp(6+x)) )))/(-2+x))/(x**2-4*x+4),x)
Output:
Timed out
Time = 0.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=-e^{\left (\frac {e^{\left (e^{\left (e^{\left (x + 6\right )} + 3\right )}\right )}}{x - 2} + \frac {\log \left (2\right )}{x - 2}\right )} \] Input:
integrate((log(2*exp(exp(exp(3)*exp(exp(6+x)))))+(2-x)*exp(3)*exp(6+x)*exp (exp(6+x))*exp(exp(3)*exp(exp(6+x))))*exp(log(2*exp(exp(exp(3)*exp(exp(6+x )))))/(-2+x))/(x^2-4*x+4),x, algorithm="maxima")
Output:
-e^(e^(e^(e^(x + 6) + 3))/(x - 2) + log(2)/(x - 2))
\[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=\int { -\frac {{\left ({\left (x - 2\right )} e^{\left (x + e^{\left (x + 6\right )} + e^{\left (e^{\left (x + 6\right )} + 3\right )} + 9\right )} - \log \left (2 \, e^{\left (e^{\left (e^{\left (e^{\left (x + 6\right )} + 3\right )}\right )}\right )}\right )\right )} \left (2 \, e^{\left (e^{\left (e^{\left (e^{\left (x + 6\right )} + 3\right )}\right )}\right )}\right )^{\left (\frac {1}{x - 2}\right )}}{x^{2} - 4 \, x + 4} \,d x } \] Input:
integrate((log(2*exp(exp(exp(3)*exp(exp(6+x)))))+(2-x)*exp(3)*exp(6+x)*exp (exp(6+x))*exp(exp(3)*exp(exp(6+x))))*exp(log(2*exp(exp(exp(3)*exp(exp(6+x )))))/(-2+x))/(x^2-4*x+4),x, algorithm="giac")
Output:
integrate(-((x - 2)*e^(x + e^(x + 6) + e^(e^(x + 6) + 3) + 9) - log(2*e^(e ^(e^(e^(x + 6) + 3)))))*(2*e^(e^(e^(e^(x + 6) + 3))))^(1/(x - 2))/(x^2 - 4 *x + 4), x)
Time = 3.32 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=-2^{\frac {1}{x-2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^6\,{\mathrm {e}}^x}\,{\mathrm {e}}^3}}{x-2}} \] Input:
int((exp(log(2*exp(exp(exp(3)*exp(exp(x + 6)))))/(x - 2))*(log(2*exp(exp(e xp(3)*exp(exp(x + 6))))) - exp(x + 6)*exp(3)*exp(exp(x + 6))*exp(exp(3)*ex p(exp(x + 6)))*(x - 2)))/(x^2 - 4*x + 4),x)
Output:
-2^(1/(x - 2))*exp(exp(exp(exp(6)*exp(x))*exp(3))/(x - 2))
Time = 0.23 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {2^{\frac {1}{-2+x}} \left (e^{e^{e^{3+e^{6+x}}}}\right )^{\frac {1}{-2+x}} \left (e^{9+e^{3+e^{6+x}}+e^{6+x}+x} (2-x)+\log \left (2 e^{e^{e^{3+e^{6+x}}}}\right )\right )}{4-4 x+x^2} \, dx=-e^{\frac {\mathrm {log}\left (2 e^{e^{e^{e^{x} e^{6}} e^{3}}}\right )}{x -2}} \] Input:
int((log(2*exp(exp(exp(3)*exp(exp(6+x)))))+(2-x)*exp(3)*exp(6+x)*exp(exp(6 +x))*exp(exp(3)*exp(exp(6+x))))*exp(log(2*exp(exp(exp(3)*exp(exp(6+x)))))/ (-2+x))/(x^2-4*x+4),x)
Output:
- e**(log(2*e**(e**(e**(e**x*e**6)*e**3)))/(x - 2))