Integrand size = 116, antiderivative size = 32 \[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx=e^{e^{x-3 (1+x) \left (-e^5+5 e^{2-e^{-4+x}+x}+x\right )}} \] Output:
exp(exp(x-3*(1+x)*(x+5*exp(-exp(-4+x)+2+x)-exp(5))))
Time = 0.26 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.19 \[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx=e^{e^{3 e^5 (1+x)-15 e^{2-e^{-4+x}+x} (1+x)-x (2+3 x)}} \] Input:
Integrate[E^(E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x)) + E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3* x))*(-2 + 3*E^5 - 6*x + E^(2 - E^(-4 + x) + x)*(-30 - 15*x + E^(-4 + x)*(1 5 + 15*x))),x]
Output:
E^E^(3*E^5*(1 + x) - 15*E^(2 - E^(-4 + x) + x)*(1 + x) - x*(2 + 3*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.
| \(\displaystyle \int \left (-6 x+e^{x-e^{x-4}+2} \left (-15 x+e^{x-4} (15 x+15)-30\right )+3 e^5-2\right ) \exp \left (\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right ) \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \left (-6 x+e^{x-e^{x-4}+2} \left (-15 x+e^{x-4} (15 x+15)-30\right )-2 \left (1-\frac {3 e^5}{2}\right )\right ) \exp \left (\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-6 x \exp \left (\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+15 \left (e^x x-e^4 x+e^x-2 e^4\right ) \exp \left (\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )-3 x^2-x-e^{x-4}+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)-2\right )-2 \left (1-\frac {3 e^5}{2}\right ) \exp \left (\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 15 \int \exp \left (-3 x^2-e^{x-4}+\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)-2\right )dx-\left (2-3 e^5\right ) \int \exp \left (-3 x^2-2 x+\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )dx-30 \int \exp \left (-3 x^2-x-e^{x-4}+\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)+2\right )dx+15 \int \exp \left (-3 x^2-e^{x-4}+\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)-2\right ) xdx-6 \int \exp \left (-3 x^2-2 x+\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right ) xdx-15 \int \exp \left (-3 x^2-x-e^{x-4}+\exp \left (-3 x^2-2 x+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)\right )+e^{x-e^{x-4}+2} (-15 x-15)+e^5 (3 x+3)+2\right ) xdx\) |
Input:
Int[E^(E^(E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x )) + E^(2 - E^(-4 + x) + x)*(-15 - 15*x) - 2*x - 3*x^2 + E^5*(3 + 3*x))*(- 2 + 3*E^5 - 6*x + E^(2 - E^(-4 + x) + x)*(-30 - 15*x + E^(-4 + x)*(15 + 15 *x))),x]
Output:
$Aborted
Time = 4.39 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12
| method | result | size |
| parallelrisch | \({\mathrm e}^{{\mathrm e}^{\left (-15 x -15\right ) {\mathrm e}^{-{\mathrm e}^{x -4}+2+x}+\left (3 x +3\right ) {\mathrm e}^{5}-3 x^{2}-2 x}}\) | \(36\) |
| risch | \({\mathrm e}^{{\mathrm e}^{3 x \,{\mathrm e}^{5}-15 \,{\mathrm e}^{-{\mathrm e}^{x -4}+2+x} x -3 x^{2}+3 \,{\mathrm e}^{5}-15 \,{\mathrm e}^{-{\mathrm e}^{x -4}+2+x}-2 x}}\) | \(46\) |
Input:
int((((15*x+15)*exp(x-4)-15*x-30)*exp(-exp(x-4)+2+x)+3*exp(5)-6*x-2)*exp(( -15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((-15*x-15)* exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x,method=_RETURNVERBOSE)
Output:
exp(exp((-15*x-15)*exp(-exp(x-4)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x))
Time = 0.08 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.03 \[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx=e^{\left (e^{\left (-3 \, x^{2} + 3 \, {\left (x + 1\right )} e^{5} - 15 \, {\left (x + 1\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x\right )}\right )} \] Input:
integrate((((15*x+15)*exp(-4+x)-15*x-30)*exp(-exp(-4+x)+2+x)+3*exp(5)-6*x- 2)*exp((-15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((- 15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x, algorithm="fric as")
Output:
e^(e^(-3*x^2 + 3*(x + 1)*e^5 - 15*(x + 1)*e^(x - e^(x - 4) + 2) - 2*x))
Time = 8.15 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx=e^{e^{- 3 x^{2} - 2 x + \left (- 15 x - 15\right ) e^{x - e^{x - 4} + 2} + \left (3 x + 3\right ) e^{5}}} \] Input:
integrate((((15*x+15)*exp(-4+x)-15*x-30)*exp(-exp(-4+x)+2+x)+3*exp(5)-6*x- 2)*exp((-15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x**2-2*x)*exp(exp(( -15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x**2-2*x)),x)
Output:
exp(exp(-3*x**2 - 2*x + (-15*x - 15)*exp(x - exp(x - 4) + 2) + (3*x + 3)*e xp(5)))
Time = 0.99 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.41 \[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx=e^{\left (e^{\left (-3 \, x^{2} + 3 \, x e^{5} - 15 \, x e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x + 3 \, e^{5} - 15 \, e^{\left (x - e^{\left (x - 4\right )} + 2\right )}\right )}\right )} \] Input:
integrate((((15*x+15)*exp(-4+x)-15*x-30)*exp(-exp(-4+x)+2+x)+3*exp(5)-6*x- 2)*exp((-15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((- 15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x, algorithm="maxi ma")
Output:
e^(e^(-3*x^2 + 3*x*e^5 - 15*x*e^(x - e^(x - 4) + 2) - 2*x + 3*e^5 - 15*e^( x - e^(x - 4) + 2)))
\[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx=\int { {\left (15 \, {\left ({\left (x + 1\right )} e^{\left (x - 4\right )} - x - 2\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 6 \, x + 3 \, e^{5} - 2\right )} e^{\left (-3 \, x^{2} + 3 \, {\left (x + 1\right )} e^{5} - 15 \, {\left (x + 1\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x + e^{\left (-3 \, x^{2} + 3 \, {\left (x + 1\right )} e^{5} - 15 \, {\left (x + 1\right )} e^{\left (x - e^{\left (x - 4\right )} + 2\right )} - 2 \, x\right )}\right )} \,d x } \] Input:
integrate((((15*x+15)*exp(-4+x)-15*x-30)*exp(-exp(-4+x)+2+x)+3*exp(5)-6*x- 2)*exp((-15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((- 15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x, algorithm="giac ")
Output:
integrate((15*((x + 1)*e^(x - 4) - x - 2)*e^(x - e^(x - 4) + 2) - 6*x + 3* e^5 - 2)*e^(-3*x^2 + 3*(x + 1)*e^5 - 15*(x + 1)*e^(x - e^(x - 4) + 2) - 2* x + e^(-3*x^2 + 3*(x + 1)*e^5 - 15*(x + 1)*e^(x - e^(x - 4) + 2) - 2*x)), x)
Time = 3.88 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.62 \[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx={\mathrm {e}}^{{\mathrm {e}}^{-15\,{\mathrm {e}}^{-{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{3\,{\mathrm {e}}^5}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-15\,x\,{\mathrm {e}}^{-{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-3\,x^2}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^5}} \] Input:
int(-exp(exp(5)*(3*x + 3) - exp(x - exp(x - 4) + 2)*(15*x + 15) - 3*x^2 - 2*x)*exp(exp(exp(5)*(3*x + 3) - exp(x - exp(x - 4) + 2)*(15*x + 15) - 3*x^ 2 - 2*x))*(6*x - 3*exp(5) + exp(x - exp(x - 4) + 2)*(15*x - exp(x - 4)*(15 *x + 15) + 30) + 2),x)
Output:
exp(exp(-15*exp(-exp(-4)*exp(x))*exp(2)*exp(x))*exp(3*exp(5))*exp(-2*x)*ex p(-15*x*exp(-exp(-4)*exp(x))*exp(2)*exp(x))*exp(-3*x^2)*exp(3*x*exp(5)))
\[ \int e^{e^{e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)}+e^{2-e^{-4+x}+x} (-15-15 x)-2 x-3 x^2+e^5 (3+3 x)} \left (-2+3 e^5-6 x+e^{2-e^{-4+x}+x} \left (-30-15 x+e^{-4+x} (15+15 x)\right )\right ) \, dx =\text {Too large to display} \] Input:
int((((15*x+15)*exp(-4+x)-15*x-30)*exp(-exp(-4+x)+2+x)+3*exp(5)-6*x-2)*exp ((-15*x-15)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)*exp(exp((-15*x-1 5)*exp(-exp(-4+x)+2+x)+(3*x+3)*exp(5)-3*x^2-2*x)),x)
Output:
(e**(3*e**5)*( - 30*int(e**((e**(3*e**5*x + 3*e**5) + 3*e**((3*e**(e**x/e* *4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15*e**x*e**2)/e**(e**x/e* *4))*e**5*x)/e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e** 2*x + 15*e**x*e**2)/e**(e**x/e**4)))/e**((e**((e**x + e**4*x)/e**4) + 3*e* *(e**x/e**4)*e**4*x**2 + e**(e**x/e**4)*e**4*x + 15*e**x*e**6*x + 15*e**x* e**6)/(e**(e**x/e**4)*e**4)),x)*e**4 + 15*int(e**((e**(3*e**5*x + 3*e**5) + 3*e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15* e**x*e**2)/e**(e**x/e**4))*e**5*x)/e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x /e**4)*x + 15*e**x*e**2*x + 15*e**x*e**2)/e**(e**x/e**4)))/e**((e**((e**x + e**4*x)/e**4) + 3*e**(e**x/e**4)*e**4*x**2 + 15*e**x*e**6*x + 15*e**x*e* *6)/(e**(e**x/e**4)*e**4)),x) + 3*int(e**((e**(3*e**5*x + 3*e**5) + 3*e**( (3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15*e**x*e** 2)/e**(e**x/e**4))*e**5*x)/e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15*e**x*e**2)/e**(e**x/e**4)))/e**((3*e**(e**x/e**4)*x **2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15*e**x*e**2)/e**(e**x/e**4)), x)*e**7 - 2*int(e**((e**(3*e**5*x + 3*e**5) + 3*e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15*e**x*e**2)/e**(e**x/e**4))*e** 5*x)/e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4)*x + 15*e**x*e**2*x + 15 *e**x*e**2)/e**(e**x/e**4)))/e**((3*e**(e**x/e**4)*x**2 + 2*e**(e**x/e**4) *x + 15*e**x*e**2*x + 15*e**x*e**2)/e**(e**x/e**4)),x)*e**2 - 15*int((e...