\(\int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} (-75+e^8 (4 x^2-4 x^3))+(-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)) \log (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}) \log (\log (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}))}{(-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)) \log (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x})} \, dx\) [368]

Optimal result

Integrand size = 232, antiderivative size = 29 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (-1+x)}\right )\right ) \] Output:

ln(ln(1/4*exp(exp(4)^2/(5+exp(x^2))^2)*x/(-1+x)))*x
 

Mathematica [A] (verified)

Time = 0.19 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (-1+x)}\right )\right ) \] Input:

Integrate[(-125 - 15*E^(2*x^2) - E^(3*x^2) + E^x^2*(-75 + E^8*(4*x^2 - 4*x 
^3)) + (-125 + E^(3*x^2)*(-1 + x) + 125*x + E^(2*x^2)*(-15 + 15*x) + E^x^2 
*(-75 + 75*x))*Log[(E^(E^8/(25 + 10*E^x^2 + E^(2*x^2)))*x)/(-4 + 4*x)]*Log 
[Log[(E^(E^8/(25 + 10*E^x^2 + E^(2*x^2)))*x)/(-4 + 4*x)]])/((-125 + E^(3*x 
^2)*(-1 + x) + 125*x + E^(2*x^2)*(-15 + 15*x) + E^x^2*(-75 + 75*x))*Log[(E 
^(E^8/(25 + 10*E^x^2 + E^(2*x^2)))*x)/(-4 + 4*x)]),x]
 

Output:

x*Log[Log[(E^(E^8/(5 + E^x^2)^2)*x)/(4*(-1 + x))]]
 

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.

\(\displaystyle \int \frac {-15 e^{2 x^2}-e^{3 x^2}+\left (e^{3 x^2} (x-1)+e^{2 x^2} (15 x-15)+e^{x^2} (75 x-75)+125 x-125\right ) \log \left (\frac {e^{\frac {e^8}{10 e^{x^2}+e^{2 x^2}+25}} x}{4 x-4}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{10 e^{x^2}+e^{2 x^2}+25}} x}{4 x-4}\right )\right )+e^{x^2} \left (e^8 \left (4 x^2-4 x^3\right )-75\right )-125}{\left (e^{3 x^2} (x-1)+e^{2 x^2} (15 x-15)+e^{x^2} (75 x-75)+125 x-125\right ) \log \left (\frac {e^{\frac {e^8}{10 e^{x^2}+e^{2 x^2}+25}} x}{4 x-4}\right )} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {15 e^{2 x^2}+e^{3 x^2}-\left (e^{3 x^2} (x-1)+e^{2 x^2} (15 x-15)+e^{x^2} (75 x-75)+125 x-125\right ) \log \left (\frac {e^{\frac {e^8}{10 e^{x^2}+e^{2 x^2}+25}} x}{4 x-4}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{10 e^{x^2}+e^{2 x^2}+25}} x}{4 x-4}\right )\right )-e^{x^2} \left (e^8 \left (4 x^2-4 x^3\right )-75\right )+125}{\left (e^{x^2}+5\right )^3 (1-x) \log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 x-4}\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {4 e^8 x^2}{\left (e^{x^2}+5\right )^2 \log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 x-4}\right )}+\frac {20 e^8 x^2}{\left (e^{x^2}+5\right )^3 \log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 x-4}\right )}+\frac {x \log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 (x-1)}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 (x-1)}\right )\right )-\log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 (x-1)}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 (x-1)}\right )\right )-1}{(x-1) \log \left (\frac {e^{\frac {e^8}{\left (e^{x^2}+5\right )^2}} x}{4 x-4}\right )}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -\int \frac {1}{(x-1) \log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx+20 e^8 \int \frac {x^2}{\left (5+e^{x^2}\right )^3 \log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx-4 e^8 \int \frac {x^2}{\left (5+e^{x^2}\right )^2 \log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx+\int \frac {\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (x-1)}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (x-1)}\right )\right )}{\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx\)

Input:

Int[(-125 - 15*E^(2*x^2) - E^(3*x^2) + E^x^2*(-75 + E^8*(4*x^2 - 4*x^3)) + 
 (-125 + E^(3*x^2)*(-1 + x) + 125*x + E^(2*x^2)*(-15 + 15*x) + E^x^2*(-75 
+ 75*x))*Log[(E^(E^8/(25 + 10*E^x^2 + E^(2*x^2)))*x)/(-4 + 4*x)]*Log[Log[( 
E^(E^8/(25 + 10*E^x^2 + E^(2*x^2)))*x)/(-4 + 4*x)]])/((-125 + E^(3*x^2)*(- 
1 + x) + 125*x + E^(2*x^2)*(-15 + 15*x) + E^x^2*(-75 + 75*x))*Log[(E^(E^8/ 
(25 + 10*E^x^2 + E^(2*x^2)))*x)/(-4 + 4*x)]),x]
 

Output:

$Aborted
 

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.10 (sec) , antiderivative size = 302, normalized size of antiderivative = 10.41

\[\ln \left (-2 \ln \left (2\right )+\ln \left (x \right )+\ln \left ({\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}\right )-\ln \left (-1+x \right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right ) \left (-\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (\frac {i}{-1+x}\right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i x \,{\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right ) \left (-\operatorname {csgn}\left (\frac {i x \,{\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (i x \right )\right ) \left (-\operatorname {csgn}\left (\frac {i x \,{\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )\right )}{2}\right ) x\]

Input:

int((((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^2)^2+(75*x-75)*exp(x^2)+125*x-125) 
*ln(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x))*ln(ln(x*exp(exp( 
4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x)))-exp(x^2)^3-15*exp(x^2)^2+((-4 
*x^3+4*x^2)*exp(4)^2-75)*exp(x^2)-125)/((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^ 
2)^2+(75*x-75)*exp(x^2)+125*x-125)/ln(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^ 
2)+25))/(-4+4*x)),x)
 

Output:

ln(-2*ln(2)+ln(x)+ln(exp(exp(8)/(exp(2*x^2)+10*exp(x^2)+25)))-ln(-1+x)-1/2 
*I*Pi*csgn(I*exp(exp(8)/(exp(2*x^2)+10*exp(x^2)+25))/(-1+x))*(-csgn(I*exp( 
exp(8)/(exp(2*x^2)+10*exp(x^2)+25))/(-1+x))+csgn(I*exp(exp(8)/(exp(2*x^2)+ 
10*exp(x^2)+25))))*(-csgn(I*exp(exp(8)/(exp(2*x^2)+10*exp(x^2)+25))/(-1+x) 
)+csgn(I/(-1+x)))-1/2*I*Pi*csgn(I*x/(-1+x)*exp(exp(8)/(exp(2*x^2)+10*exp(x 
^2)+25)))*(-csgn(I*x/(-1+x)*exp(exp(8)/(exp(2*x^2)+10*exp(x^2)+25)))+csgn( 
I*x))*(-csgn(I*x/(-1+x)*exp(exp(8)/(exp(2*x^2)+10*exp(x^2)+25)))+csgn(I*ex 
p(exp(8)/(exp(2*x^2)+10*exp(x^2)+25))/(-1+x))))*x
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (\log \left (\frac {x e^{\left (\frac {e^{8}}{e^{\left (2 \, x^{2}\right )} + 10 \, e^{\left (x^{2}\right )} + 25}\right )}}{4 \, {\left (x - 1\right )}}\right )\right ) \] Input:

integrate((((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^2)^2+(75*x-75)*exp(x^2)+125* 
x-125)*log(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x))*log(log(x 
*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x)))-exp(x^2)^3-15*exp(x^ 
2)^2+((-4*x^3+4*x^2)*exp(4)^2-75)*exp(x^2)-125)/((-1+x)*exp(x^2)^3+(15*x-1 
5)*exp(x^2)^2+(75*x-75)*exp(x^2)+125*x-125)/log(x*exp(exp(4)^2/(exp(x^2)^2 
+10*exp(x^2)+25))/(-4+4*x)),x, algorithm="fricas")
 

Output:

x*log(log(1/4*x*e^(e^8/(e^(2*x^2) + 10*e^(x^2) + 25))/(x - 1)))
 

Sympy [F(-1)]

Timed out. \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=\text {Timed out} \] Input:

integrate((((-1+x)*exp(x**2)**3+(15*x-15)*exp(x**2)**2+(75*x-75)*exp(x**2) 
+125*x-125)*ln(x*exp(exp(4)**2/(exp(x**2)**2+10*exp(x**2)+25))/(-4+4*x))*l 
n(ln(x*exp(exp(4)**2/(exp(x**2)**2+10*exp(x**2)+25))/(-4+4*x)))-exp(x**2)* 
*3-15*exp(x**2)**2+((-4*x**3+4*x**2)*exp(4)**2-75)*exp(x**2)-125)/((-1+x)* 
exp(x**2)**3+(15*x-15)*exp(x**2)**2+(75*x-75)*exp(x**2)+125*x-125)/ln(x*ex 
p(exp(4)**2/(exp(x**2)**2+10*exp(x**2)+25))/(-4+4*x)),x)
 

Output:

Timed out
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (24) = 48\).

Time = 0.22 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.62 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (-{\left (2 \, \log \left (2\right ) + \log \left (x - 1\right )\right )} e^{\left (2 \, x^{2}\right )} - 10 \, {\left (2 \, \log \left (2\right ) + \log \left (x - 1\right )\right )} e^{\left (x^{2}\right )} + {\left (e^{\left (2 \, x^{2}\right )} + 10 \, e^{\left (x^{2}\right )} + 25\right )} \log \left (x\right ) + e^{8} - 50 \, \log \left (2\right ) - 25 \, \log \left (x - 1\right )\right ) - 2 \, x \log \left (e^{\left (x^{2}\right )} + 5\right ) \] Input:

integrate((((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^2)^2+(75*x-75)*exp(x^2)+125* 
x-125)*log(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x))*log(log(x 
*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x)))-exp(x^2)^3-15*exp(x^ 
2)^2+((-4*x^3+4*x^2)*exp(4)^2-75)*exp(x^2)-125)/((-1+x)*exp(x^2)^3+(15*x-1 
5)*exp(x^2)^2+(75*x-75)*exp(x^2)+125*x-125)/log(x*exp(exp(4)^2/(exp(x^2)^2 
+10*exp(x^2)+25))/(-4+4*x)),x, algorithm="maxima")
 

Output:

x*log(-(2*log(2) + log(x - 1))*e^(2*x^2) - 10*(2*log(2) + log(x - 1))*e^(x 
^2) + (e^(2*x^2) + 10*e^(x^2) + 25)*log(x) + e^8 - 50*log(2) - 25*log(x - 
1)) - 2*x*log(e^(x^2) + 5)
 

Giac [F(-1)]

Timed out. \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=\text {Timed out} \] Input:

integrate((((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^2)^2+(75*x-75)*exp(x^2)+125* 
x-125)*log(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x))*log(log(x 
*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x)))-exp(x^2)^3-15*exp(x^ 
2)^2+((-4*x^3+4*x^2)*exp(4)^2-75)*exp(x^2)-125)/((-1+x)*exp(x^2)^3+(15*x-1 
5)*exp(x^2)^2+(75*x-75)*exp(x^2)+125*x-125)/log(x*exp(exp(4)^2/(exp(x^2)^2 
+10*exp(x^2)+25))/(-4+4*x)),x, algorithm="giac")
 

Output:

Timed out
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=-\int \frac {15\,{\mathrm {e}}^{2\,x^2}+{\mathrm {e}}^{3\,x^2}-{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^8\,\left (4\,x^2-4\,x^3\right )-75\right )-\ln \left (\ln \left (\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^8}{10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25}}}{4\,x-4}\right )\right )\,\ln \left (\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^8}{10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25}}}{4\,x-4}\right )\,\left (125\,x+{\mathrm {e}}^{2\,x^2}\,\left (15\,x-15\right )+{\mathrm {e}}^{3\,x^2}\,\left (x-1\right )+{\mathrm {e}}^{x^2}\,\left (75\,x-75\right )-125\right )+125}{\ln \left (\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^8}{10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25}}}{4\,x-4}\right )\,\left (125\,x+{\mathrm {e}}^{2\,x^2}\,\left (15\,x-15\right )+{\mathrm {e}}^{3\,x^2}\,\left (x-1\right )+{\mathrm {e}}^{x^2}\,\left (75\,x-75\right )-125\right )} \,d x \] Input:

int(-(15*exp(2*x^2) + exp(3*x^2) - exp(x^2)*(exp(8)*(4*x^2 - 4*x^3) - 75) 
- log(log((x*exp(exp(8)/(10*exp(x^2) + exp(2*x^2) + 25)))/(4*x - 4)))*log( 
(x*exp(exp(8)/(10*exp(x^2) + exp(2*x^2) + 25)))/(4*x - 4))*(125*x + exp(2* 
x^2)*(15*x - 15) + exp(3*x^2)*(x - 1) + exp(x^2)*(75*x - 75) - 125) + 125) 
/(log((x*exp(exp(8)/(10*exp(x^2) + exp(2*x^2) + 25)))/(4*x - 4))*(125*x + 
exp(2*x^2)*(15*x - 15) + exp(3*x^2)*(x - 1) + exp(x^2)*(75*x - 75) - 125)) 
,x)
 

Output:

-int((15*exp(2*x^2) + exp(3*x^2) - exp(x^2)*(exp(8)*(4*x^2 - 4*x^3) - 75) 
- log(log((x*exp(exp(8)/(10*exp(x^2) + exp(2*x^2) + 25)))/(4*x - 4)))*log( 
(x*exp(exp(8)/(10*exp(x^2) + exp(2*x^2) + 25)))/(4*x - 4))*(125*x + exp(2* 
x^2)*(15*x - 15) + exp(3*x^2)*(x - 1) + exp(x^2)*(75*x - 75) - 125) + 125) 
/(log((x*exp(exp(8)/(10*exp(x^2) + exp(2*x^2) + 25)))/(4*x - 4))*(125*x + 
exp(2*x^2)*(15*x - 15) + exp(3*x^2)*(x - 1) + exp(x^2)*(75*x - 75) - 125)) 
, x)
 

Reduce [F]

\[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=\int \frac {\left (\left (x -1\right ) \left ({\mathrm e}^{x^{2}}\right )^{3}+\left (15 x -15\right ) \left ({\mathrm e}^{x^{2}}\right )^{2}+\left (75 x -75\right ) {\mathrm e}^{x^{2}}+125 x -125\right ) \mathrm {log}\left (\frac {x \,{\mathrm e}^{\frac {\left ({\mathrm e}^{4}\right )^{2}}{\left ({\mathrm e}^{x^{2}}\right )^{2}+10 \,{\mathrm e}^{x^{2}}+25}}}{-4+4 x}\right ) \mathrm {log}\left (\mathrm {log}\left (\frac {x \,{\mathrm e}^{\frac {\left ({\mathrm e}^{4}\right )^{2}}{\left ({\mathrm e}^{x^{2}}\right )^{2}+10 \,{\mathrm e}^{x^{2}}+25}}}{-4+4 x}\right )\right )-\left ({\mathrm e}^{x^{2}}\right )^{3}-15 \left ({\mathrm e}^{x^{2}}\right )^{2}+\left (\left (-4 x^{3}+4 x^{2}\right ) \left ({\mathrm e}^{4}\right )^{2}-75\right ) {\mathrm e}^{x^{2}}-125}{\left (\left (x -1\right ) \left ({\mathrm e}^{x^{2}}\right )^{3}+\left (15 x -15\right ) \left ({\mathrm e}^{x^{2}}\right )^{2}+\left (75 x -75\right ) {\mathrm e}^{x^{2}}+125 x -125\right ) \mathrm {log}\left (\frac {x \,{\mathrm e}^{\frac {\left ({\mathrm e}^{4}\right )^{2}}{\left ({\mathrm e}^{x^{2}}\right )^{2}+10 \,{\mathrm e}^{x^{2}}+25}}}{-4+4 x}\right )}d x \] Input:

int((((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^2)^2+(75*x-75)*exp(x^2)+125*x-125) 
*log(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x))*log(log(x*exp(e 
xp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x)))-exp(x^2)^3-15*exp(x^2)^2+( 
(-4*x^3+4*x^2)*exp(4)^2-75)*exp(x^2)-125)/((-1+x)*exp(x^2)^3+(15*x-15)*exp 
(x^2)^2+(75*x-75)*exp(x^2)+125*x-125)/log(x*exp(exp(4)^2/(exp(x^2)^2+10*ex 
p(x^2)+25))/(-4+4*x)),x)
 

Output:

int((((-1+x)*exp(x^2)^3+(15*x-15)*exp(x^2)^2+(75*x-75)*exp(x^2)+125*x-125) 
*log(x*exp(exp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x))*log(log(x*exp(e 
xp(4)^2/(exp(x^2)^2+10*exp(x^2)+25))/(-4+4*x)))-exp(x^2)^3-15*exp(x^2)^2+( 
(-4*x^3+4*x^2)*exp(4)^2-75)*exp(x^2)-125)/((-1+x)*exp(x^2)^3+(15*x-15)*exp 
(x^2)^2+(75*x-75)*exp(x^2)+125*x-125)/log(x*exp(exp(4)^2/(exp(x^2)^2+10*ex 
p(x^2)+25))/(-4+4*x)),x)