Integrand size = 63, antiderivative size = 24 \[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=e^{e^{e^{e^{e^x}+x^2+5 \left (-x+x^2\right )}}} \] Output:
exp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)))
Time = 0.74 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=e^{e^{e^{e^{e^x}-5 x+6 x^2}}} \] Input:
Integrate[E^(E^E^x + E^E^(E^E^x - 5*x + 6*x^2) + E^(E^E^x - 5*x + 6*x^2) - 5*x + 6*x^2)*(-5 + E^(E^x + x) + 12*x),x]
Output:
E^E^E^(E^E^x - 5*x + 6*x^2)
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.
\(\displaystyle \int \left (12 x+e^{x+e^x}-5\right ) \exp \left (6 x^2+e^{e^{6 x^2-5 x+e^{e^x}}}+e^{6 x^2-5 x+e^{e^x}}-5 x+e^{e^x}\right ) \, dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (12 x \exp \left (6 x^2+e^{e^{6 x^2-5 x+e^{e^x}}}+e^{6 x^2-5 x+e^{e^x}}-5 x+e^{e^x}\right )-5 \exp \left (6 x^2+e^{e^{6 x^2-5 x+e^{e^x}}}+e^{6 x^2-5 x+e^{e^x}}-5 x+e^{e^x}\right )+\exp \left (6 x^2+e^{e^{6 x^2-5 x+e^{e^x}}}+e^{6 x^2-5 x+e^{e^x}}-4 x+e^{e^x}+e^x\right )\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -5 \int \exp \left (6 x^2-5 x+e^{e^x}+e^{e^{6 x^2-5 x+e^{e^x}}}+e^{6 x^2-5 x+e^{e^x}}\right )dx+\int \exp \left (6 x^2-4 x+e^{e^x}+e^{e^{6 x^2-5 x+e^{e^x}}}+e^x+e^{6 x^2-5 x+e^{e^x}}\right )dx+12 \int \exp \left (6 x^2-5 x+e^{e^x}+e^{e^{6 x^2-5 x+e^{e^x}}}+e^{6 x^2-5 x+e^{e^x}}\right ) xdx\) |
Input:
Int[E^(E^E^x + E^E^(E^E^x - 5*x + 6*x^2) + E^(E^E^x - 5*x + 6*x^2) - 5*x + 6*x^2)*(-5 + E^(E^x + x) + 12*x),x]
Output:
$Aborted
Time = 0.56 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}+6 x^{2}-5 x}}}\) | \(16\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}+6 x^{2}-5 x}}}\) | \(20\) |
default | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}+6 x^{2}-5 x}}}\) | \(20\) |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}+6 x^{2}-5 x}}}\) | \(20\) |
Input:
int((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*exp(exp (1/exp(-exp(exp(x))-6*x^2+5*x)))/exp(-exp(exp(x))-6*x^2+5*x),x,method=_RET URNVERBOSE)
Output:
exp(exp(exp(exp(exp(x))+6*x^2-5*x)))
Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (15) = 30\).
Time = 0.11 (sec) , antiderivative size = 128, normalized size of antiderivative = 5.33 \[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + x\right )} + e^{\left (x + e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )}\right )} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} - {\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} - e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )}\right )} \] Input:
integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*e xp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)))/exp(-exp(exp(x))-6*x^2+5*x),x, algo rithm="fricas")
Output:
e^(((6*x^2 - 5*x)*e^x + e^(((6*x^2 - 5*x)*e^x + e^(x + e^x))*e^(-x) + x) + e^(x + e^(((6*x^2 - 5*x)*e^x + e^(x + e^x))*e^(-x))) + e^(x + e^x))*e^(-x ) - ((6*x^2 - 5*x)*e^x + e^(x + e^x))*e^(-x) - e^(((6*x^2 - 5*x)*e^x + e^( x + e^x))*e^(-x)))
Time = 26.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=e^{e^{e^{6 x^{2} - 5 x + e^{e^{x}}}}} \] Input:
integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x**2+5*x))* exp(exp(1/exp(-exp(exp(x))-6*x**2+5*x)))/exp(-exp(exp(x))-6*x**2+5*x),x)
Output:
exp(exp(exp(6*x**2 - 5*x + exp(exp(x)))))
Time = 0.45 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62 \[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=e^{\left (e^{\left (e^{\left (6 \, x^{2} - 5 \, x + e^{\left (e^{x}\right )}\right )}\right )}\right )} \] Input:
integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*e xp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)))/exp(-exp(exp(x))-6*x^2+5*x),x, algo rithm="maxima")
Output:
e^(e^(e^(6*x^2 - 5*x + e^(e^x))))
\[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=\int { {\left (12 \, x + e^{\left (x + e^{x}\right )} - 5\right )} e^{\left (6 \, x^{2} - 5 \, x + e^{\left (6 \, x^{2} - 5 \, x + e^{\left (e^{x}\right )}\right )} + e^{\left (e^{\left (6 \, x^{2} - 5 \, x + e^{\left (e^{x}\right )}\right )}\right )} + e^{\left (e^{x}\right )}\right )} \,d x } \] Input:
integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*e xp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)))/exp(-exp(exp(x))-6*x^2+5*x),x, algo rithm="giac")
Output:
integrate((12*x + e^(x + e^x) - 5)*e^(6*x^2 - 5*x + e^(6*x^2 - 5*x + e^(e^ x)) + e^(e^(6*x^2 - 5*x + e^(e^x))) + e^(e^x)), x)
Time = 4.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx={\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{6\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}} \] Input:
int(exp(exp(exp(x)) - 5*x + 6*x^2)*exp(exp(exp(exp(x)) - 5*x + 6*x^2))*exp (exp(exp(exp(exp(x)) - 5*x + 6*x^2)))*(12*x + exp(exp(x))*exp(x) - 5),x)
Output:
exp(exp(exp(-5*x)*exp(6*x^2)*exp(exp(exp(x)))))
\[ \int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} \left (-5+e^{e^x+x}+12 x\right ) \, dx=\int \frac {e^{\frac {e^{e^{e^{x}}+6 x^{2}}+e^{e^{x}+5 x}+e^{\frac {e^{e^{e^{x}}+6 x^{2}}+5 e^{5 x} x}{e^{5 x}}}+e^{6 x}+6 e^{5 x} x^{2}}{e^{5 x}}}}{e^{4 x}}d x -5 \left (\int \frac {e^{\frac {e^{e^{e^{x}}+6 x^{2}}+e^{e^{x}+5 x}+e^{\frac {e^{e^{e^{x}}+6 x^{2}}+5 e^{5 x} x}{e^{5 x}}}+6 e^{5 x} x^{2}}{e^{5 x}}}}{e^{5 x}}d x \right )+12 \left (\int \frac {e^{\frac {e^{e^{e^{x}}+6 x^{2}}+e^{e^{x}+5 x}+e^{\frac {e^{e^{e^{x}}+6 x^{2}}+5 e^{5 x} x}{e^{5 x}}}+6 e^{5 x} x^{2}}{e^{5 x}}} x}{e^{5 x}}d x \right ) \] Input:
int((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*exp(exp (1/exp(-exp(exp(x))-6*x^2+5*x)))/exp(-exp(exp(x))-6*x^2+5*x),x)
Output:
int(e**((e**(e**(e**x) + 6*x**2) + e**(e**x + 5*x) + e**((e**(e**(e**x) + 6*x**2) + 5*e**(5*x)*x)/e**(5*x)) + e**(6*x) + 6*e**(5*x)*x**2)/e**(5*x))/ e**(4*x),x) - 5*int(e**((e**(e**(e**x) + 6*x**2) + e**(e**x + 5*x) + e**(( e**(e**(e**x) + 6*x**2) + 5*e**(5*x)*x)/e**(5*x)) + 6*e**(5*x)*x**2)/e**(5 *x))/e**(5*x),x) + 12*int((e**((e**(e**(e**x) + 6*x**2) + e**(e**x + 5*x) + e**((e**(e**(e**x) + 6*x**2) + 5*e**(5*x)*x)/e**(5*x)) + 6*e**(5*x)*x**2 )/e**(5*x))*x)/e**(5*x),x)