Integrand size = 232, antiderivative size = 29 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (-1+x)}\right )\right ) \]
Time = 0.28 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (-1+x)}\right )\right ) \]
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]
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 |
| \(\displaystyle -\int \frac {1}{(x-1) \log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx+20 e^8 \int \frac {x^2}{\left (5+e^{x^2}\right )^3 \log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx-4 e^8 \int \frac {x^2}{\left (5+e^{x^2}\right )^2 \log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx+\int \frac {\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (x-1)}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 (x-1)}\right )\right )}{\log \left (\frac {e^{\frac {e^8}{\left (5+e^{x^2}\right )^2}} x}{4 x-4}\right )}dx\) |
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]
3.4.68.3.1 Defintions of rubi rules used
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.08 (sec) , antiderivative size = 302, normalized size of antiderivative = 10.41
\[\ln \left (-2 \ln \left (2\right )+\ln \left (x \right )+\ln \left ({\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}\right )-\ln \left (-1+x \right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right ) \left (-\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (\frac {i}{-1+x}\right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i x \,{\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right ) \left (-\operatorname {csgn}\left (\frac {i x \,{\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (i x \right )\right ) \left (-\operatorname {csgn}\left (\frac {i x \,{\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )+\operatorname {csgn}\left (\frac {i {\mathrm e}^{\frac {{\mathrm e}^{8}}{{\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25}}}{-1+x}\right )\right )}{2}\right ) x\]
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)
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
Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.10 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (\log \left (\frac {x e^{\left (\frac {e^{8}}{e^{\left (2 \, x^{2}\right )} + 10 \, e^{\left (x^{2}\right )} + 25}\right )}}{4 \, {\left (x - 1\right )}}\right )\right ) \]
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=\
Timed out. \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=\text {Timed out} \]
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)
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (24) = 48\).
Time = 0.38 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.62 \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=x \log \left (-{\left (2 \, \log \left (2\right ) + \log \left (x - 1\right )\right )} e^{\left (2 \, x^{2}\right )} - 10 \, {\left (2 \, \log \left (2\right ) + \log \left (x - 1\right )\right )} e^{\left (x^{2}\right )} + {\left (e^{\left (2 \, x^{2}\right )} + 10 \, e^{\left (x^{2}\right )} + 25\right )} \log \left (x\right ) + e^{8} - 50 \, \log \left (2\right ) - 25 \, \log \left (x - 1\right )\right ) - 2 \, x \log \left (e^{\left (x^{2}\right )} + 5\right ) \]
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=\
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)
Timed out. \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=\text {Timed out} \]
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=\
Timed out. \[ \int \frac {-125-15 e^{2 x^2}-e^{3 x^2}+e^{x^2} \left (-75+e^8 \left (4 x^2-4 x^3\right )\right )+\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right ) \log \left (\log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )\right )}{\left (-125+e^{3 x^2} (-1+x)+125 x+e^{2 x^2} (-15+15 x)+e^{x^2} (-75+75 x)\right ) \log \left (\frac {e^{\frac {e^8}{25+10 e^{x^2}+e^{2 x^2}}} x}{-4+4 x}\right )} \, dx=-\int \frac {15\,{\mathrm {e}}^{2\,x^2}+{\mathrm {e}}^{3\,x^2}-{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^8\,\left (4\,x^2-4\,x^3\right )-75\right )-\ln \left (\ln \left (\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^8}{10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25}}}{4\,x-4}\right )\right )\,\ln \left (\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^8}{10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25}}}{4\,x-4}\right )\,\left (125\,x+{\mathrm {e}}^{2\,x^2}\,\left (15\,x-15\right )+{\mathrm {e}}^{3\,x^2}\,\left (x-1\right )+{\mathrm {e}}^{x^2}\,\left (75\,x-75\right )-125\right )+125}{\ln \left (\frac {x\,{\mathrm {e}}^{\frac {{\mathrm {e}}^8}{10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25}}}{4\,x-4}\right )\,\left (125\,x+{\mathrm {e}}^{2\,x^2}\,\left (15\,x-15\right )+{\mathrm {e}}^{3\,x^2}\,\left (x-1\right )+{\mathrm {e}}^{x^2}\,\left (75\,x-75\right )-125\right )} \,d x \]
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)
-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)