Integrand size = 247, antiderivative size = 29 \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=\frac {e^{e^2}-x}{x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \] Output:
(exp(exp(2))-x)/(ln(ln(-3*exp(x^2)*x+exp(4)-1))+x)
Time = 0.12 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=\frac {e^{e^2}-x}{x+\log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \] Input:
Integrate[(E^(E^2 + x^2)*(-3 - 6*x^2) + E^x^2*(3*x + 6*x^3) + E^E^2*(-1 + E^4 - 3*E^x^2*x)*Log[-1 + E^4 - 3*E^x^2*x] + (-1 + E^4 - 3*E^x^2*x)*Log[-1 + E^4 - 3*E^x^2*x]*Log[Log[-1 + E^4 - 3*E^x^2*x]])/((x^2 - E^4*x^2 + 3*E^ x^2*x^3)*Log[-1 + E^4 - 3*E^x^2*x] + (2*x - 2*E^4*x + 6*E^x^2*x^2)*Log[-1 + E^4 - 3*E^x^2*x]*Log[Log[-1 + E^4 - 3*E^x^2*x]] + (1 - E^4 + 3*E^x^2*x)* Log[-1 + E^4 - 3*E^x^2*x]*Log[Log[-1 + E^4 - 3*E^x^2*x]]^2),x]
Output:
(E^E^2 - x)/(x + Log[Log[-1 + E^4 - 3*E^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.
| \(\displaystyle \int \frac {e^{x^2+e^2} \left (-6 x^2-3\right )+e^{e^2} \left (-3 e^{x^2} x+e^4-1\right ) \log \left (-3 e^{x^2} x+e^4-1\right )+\left (-3 e^{x^2} x+e^4-1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+e^{x^2} \left (6 x^3+3 x\right )}{\left (3 e^{x^2} x-e^4+1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \log ^2\left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+\left (6 e^{x^2} x^2-2 e^4 x+2 x\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+\left (-e^4 x^2+x^2+3 e^{x^2} x^3\right ) \log \left (-3 e^{x^2} x+e^4-1\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-\frac {3 e^{x^2} \left (e^{e^2}-x\right ) \left (2 x^2+1\right )}{\left (3 e^{x^2} x-e^4+1\right ) \log \left (-3 e^{x^2} x+e^4-1\right )}-\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )-e^{e^2}}{\left (\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {\left (e^4-1\right ) \left (e^{e^2}-x\right ) \left (2 x^2+1\right )}{x \left (-3 e^{x^2} x+e^4-1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \left (\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+x\right )^2}+\frac {2 x^3-2 e^{e^2} x^2-e^{e^2} x \log \left (-3 e^{x^2} x+e^4-1\right )-x \log \left (-3 e^{x^2} x+e^4-1\right ) \log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+x-e^{e^2}}{x \log \left (-3 e^{x^2} x+e^4-1\right ) \left (\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )+x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \int \frac {1}{-x-\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )}dx-e^{e^2} \int \frac {1}{\left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx+\int \frac {x}{\left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx+\int \frac {1}{\log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx-e^{e^2} \int \frac {1}{x \log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx-2 e^{e^2} \int \frac {x}{\log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx+2 \int \frac {x^2}{\log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx+\left (1-e^4\right ) \int \frac {1}{\left (-3 e^{x^2} x+e^4-1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx+e^{e^2} \left (1-e^4\right ) \int \frac {1}{x \left (3 e^{x^2} x-e^4+1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx+2 e^{e^2} \left (1-e^4\right ) \int \frac {x}{\left (3 e^{x^2} x-e^4+1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx-2 \left (1-e^4\right ) \int \frac {x^2}{\left (3 e^{x^2} x-e^4+1\right ) \log \left (-3 e^{x^2} x+e^4-1\right ) \left (x+\log \left (\log \left (-3 e^{x^2} x+e^4-1\right )\right )\right )^2}dx\) |
Input:
Int[(E^(E^2 + x^2)*(-3 - 6*x^2) + E^x^2*(3*x + 6*x^3) + E^E^2*(-1 + E^4 - 3*E^x^2*x)*Log[-1 + E^4 - 3*E^x^2*x] + (-1 + E^4 - 3*E^x^2*x)*Log[-1 + E^4 - 3*E^x^2*x]*Log[Log[-1 + E^4 - 3*E^x^2*x]])/((x^2 - E^4*x^2 + 3*E^x^2*x^ 3)*Log[-1 + E^4 - 3*E^x^2*x] + (2*x - 2*E^4*x + 6*E^x^2*x^2)*Log[-1 + E^4 - 3*E^x^2*x]*Log[Log[-1 + E^4 - 3*E^x^2*x]] + (1 - E^4 + 3*E^x^2*x)*Log[-1 + E^4 - 3*E^x^2*x]*Log[Log[-1 + E^4 - 3*E^x^2*x]]^2),x]
Output:
$Aborted
Time = 31.44 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90
| method | result | size |
| risch | \(\frac {{\mathrm e}^{{\mathrm e}^{2}}-x}{\ln \left (\ln \left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )\right )+x}\) | \(26\) |
| parallelrisch | \(\frac {9 \,{\mathrm e}^{{\mathrm e}^{2}}-9 x}{9 \ln \left (\ln \left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )\right )+9 x}\) | \(29\) |
Input:
int(((-3*exp(x^2)*x+exp(4)-1)*ln(-3*exp(x^2)*x+exp(4)-1)*ln(ln(-3*exp(x^2) *x+exp(4)-1))+(-3*exp(x^2)*x+exp(4)-1)*exp(exp(2))*ln(-3*exp(x^2)*x+exp(4) -1)+(-6*x^2-3)*exp(x^2)*exp(exp(2))+(6*x^3+3*x)*exp(x^2))/((3*exp(x^2)*x+1 -exp(4))*ln(-3*exp(x^2)*x+exp(4)-1)*ln(ln(-3*exp(x^2)*x+exp(4)-1))^2+(6*x^ 2*exp(x^2)-2*x*exp(4)+2*x)*ln(-3*exp(x^2)*x+exp(4)-1)*ln(ln(-3*exp(x^2)*x+ exp(4)-1))+(3*x^3*exp(x^2)-x^2*exp(4)+x^2)*ln(-3*exp(x^2)*x+exp(4)-1)),x,m ethod=_RETURNVERBOSE)
Output:
(exp(exp(2))-x)/(ln(ln(-3*exp(x^2)*x+exp(4)-1))+x)
Time = 0.10 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=-\frac {x - e^{\left (e^{2}\right )}}{x + \log \left (\log \left (-{\left (3 \, x e^{\left (x^{2} + e^{2}\right )} - {\left (e^{4} - 1\right )} e^{\left (e^{2}\right )}\right )} e^{\left (-e^{2}\right )}\right )\right )} \] Input:
integrate(((-3*exp(x^2)*x+exp(4)-1)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3 *exp(x^2)*x+exp(4)-1))+(-3*exp(x^2)*x+exp(4)-1)*exp(exp(2))*log(-3*exp(x^2 )*x+exp(4)-1)+(-6*x^2-3)*exp(x^2)*exp(exp(2))+(6*x^3+3*x)*exp(x^2))/((3*ex p(x^2)*x+1-exp(4))*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x^2)*x+exp(4 )-1))^2+(6*exp(x^2)*x^2-2*x*exp(4)+2*x)*log(-3*exp(x^2)*x+exp(4)-1)*log(lo g(-3*exp(x^2)*x+exp(4)-1))+(3*x^3*exp(x^2)-x^2*exp(4)+x^2)*log(-3*exp(x^2) *x+exp(4)-1)),x, algorithm="fricas")
Output:
-(x - e^(e^2))/(x + log(log(-(3*x*e^(x^2 + e^2) - (e^4 - 1)*e^(e^2))*e^(-e ^2))))
Time = 0.76 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83 \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=\frac {- x + e^{e^{2}}}{x + \log {\left (\log {\left (- 3 x e^{x^{2}} - 1 + e^{4} \right )} \right )}} \] Input:
integrate(((-3*exp(x**2)*x+exp(4)-1)*ln(-3*exp(x**2)*x+exp(4)-1)*ln(ln(-3* exp(x**2)*x+exp(4)-1))+(-3*exp(x**2)*x+exp(4)-1)*exp(exp(2))*ln(-3*exp(x** 2)*x+exp(4)-1)+(-6*x**2-3)*exp(x**2)*exp(exp(2))+(6*x**3+3*x)*exp(x**2))/( (3*exp(x**2)*x+1-exp(4))*ln(-3*exp(x**2)*x+exp(4)-1)*ln(ln(-3*exp(x**2)*x+ exp(4)-1))**2+(6*exp(x**2)*x**2-2*x*exp(4)+2*x)*ln(-3*exp(x**2)*x+exp(4)-1 )*ln(ln(-3*exp(x**2)*x+exp(4)-1))+(3*exp(x**2)*x**3-x**2*exp(4)+x**2)*ln(- 3*exp(x**2)*x+exp(4)-1)),x)
Output:
(-x + exp(exp(2)))/(x + log(log(-3*x*exp(x**2) - 1 + exp(4))))
Time = 0.12 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=-\frac {x - e^{\left (e^{2}\right )}}{x + \log \left (\log \left (-3 \, x e^{\left (x^{2}\right )} + e^{4} - 1\right )\right )} \] Input:
integrate(((-3*exp(x^2)*x+exp(4)-1)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3 *exp(x^2)*x+exp(4)-1))+(-3*exp(x^2)*x+exp(4)-1)*exp(exp(2))*log(-3*exp(x^2 )*x+exp(4)-1)+(-6*x^2-3)*exp(x^2)*exp(exp(2))+(6*x^3+3*x)*exp(x^2))/((3*ex p(x^2)*x+1-exp(4))*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x^2)*x+exp(4 )-1))^2+(6*exp(x^2)*x^2-2*x*exp(4)+2*x)*log(-3*exp(x^2)*x+exp(4)-1)*log(lo g(-3*exp(x^2)*x+exp(4)-1))+(3*x^3*exp(x^2)-x^2*exp(4)+x^2)*log(-3*exp(x^2) *x+exp(4)-1)),x, algorithm="maxima")
Output:
-(x - e^(e^2))/(x + log(log(-3*x*e^(x^2) + e^4 - 1)))
Leaf count of result is larger than twice the leaf count of optimal. 469 vs. \(2 (26) = 52\).
Time = 33.75 (sec) , antiderivative size = 469, normalized size of antiderivative = 16.17 \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx =\text {Too large to display} \] Input:
integrate(((-3*exp(x^2)*x+exp(4)-1)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3 *exp(x^2)*x+exp(4)-1))+(-3*exp(x^2)*x+exp(4)-1)*exp(exp(2))*log(-3*exp(x^2 )*x+exp(4)-1)+(-6*x^2-3)*exp(x^2)*exp(exp(2))+(6*x^3+3*x)*exp(x^2))/((3*ex p(x^2)*x+1-exp(4))*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x^2)*x+exp(4 )-1))^2+(6*exp(x^2)*x^2-2*x*exp(4)+2*x)*log(-3*exp(x^2)*x+exp(4)-1)*log(lo g(-3*exp(x^2)*x+exp(4)-1))+(3*x^3*exp(x^2)-x^2*exp(4)+x^2)*log(-3*exp(x^2) *x+exp(4)-1)),x, algorithm="giac")
Output:
-(6*x^3*e^(x^2) + 3*x^2*e^(x^2)*log(-3*x*e^(x^2) + e^4 - 1) - 6*x^2*e^(x^2 + e^2) - 3*x*e^(x^2 + e^2)*log(-3*x*e^(x^2) + e^4 - 1) + e^4*log(-3*x*e^( x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1)) + 3*x*e^(x^2) + e^(e^2 + 4)*log(-3*x*e^(x^2) + e^4 - 1) - e^(e^2)*log(-3*x*e^(x^2) + e^4 - 1) - log (-3*x*e^(x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1)) - 3*e^(x^2 + e^2 ))/(6*x^3*e^(x^2) + 3*x^2*e^(x^2)*log(-3*x*e^(x^2) + e^4 - 1) + 6*x^2*e^(x ^2)*log(log(-3*x*e^(x^2) + e^4 - 1)) + 3*x*e^(x^2)*log(-3*x*e^(x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1)) - x*e^4*log(-3*x*e^(x^2) + e^4 - 1) - e^4*log(-3*x*e^(x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1)) + 3*x*e ^(x^2) + x*log(-3*x*e^(x^2) + e^4 - 1) + 3*e^(x^2)*log(log(-3*x*e^(x^2) + e^4 - 1)) + log(-3*x*e^(x^2) + e^4 - 1)*log(log(-3*x*e^(x^2) + e^4 - 1))) + (e^4*log(-3*x*e^(x^2) + e^4 - 1) - log(-3*x*e^(x^2) + e^4 - 1))/(6*x^2*e ^(x^2) + 3*x*e^(x^2)*log(-3*x*e^(x^2) + e^4 - 1) - e^4*log(-3*x*e^(x^2) + e^4 - 1) + 3*e^(x^2) + log(-3*x*e^(x^2) + e^4 - 1))
Timed out. \[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=\int -\frac {\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\ln \left (\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\right )\,\left (3\,x\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^4+1\right )-{\mathrm {e}}^{x^2}\,\left (6\,x^3+3\,x\right )+\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (3\,x\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^4+1\right )+{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (6\,x^2+3\right )}{\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\left (3\,x\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^4+1\right )\,{\ln \left (\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\right )}^2+\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\left (2\,x-2\,x\,{\mathrm {e}}^4+6\,x^2\,{\mathrm {e}}^{x^2}\right )\,\ln \left (\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\right )+\ln \left ({\mathrm {e}}^4-3\,x\,{\mathrm {e}}^{x^2}-1\right )\,\left (3\,x^3\,{\mathrm {e}}^{x^2}-x^2\,{\mathrm {e}}^4+x^2\right )} \,d x \] Input:
int(-(log(exp(4) - 3*x*exp(x^2) - 1)*log(log(exp(4) - 3*x*exp(x^2) - 1))*( 3*x*exp(x^2) - exp(4) + 1) - exp(x^2)*(3*x + 6*x^3) + log(exp(4) - 3*x*exp (x^2) - 1)*exp(exp(2))*(3*x*exp(x^2) - exp(4) + 1) + exp(x^2)*exp(exp(2))* (6*x^2 + 3))/(log(exp(4) - 3*x*exp(x^2) - 1)*(3*x^3*exp(x^2) - x^2*exp(4) + x^2) + log(exp(4) - 3*x*exp(x^2) - 1)*log(log(exp(4) - 3*x*exp(x^2) - 1) )*(2*x - 2*x*exp(4) + 6*x^2*exp(x^2)) + log(exp(4) - 3*x*exp(x^2) - 1)*log (log(exp(4) - 3*x*exp(x^2) - 1))^2*(3*x*exp(x^2) - exp(4) + 1)),x)
Output:
int(-(log(exp(4) - 3*x*exp(x^2) - 1)*log(log(exp(4) - 3*x*exp(x^2) - 1))*( 3*x*exp(x^2) - exp(4) + 1) - exp(x^2)*(3*x + 6*x^3) + log(exp(4) - 3*x*exp (x^2) - 1)*exp(exp(2))*(3*x*exp(x^2) - exp(4) + 1) + exp(x^2)*exp(exp(2))* (6*x^2 + 3))/(log(exp(4) - 3*x*exp(x^2) - 1)*(3*x^3*exp(x^2) - x^2*exp(4) + x^2) + log(exp(4) - 3*x*exp(x^2) - 1)*log(log(exp(4) - 3*x*exp(x^2) - 1) )*(2*x - 2*x*exp(4) + 6*x^2*exp(x^2)) + log(exp(4) - 3*x*exp(x^2) - 1)*log (log(exp(4) - 3*x*exp(x^2) - 1))^2*(3*x*exp(x^2) - exp(4) + 1)), x)
\[ \int \frac {e^{e^2+x^2} \left (-3-6 x^2\right )+e^{x^2} \left (3 x+6 x^3\right )+e^{e^2} \left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (-1+e^4-3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )}{\left (x^2-e^4 x^2+3 e^{x^2} x^3\right ) \log \left (-1+e^4-3 e^{x^2} x\right )+\left (2 x-2 e^4 x+6 e^{x^2} x^2\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log \left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )+\left (1-e^4+3 e^{x^2} x\right ) \log \left (-1+e^4-3 e^{x^2} x\right ) \log ^2\left (\log \left (-1+e^4-3 e^{x^2} x\right )\right )} \, dx=\int \frac {\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right ) \mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right ) \mathrm {log}\left (\mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )\right )+\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right ) {\mathrm e}^{{\mathrm e}^{2}} \mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )+\left (-6 x^{2}-3\right ) {\mathrm e}^{x^{2}} {\mathrm e}^{{\mathrm e}^{2}}+\left (6 x^{3}+3 x \right ) {\mathrm e}^{x^{2}}}{\left (3 \,{\mathrm e}^{x^{2}} x +1-{\mathrm e}^{4}\right ) \mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right ) {\mathrm {log}\left (\mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )\right )}^{2}+\left (6 \,{\mathrm e}^{x^{2}} x^{2}-2 x \,{\mathrm e}^{4}+2 x \right ) \mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right ) \mathrm {log}\left (\mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )\right )+\left (3 \,{\mathrm e}^{x^{2}} x^{3}-x^{2} {\mathrm e}^{4}+x^{2}\right ) \mathrm {log}\left (-3 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{4}-1\right )}d x \] Input:
int(((-3*exp(x^2)*x+exp(4)-1)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x ^2)*x+exp(4)-1))+(-3*exp(x^2)*x+exp(4)-1)*exp(exp(2))*log(-3*exp(x^2)*x+ex p(4)-1)+(-6*x^2-3)*exp(x^2)*exp(exp(2))+(6*x^3+3*x)*exp(x^2))/((3*exp(x^2) *x+1-exp(4))*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x^2)*x+exp(4)-1))^ 2+(6*exp(x^2)*x^2-2*x*exp(4)+2*x)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*e xp(x^2)*x+exp(4)-1))+(3*exp(x^2)*x^3-x^2*exp(4)+x^2)*log(-3*exp(x^2)*x+exp (4)-1)),x)
Output:
int(((-3*exp(x^2)*x+exp(4)-1)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x ^2)*x+exp(4)-1))+(-3*exp(x^2)*x+exp(4)-1)*exp(exp(2))*log(-3*exp(x^2)*x+ex p(4)-1)+(-6*x^2-3)*exp(x^2)*exp(exp(2))+(6*x^3+3*x)*exp(x^2))/((3*exp(x^2) *x+1-exp(4))*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*exp(x^2)*x+exp(4)-1))^ 2+(6*exp(x^2)*x^2-2*x*exp(4)+2*x)*log(-3*exp(x^2)*x+exp(4)-1)*log(log(-3*e xp(x^2)*x+exp(4)-1))+(3*exp(x^2)*x^3-x^2*exp(4)+x^2)*log(-3*exp(x^2)*x+exp (4)-1)),x)