\(\int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} (-3-3 e^x x-3 \log (x))+(-3 e^{2 x}+3 x^2) \log (x)+(-3 e^{-3+e^x}-3 e^{2 x}+3 x^2) \log (-e^{-3+e^x}-e^{2 x}+x^2)}{(-3 e^{2 x} x+3 x^3) \log (x)+(e^{2 x} x^2-x^4) \log ^2(x)+e^{-3+e^x} (-3 x \log (x)+x^2 \log ^2(x))+(-3 e^{2 x} x+3 x^3+(2 e^{2 x} x^2-2 x^4) \log (x)+e^{-3+e^x} (-3 x+2 x^2 \log (x))) \log (-e^{-3+e^x}-e^{2 x}+x^2)+(e^{-3+e^x} x^2+e^{2 x} x^2-x^4) \log ^2(-e^{-3+e^x}-e^{2 x}+x^2)} \, dx\) [2581]

Optimal result

Integrand size = 284, antiderivative size = 35 \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=\log \left (\frac {x}{x-\frac {3}{\log (x)+\log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}}\right ) \] Output:

ln(x/(x-3/(ln(-exp(exp(x)-3)-exp(x)^2+x^2)+ln(x))))
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(74\) vs. \(2(35)=70\).

Time = 0.15 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.11 \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=-3 \left (-\frac {\log (x)}{3}-\frac {1}{3} \log \left (\log (x)+\log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )\right )+\frac {1}{3} \log \left (3-x \log (x)-x \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )\right )\right ) \] Input:

Integrate[(E^(2*x)*(-3 - 6*x) + 9*x^2 + E^(-3 + E^x)*(-3 - 3*E^x*x - 3*Log 
[x]) + (-3*E^(2*x) + 3*x^2)*Log[x] + (-3*E^(-3 + E^x) - 3*E^(2*x) + 3*x^2) 
*Log[-E^(-3 + E^x) - E^(2*x) + x^2])/((-3*E^(2*x)*x + 3*x^3)*Log[x] + (E^( 
2*x)*x^2 - x^4)*Log[x]^2 + E^(-3 + E^x)*(-3*x*Log[x] + x^2*Log[x]^2) + (-3 
*E^(2*x)*x + 3*x^3 + (2*E^(2*x)*x^2 - 2*x^4)*Log[x] + E^(-3 + E^x)*(-3*x + 
 2*x^2*Log[x]))*Log[-E^(-3 + E^x) - E^(2*x) + x^2] + (E^(-3 + E^x)*x^2 + E 
^(2*x)*x^2 - x^4)*Log[-E^(-3 + E^x) - E^(2*x) + x^2]^2),x]
 

Output:

-3*(-1/3*Log[x] - Log[Log[x] + Log[-E^(-3 + E^x) - E^(2*x) + x^2]]/3 + Log 
[3 - x*Log[x] - x*Log[-E^(-3 + E^x) - E^(2*x) + x^2]]/3)
 

Rubi [F]

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.

\(\displaystyle \int \frac {9 x^2+\left (3 x^2-3 e^{2 x}\right ) \log (x)+\left (3 x^2-3 e^{e^x-3}-3 e^{2 x}\right ) \log \left (x^2-e^{e^x-3}-e^{2 x}\right )+e^{2 x} (-6 x-3)+e^{e^x-3} \left (-3 e^x x-3 \log (x)-3\right )}{\left (3 x^3-3 e^{2 x} x\right ) \log (x)+e^{e^x-3} \left (x^2 \log ^2(x)-3 x \log (x)\right )+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+\left (-x^4+e^{e^x-3} x^2+e^{2 x} x^2\right ) \log ^2\left (x^2-e^{e^x-3}-e^{2 x}\right )+\left (3 x^3+e^{e^x-3} \left (2 x^2 \log (x)-3 x\right )+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)-3 e^{2 x} x\right ) \log \left (x^2-e^{e^x-3}-e^{2 x}\right )} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {e^3 \left (-9 x^2-\left (3 x^2-3 e^{2 x}\right ) \log (x)-\left (3 x^2-3 e^{e^x-3}-3 e^{2 x}\right ) \log \left (x^2-e^{e^x-3}-e^{2 x}\right )-e^{2 x} (-6 x-3)-e^{e^x-3} \left (-3 e^x x-3 \log (x)-3\right )\right )}{x \left (-e^3 x^2+e^{e^x}+e^{2 x+3}\right ) \left (\log \left (x^2-e^{e^x-3}-e^{2 x}\right )+\log (x)\right ) \left (-x \log \left (x^2-e^{e^x-3}-e^{2 x}\right )-x \log (x)+3\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle e^3 \int -\frac {3 \left (3 x^2-e^{2 x} (2 x+1)-\left (e^{2 x}-x^2\right ) \log (x)-e^{-3+e^x} \left (e^x x+\log (x)+1\right )-\left (-x^2+e^{-3+e^x}+e^{2 x}\right ) \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right )}{x \left (-e^3 x^2+e^{e^x}+e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (-x \log (x)-x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )+3\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle -3 e^3 \int \frac {3 x^2-e^{2 x} (2 x+1)-\left (e^{2 x}-x^2\right ) \log (x)-e^{-3+e^x} \left (e^x x+\log (x)+1\right )-\left (-x^2+e^{-3+e^x}+e^{2 x}\right ) \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )}{x \left (-e^3 x^2+e^{e^x}+e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (-x \log (x)-x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )+3\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -3 e^3 \int \left (\frac {2 e^3 x^2-2 e^3 x-2 e^{e^x}+e^{x+e^x}}{e^3 \left (-e^3 x^2+e^{e^x}+e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}+\frac {2 x+\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )+1}{e^3 x \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -3 e^3 \left (-\frac {2 \int \frac {1}{\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )}dx}{3 e^3}-\frac {\int \frac {1}{x \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right )}dx}{3 e^3}+\frac {\int \frac {1}{x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3}dx}{3 e^3}+\frac {\int \frac {1}{x \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}dx}{e^3}+\frac {2 \int \frac {x}{x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3}dx}{3 e^3}-\frac {2 \int \frac {e^{e^x}}{\left (-e^3 x^2+e^{e^x}+e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}dx}{e^3}+\frac {\int \frac {e^{x+e^x}}{\left (-e^3 x^2+e^{e^x}+e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}dx}{e^3}+2 \int \frac {x}{\left (e^3 x^2-e^{e^x}-e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}dx-2 \int \frac {x^2}{\left (e^3 x^2-e^{e^x}-e^{2 x+3}\right ) \left (\log (x)+\log \left (x^2-e^{-3+e^x}-e^{2 x}\right )\right ) \left (x \log (x)+x \log \left (x^2-e^{-3+e^x}-e^{2 x}\right )-3\right )}dx\right )\)

Input:

Int[(E^(2*x)*(-3 - 6*x) + 9*x^2 + E^(-3 + E^x)*(-3 - 3*E^x*x - 3*Log[x]) + 
 (-3*E^(2*x) + 3*x^2)*Log[x] + (-3*E^(-3 + E^x) - 3*E^(2*x) + 3*x^2)*Log[- 
E^(-3 + E^x) - E^(2*x) + x^2])/((-3*E^(2*x)*x + 3*x^3)*Log[x] + (E^(2*x)*x 
^2 - x^4)*Log[x]^2 + E^(-3 + E^x)*(-3*x*Log[x] + x^2*Log[x]^2) + (-3*E^(2* 
x)*x + 3*x^3 + (2*E^(2*x)*x^2 - 2*x^4)*Log[x] + E^(-3 + E^x)*(-3*x + 2*x^2 
*Log[x]))*Log[-E^(-3 + E^x) - E^(2*x) + x^2] + (E^(-3 + E^x)*x^2 + E^(2*x) 
*x^2 - x^4)*Log[-E^(-3 + E^x) - E^(2*x) + x^2]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.60

\[\ln \left (\ln \left (-{\mathrm e}^{{\mathrm e}^{x}-3}-{\mathrm e}^{2 x}+x^{2}\right )+\ln \left (x \right )\right )-\ln \left (\ln \left (-{\mathrm e}^{{\mathrm e}^{x}-3}-{\mathrm e}^{2 x}+x^{2}\right )+\frac {x \ln \left (x \right )-3}{x}\right )\]

Input:

int(((-3*exp(exp(x)-3)-3*exp(x)^2+3*x^2)*ln(-exp(exp(x)-3)-exp(x)^2+x^2)+( 
-3*ln(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)^2+3*x^2)*ln(x)+(-6*x-3)*ex 
p(x)^2+9*x^2)/((x^2*exp(exp(x)-3)+exp(x)^2*x^2-x^4)*ln(-exp(exp(x)-3)-exp( 
x)^2+x^2)^2+((2*x^2*ln(x)-3*x)*exp(exp(x)-3)+(2*exp(x)^2*x^2-2*x^4)*ln(x)- 
3*x*exp(x)^2+3*x^3)*ln(-exp(exp(x)-3)-exp(x)^2+x^2)+(x^2*ln(x)^2-3*x*ln(x) 
)*exp(exp(x)-3)+(exp(x)^2*x^2-x^4)*ln(x)^2+(-3*x*exp(x)^2+3*x^3)*ln(x)),x)
 

Output:

ln(ln(-exp(exp(x)-3)-exp(2*x)+x^2)+ln(x))-ln(ln(-exp(exp(x)-3)-exp(2*x)+x^ 
2)+1/x*(x*ln(x)-3))
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.60 \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=-\log \left (\frac {x \log \left (x^{2} - e^{\left (2 \, x\right )} - e^{\left (e^{x} - 3\right )}\right ) + x \log \left (x\right ) - 3}{x}\right ) + \log \left (\log \left (x^{2} - e^{\left (2 \, x\right )} - e^{\left (e^{x} - 3\right )}\right ) + \log \left (x\right )\right ) \] Input:

integrate(((-3*exp(exp(x)-3)-3*exp(x)^2+3*x^2)*log(-exp(exp(x)-3)-exp(x)^2 
+x^2)+(-3*log(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)^2+3*x^2)*log(x)+(- 
6*x-3)*exp(x)^2+9*x^2)/((x^2*exp(exp(x)-3)+exp(x)^2*x^2-x^4)*log(-exp(exp( 
x)-3)-exp(x)^2+x^2)^2+((2*x^2*log(x)-3*x)*exp(exp(x)-3)+(2*exp(x)^2*x^2-2* 
x^4)*log(x)-3*x*exp(x)^2+3*x^3)*log(-exp(exp(x)-3)-exp(x)^2+x^2)+(x^2*log( 
x)^2-3*x*log(x))*exp(exp(x)-3)+(exp(x)^2*x^2-x^4)*log(x)^2+(-3*x*exp(x)^2+ 
3*x^3)*log(x)),x, algorithm="fricas")
 

Output:

-log((x*log(x^2 - e^(2*x) - e^(e^x - 3)) + x*log(x) - 3)/x) + log(log(x^2 
- e^(2*x) - e^(e^x - 3)) + log(x))
 

Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate(((-3*exp(exp(x)-3)-3*exp(x)**2+3*x**2)*ln(-exp(exp(x)-3)-exp(x)* 
*2+x**2)+(-3*ln(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)**2+3*x**2)*ln(x) 
+(-6*x-3)*exp(x)**2+9*x**2)/((x**2*exp(exp(x)-3)+exp(x)**2*x**2-x**4)*ln(- 
exp(exp(x)-3)-exp(x)**2+x**2)**2+((2*x**2*ln(x)-3*x)*exp(exp(x)-3)+(2*exp( 
x)**2*x**2-2*x**4)*ln(x)-3*x*exp(x)**2+3*x**3)*ln(-exp(exp(x)-3)-exp(x)**2 
+x**2)+(x**2*ln(x)**2-3*x*ln(x))*exp(exp(x)-3)+(exp(x)**2*x**2-x**4)*ln(x) 
**2+(-3*x*exp(x)**2+3*x**3)*ln(x)),x)
 

Output:

Exception raised: PolynomialError >> 1/(-_t1**2*x**2 - _t2*x**2 + x**4) co 
ntains an element of the set of generators.
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (32) = 64\).

Time = 0.41 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.89 \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=-\log \left (\frac {x \log \left (x^{2} e^{3} - e^{\left (2 \, x + 3\right )} - e^{\left (e^{x}\right )}\right ) + x \log \left (x\right ) - 3 \, x - 3}{x}\right ) + \log \left (\log \left (x^{2} e^{3} - e^{\left (2 \, x + 3\right )} - e^{\left (e^{x}\right )}\right ) + \log \left (x\right ) - 3\right ) \] Input:

integrate(((-3*exp(exp(x)-3)-3*exp(x)^2+3*x^2)*log(-exp(exp(x)-3)-exp(x)^2 
+x^2)+(-3*log(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)^2+3*x^2)*log(x)+(- 
6*x-3)*exp(x)^2+9*x^2)/((x^2*exp(exp(x)-3)+exp(x)^2*x^2-x^4)*log(-exp(exp( 
x)-3)-exp(x)^2+x^2)^2+((2*x^2*log(x)-3*x)*exp(exp(x)-3)+(2*exp(x)^2*x^2-2* 
x^4)*log(x)-3*x*exp(x)^2+3*x^3)*log(-exp(exp(x)-3)-exp(x)^2+x^2)+(x^2*log( 
x)^2-3*x*log(x))*exp(exp(x)-3)+(exp(x)^2*x^2-x^4)*log(x)^2+(-3*x*exp(x)^2+ 
3*x^3)*log(x)),x, algorithm="maxima")
 

Output:

-log((x*log(x^2*e^3 - e^(2*x + 3) - e^(e^x)) + x*log(x) - 3*x - 3)/x) + lo 
g(log(x^2*e^3 - e^(2*x + 3) - e^(e^x)) + log(x) - 3)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (32) = 64\).

Time = 1.14 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.34 \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=-\log \left (x \log \left ({\left (x^{2} e^{\left (x + 3\right )} - e^{\left (3 \, x + 3\right )} - e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right ) + x \log \left (x\right ) - 3 \, x - 3\right ) + \log \left (x\right ) + \log \left (\log \left ({\left (x^{2} e^{\left (x + 3\right )} - e^{\left (3 \, x + 3\right )} - e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right ) + \log \left (x\right ) - 3\right ) \] Input:

integrate(((-3*exp(exp(x)-3)-3*exp(x)^2+3*x^2)*log(-exp(exp(x)-3)-exp(x)^2 
+x^2)+(-3*log(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)^2+3*x^2)*log(x)+(- 
6*x-3)*exp(x)^2+9*x^2)/((x^2*exp(exp(x)-3)+exp(x)^2*x^2-x^4)*log(-exp(exp( 
x)-3)-exp(x)^2+x^2)^2+((2*x^2*log(x)-3*x)*exp(exp(x)-3)+(2*exp(x)^2*x^2-2* 
x^4)*log(x)-3*x*exp(x)^2+3*x^3)*log(-exp(exp(x)-3)-exp(x)^2+x^2)+(x^2*log( 
x)^2-3*x*log(x))*exp(exp(x)-3)+(exp(x)^2*x^2-x^4)*log(x)^2+(-3*x*exp(x)^2+ 
3*x^3)*log(x)),x, algorithm="giac")
 

Output:

-log(x*log((x^2*e^(x + 3) - e^(3*x + 3) - e^(x + e^x))*e^(-x)) + x*log(x) 
- 3*x - 3) + log(x) + log(log((x^2*e^(x + 3) - e^(3*x + 3) - e^(x + e^x))* 
e^(-x)) + log(x) - 3)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=\int -\frac {{\mathrm {e}}^{{\mathrm {e}}^x-3}\,\left (3\,\ln \left (x\right )+3\,x\,{\mathrm {e}}^x+3\right )+\ln \left (x\right )\,\left (3\,{\mathrm {e}}^{2\,x}-3\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (6\,x+3\right )+\ln \left (x^2-{\mathrm {e}}^{{\mathrm {e}}^x-3}-{\mathrm {e}}^{2\,x}\right )\,\left (3\,{\mathrm {e}}^{2\,x}+3\,{\mathrm {e}}^{{\mathrm {e}}^x-3}-3\,x^2\right )-9\,x^2}{{\mathrm {e}}^{{\mathrm {e}}^x-3}\,\left (x^2\,{\ln \left (x\right )}^2-3\,x\,\ln \left (x\right )\right )+{\ln \left (x\right )}^2\,\left (x^2\,{\mathrm {e}}^{2\,x}-x^4\right )+{\ln \left (x^2-{\mathrm {e}}^{{\mathrm {e}}^x-3}-{\mathrm {e}}^{2\,x}\right )}^2\,\left (x^2\,{\mathrm {e}}^{2\,x}-x^4+x^2\,{\mathrm {e}}^{{\mathrm {e}}^x-3}\right )-\ln \left (x^2-{\mathrm {e}}^{{\mathrm {e}}^x-3}-{\mathrm {e}}^{2\,x}\right )\,\left (3\,x\,{\mathrm {e}}^{2\,x}-\ln \left (x\right )\,\left (2\,x^2\,{\mathrm {e}}^{2\,x}-2\,x^4\right )+{\mathrm {e}}^{{\mathrm {e}}^x-3}\,\left (3\,x-2\,x^2\,\ln \left (x\right )\right )-3\,x^3\right )-\ln \left (x\right )\,\left (3\,x\,{\mathrm {e}}^{2\,x}-3\,x^3\right )} \,d x \] Input:

int(-(exp(exp(x) - 3)*(3*log(x) + 3*x*exp(x) + 3) + log(x)*(3*exp(2*x) - 3 
*x^2) + exp(2*x)*(6*x + 3) + log(x^2 - exp(exp(x) - 3) - exp(2*x))*(3*exp( 
2*x) + 3*exp(exp(x) - 3) - 3*x^2) - 9*x^2)/(exp(exp(x) - 3)*(x^2*log(x)^2 
- 3*x*log(x)) + log(x)^2*(x^2*exp(2*x) - x^4) + log(x^2 - exp(exp(x) - 3) 
- exp(2*x))^2*(x^2*exp(2*x) - x^4 + x^2*exp(exp(x) - 3)) - log(x^2 - exp(e 
xp(x) - 3) - exp(2*x))*(3*x*exp(2*x) - log(x)*(2*x^2*exp(2*x) - 2*x^4) + e 
xp(exp(x) - 3)*(3*x - 2*x^2*log(x)) - 3*x^3) - log(x)*(3*x*exp(2*x) - 3*x^ 
3)),x)
                                                                                    
                                                                                    
 

Output:

int(-(exp(exp(x) - 3)*(3*log(x) + 3*x*exp(x) + 3) + log(x)*(3*exp(2*x) - 3 
*x^2) + exp(2*x)*(6*x + 3) + log(x^2 - exp(exp(x) - 3) - exp(2*x))*(3*exp( 
2*x) + 3*exp(exp(x) - 3) - 3*x^2) - 9*x^2)/(exp(exp(x) - 3)*(x^2*log(x)^2 
- 3*x*log(x)) + log(x)^2*(x^2*exp(2*x) - x^4) + log(x^2 - exp(exp(x) - 3) 
- exp(2*x))^2*(x^2*exp(2*x) - x^4 + x^2*exp(exp(x) - 3)) - log(x^2 - exp(e 
xp(x) - 3) - exp(2*x))*(3*x*exp(2*x) - log(x)*(2*x^2*exp(2*x) - 2*x^4) + e 
xp(exp(x) - 3)*(3*x - 2*x^2*log(x)) - 3*x^3) - log(x)*(3*x*exp(2*x) - 3*x^ 
3)), x)
 

Reduce [F]

\[ \int \frac {e^{2 x} (-3-6 x)+9 x^2+e^{-3+e^x} \left (-3-3 e^x x-3 \log (x)\right )+\left (-3 e^{2 x}+3 x^2\right ) \log (x)+\left (-3 e^{-3+e^x}-3 e^{2 x}+3 x^2\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )}{\left (-3 e^{2 x} x+3 x^3\right ) \log (x)+\left (e^{2 x} x^2-x^4\right ) \log ^2(x)+e^{-3+e^x} \left (-3 x \log (x)+x^2 \log ^2(x)\right )+\left (-3 e^{2 x} x+3 x^3+\left (2 e^{2 x} x^2-2 x^4\right ) \log (x)+e^{-3+e^x} \left (-3 x+2 x^2 \log (x)\right )\right ) \log \left (-e^{-3+e^x}-e^{2 x}+x^2\right )+\left (e^{-3+e^x} x^2+e^{2 x} x^2-x^4\right ) \log ^2\left (-e^{-3+e^x}-e^{2 x}+x^2\right )} \, dx=\text {too large to display} \] Input:

int(((-3*exp(exp(x)-3)-3*exp(x)^2+3*x^2)*log(-exp(exp(x)-3)-exp(x)^2+x^2)+ 
(-3*log(x)-3*exp(x)*x-3)*exp(exp(x)-3)+(-3*exp(x)^2+3*x^2)*log(x)+(-6*x-3) 
*exp(x)^2+9*x^2)/((x^2*exp(exp(x)-3)+exp(x)^2*x^2-x^4)*log(-exp(exp(x)-3)- 
exp(x)^2+x^2)^2+((2*x^2*log(x)-3*x)*exp(exp(x)-3)+(2*exp(x)^2*x^2-2*x^4)*l 
og(x)-3*x*exp(x)^2+3*x^3)*log(-exp(exp(x)-3)-exp(x)^2+x^2)+(x^2*log(x)^2-3 
*x*log(x))*exp(exp(x)-3)+(exp(x)^2*x^2-x^4)*log(x)^2+(-3*x*exp(x)^2+3*x^3) 
*log(x)),x)
 

Output:

3*( - int(e**(e**x)/(e**(e**x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x* 
*2)/e**3)**2*x**2 + 2*e**(e**x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x 
**2)/e**3)*log(x)*x**2 - 3*e**(e**x)*log(( - e**(e**x) - e**(2*x)*e**3 + e 
**3*x**2)/e**3)*x + e**(e**x)*log(x)**2*x**2 - 3*e**(e**x)*log(x)*x + e**( 
2*x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)**2*e**3*x**2 + 2 
*e**(2*x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)*log(x)*e**3 
*x**2 - 3*e**(2*x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)*e* 
*3*x + e**(2*x)*log(x)**2*e**3*x**2 - 3*e**(2*x)*log(x)*e**3*x - log(( - e 
**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)**2*e**3*x**4 - 2*log(( - e**(e 
**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)*log(x)*e**3*x**4 + 3*log(( - e**(e 
**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)*e**3*x**3 - log(x)**2*e**3*x**4 + 
3*log(x)*e**3*x**3),x) - int(e**(e**x + x)/(e**(e**x)*log(( - e**(e**x) - 
e**(2*x)*e**3 + e**3*x**2)/e**3)**2*x + 2*e**(e**x)*log(( - e**(e**x) - e* 
*(2*x)*e**3 + e**3*x**2)/e**3)*log(x)*x - 3*e**(e**x)*log(( - e**(e**x) - 
e**(2*x)*e**3 + e**3*x**2)/e**3) + e**(e**x)*log(x)**2*x - 3*e**(e**x)*log 
(x) + e**(2*x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)**2*e** 
3*x + 2*e**(2*x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)*log( 
x)*e**3*x - 3*e**(2*x)*log(( - e**(e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3 
)*e**3 + e**(2*x)*log(x)**2*e**3*x - 3*e**(2*x)*log(x)*e**3 - log(( - e**( 
e**x) - e**(2*x)*e**3 + e**3*x**2)/e**3)**2*e**3*x**3 - 2*log(( - e**(e...