\(\int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+(-4 x^4-2 x^2 \log (2)) \log (-25+\log (x^2))+x^3 \log ^2(-25+\log (x^2))} (-50 x-8 x^3-500 x^4+(-4 x-300 x^2) \log (2)-25 \log ^2(2)+(2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)) \log (x^2)+(4 x^2+400 x^3+100 x \log (2)+(-16 x^3-4 x \log (2)) \log (x^2)) \log (-25+\log (x^2))+(-75 x^2+3 x^2 \log (x^2)) \log ^2(-25+\log (x^2)))}{-25+\log (x^2)} \, dx\) [1074]

Optimal result

Integrand size = 190, antiderivative size = 28 \[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=e^{-4+x \left (x+\left (\log (2)+x \left (2 x-\log \left (-25+\log \left (x^2\right )\right )\right )\right )^2\right )} \] Output:

exp((x+(ln(2)+(2*x-ln(ln(x^2)-25))*x)^2)*x-4)
                                                                                    
                                                                                    
 

Mathematica [F]

\[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=\int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx \] Input:

Integrate[(E^(-4 + x^2 + 4*x^5 + 4*x^3*Log[2] + x*Log[2]^2 + (-4*x^4 - 2*x 
^2*Log[2])*Log[-25 + Log[x^2]] + x^3*Log[-25 + Log[x^2]]^2)*(-50*x - 8*x^3 
 - 500*x^4 + (-4*x - 300*x^2)*Log[2] - 25*Log[2]^2 + (2*x + 20*x^4 + 12*x^ 
2*Log[2] + Log[2]^2)*Log[x^2] + (4*x^2 + 400*x^3 + 100*x*Log[2] + (-16*x^3 
 - 4*x*Log[2])*Log[x^2])*Log[-25 + Log[x^2]] + (-75*x^2 + 3*x^2*Log[x^2])* 
Log[-25 + Log[x^2]]^2))/(-25 + Log[x^2]),x]
 

Output:

Integrate[(E^(-4 + x^2 + 4*x^5 + 4*x^3*Log[2] + x*Log[2]^2 + (-4*x^4 - 2*x 
^2*Log[2])*Log[-25 + Log[x^2]] + x^3*Log[-25 + Log[x^2]]^2)*(-50*x - 8*x^3 
 - 500*x^4 + (-4*x - 300*x^2)*Log[2] - 25*Log[2]^2 + (2*x + 20*x^4 + 12*x^ 
2*Log[2] + Log[2]^2)*Log[x^2] + (4*x^2 + 400*x^3 + 100*x*Log[2] + (-16*x^3 
 - 4*x*Log[2])*Log[x^2])*Log[-25 + Log[x^2]] + (-75*x^2 + 3*x^2*Log[x^2])* 
Log[-25 + Log[x^2]]^2))/(-25 + Log[x^2]), 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.

\(\displaystyle \int \frac {\left (-500 x^4-8 x^3+\left (3 x^2 \log \left (x^2\right )-75 x^2\right ) \log ^2\left (\log \left (x^2\right )-25\right )+\left (-300 x^2-4 x\right ) \log (2)+\left (20 x^4+12 x^2 \log (2)+2 x+\log ^2(2)\right ) \log \left (x^2\right )+\left (400 x^3+4 x^2+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )+100 x \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )-50 x-25 \log ^2(2)\right ) \exp \left (4 x^5+4 x^3 \log (2)+x^2+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )}{\log \left (x^2\right )-25} \, dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (3 x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \exp \left (4 x^5+4 x^3 \log (2)+x^2+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )-\frac {4 x \left (-100 x^2+4 x^2 \log \left (x^2\right )+\log (2) \log \left (x^2\right )-x-25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \exp \left (4 x^5+4 x^3 \log (2)+x^2+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )}{\log \left (x^2\right )-25}+\frac {\left (500 x^4+8 x^3-\log ^2(2) \log \left (x^2\right )-12 x^2 \log (2) \log \left (x^2\right )+300 x^2 \log (2)-2 x \log \left (x^2\right )-20 x^4 \log \left (x^2\right )+50 x \left (1+\frac {2 \log (2)}{25}\right )+25 \log ^2(2)\right ) \exp \left (4 x^5+4 x^3 \log (2)+x^2+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )}{25-\log \left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (4 x^5+x^2+x^3 \log ^2\left (\log \left (x^2\right )-25\right )+x \log ^2(2)-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-125\ 4^{2 x^3+1} x^4 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+3} x^3 \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 16^{x^3} x^2 \log ^2\left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+4^{2 x^3+1} x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )+16^{x^3} \log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \log (2) \log \left (\log \left (x^2\right )-25\right )-16 x^3 \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right ) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-2^{4 x^3+1} x (25+\log (4)) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-25\ 16^{x^3} \log ^2(2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )-75\ 4^{2 x^3+1} x^2 \log (2) \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 16^{x^3} \left (\log \left (x^2\right )-25\right )^{-4 x^4-x^2 \log (4)-1} \left (-500 x^4-8 x^3-75 x^2 \log ^2\left (\log \left (x^2\right )-25\right )-300 x^2 \log (2)+4 x \left (100 x^2+x+25 \log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+\log \left (x^2\right ) \left (20 x^4+3 x^2 \log ^2\left (\log \left (x^2\right )-25\right )+12 x^2 \log (2)-4 x \left (4 x^2+\log (2)\right ) \log \left (\log \left (x^2\right )-25\right )+2 x+\log ^2(2)\right )-50 x \left (1+\frac {2 \log (2)}{25}\right )-25 \log ^2(2)\right ) \exp \left (x \left (4 x^4+x^2 \log ^2\left (\log \left (x^2\right )-25\right )+x+\log ^2(2)\right )-4\right )dx\)

Input:

Int[(E^(-4 + x^2 + 4*x^5 + 4*x^3*Log[2] + x*Log[2]^2 + (-4*x^4 - 2*x^2*Log 
[2])*Log[-25 + Log[x^2]] + x^3*Log[-25 + Log[x^2]]^2)*(-50*x - 8*x^3 - 500 
*x^4 + (-4*x - 300*x^2)*Log[2] - 25*Log[2]^2 + (2*x + 20*x^4 + 12*x^2*Log[ 
2] + Log[2]^2)*Log[x^2] + (4*x^2 + 400*x^3 + 100*x*Log[2] + (-16*x^3 - 4*x 
*Log[2])*Log[x^2])*Log[-25 + Log[x^2]] + (-75*x^2 + 3*x^2*Log[x^2])*Log[-2 
5 + Log[x^2]]^2))/(-25 + Log[x^2]),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(27)=54\).

Time = 15.88 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11

method	result	size
parallelrisch	\({\mathrm e}^{x^{3} {\ln \left (\ln \left (x^{2}\right )-25\right )}^{2}+\left (-2 x^{2} \ln \left (2\right )-4 x^{4}\right ) \ln \left (\ln \left (x^{2}\right )-25\right )+x \ln \left (2\right )^{2}+4 x^{3} \ln \left (2\right )+4 x^{5}+x^{2}-4}\)	\(59\)

Input:

int(((3*x^2*ln(x^2)-75*x^2)*ln(ln(x^2)-25)^2+((-4*x*ln(2)-16*x^3)*ln(x^2)+ 
100*x*ln(2)+400*x^3+4*x^2)*ln(ln(x^2)-25)+(ln(2)^2+12*x^2*ln(2)+20*x^4+2*x 
)*ln(x^2)-25*ln(2)^2+(-300*x^2-4*x)*ln(2)-500*x^4-8*x^3-50*x)*exp(x^3*ln(l 
n(x^2)-25)^2+(-2*x^2*ln(2)-4*x^4)*ln(ln(x^2)-25)+x*ln(2)^2+4*x^3*ln(2)+4*x 
^5+x^2-4)/(ln(x^2)-25),x,method=_RETURNVERBOSE)
 

Output:

exp(x^3*ln(ln(x^2)-25)^2+(-2*x^2*ln(2)-4*x^4)*ln(ln(x^2)-25)+x*ln(2)^2+4*x 
^3*ln(2)+4*x^5+x^2-4)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (27) = 54\).

Time = 0.07 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=e^{\left (4 \, x^{5} + x^{3} \log \left (\log \left (x^{2}\right ) - 25\right )^{2} + 4 \, x^{3} \log \left (2\right ) + x \log \left (2\right )^{2} + x^{2} - 2 \, {\left (2 \, x^{4} + x^{2} \log \left (2\right )\right )} \log \left (\log \left (x^{2}\right ) - 25\right ) - 4\right )} \] Input:

integrate(((3*x^2*log(x^2)-75*x^2)*log(log(x^2)-25)^2+((-4*x*log(2)-16*x^3 
)*log(x^2)+100*x*log(2)+400*x^3+4*x^2)*log(log(x^2)-25)+(log(2)^2+12*x^2*l 
og(2)+20*x^4+2*x)*log(x^2)-25*log(2)^2+(-300*x^2-4*x)*log(2)-500*x^4-8*x^3 
-50*x)*exp(x^3*log(log(x^2)-25)^2+(-2*x^2*log(2)-4*x^4)*log(log(x^2)-25)+x 
*log(2)^2+4*x^3*log(2)+4*x^5+x^2-4)/(log(x^2)-25),x, algorithm="fricas")
 

Output:

e^(4*x^5 + x^3*log(log(x^2) - 25)^2 + 4*x^3*log(2) + x*log(2)^2 + x^2 - 2* 
(2*x^4 + x^2*log(2))*log(log(x^2) - 25) - 4)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (24) = 48\).

Time = 0.79 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=e^{4 x^{5} + x^{3} \log {\left (\log {\left (x^{2} \right )} - 25 \right )}^{2} + 4 x^{3} \log {\left (2 \right )} + x^{2} + x \log {\left (2 \right )}^{2} + \left (- 4 x^{4} - 2 x^{2} \log {\left (2 \right )}\right ) \log {\left (\log {\left (x^{2} \right )} - 25 \right )} - 4} \] Input:

integrate(((3*x**2*ln(x**2)-75*x**2)*ln(ln(x**2)-25)**2+((-4*x*ln(2)-16*x* 
*3)*ln(x**2)+100*x*ln(2)+400*x**3+4*x**2)*ln(ln(x**2)-25)+(ln(2)**2+12*x** 
2*ln(2)+20*x**4+2*x)*ln(x**2)-25*ln(2)**2+(-300*x**2-4*x)*ln(2)-500*x**4-8 
*x**3-50*x)*exp(x**3*ln(ln(x**2)-25)**2+(-2*x**2*ln(2)-4*x**4)*ln(ln(x**2) 
-25)+x*ln(2)**2+4*x**3*ln(2)+4*x**5+x**2-4)/(ln(x**2)-25),x)
 

Output:

exp(4*x**5 + x**3*log(log(x**2) - 25)**2 + 4*x**3*log(2) + x**2 + x*log(2) 
**2 + (-4*x**4 - 2*x**2*log(2))*log(log(x**2) - 25) - 4)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (27) = 54\).

Time = 0.33 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=e^{\left (4 \, x^{5} - 4 \, x^{4} \log \left (2 \, \log \left (x\right ) - 25\right ) + x^{3} \log \left (2 \, \log \left (x\right ) - 25\right )^{2} + 4 \, x^{3} \log \left (2\right ) - 2 \, x^{2} \log \left (2\right ) \log \left (2 \, \log \left (x\right ) - 25\right ) + x \log \left (2\right )^{2} + x^{2} - 4\right )} \] Input:

integrate(((3*x^2*log(x^2)-75*x^2)*log(log(x^2)-25)^2+((-4*x*log(2)-16*x^3 
)*log(x^2)+100*x*log(2)+400*x^3+4*x^2)*log(log(x^2)-25)+(log(2)^2+12*x^2*l 
og(2)+20*x^4+2*x)*log(x^2)-25*log(2)^2+(-300*x^2-4*x)*log(2)-500*x^4-8*x^3 
-50*x)*exp(x^3*log(log(x^2)-25)^2+(-2*x^2*log(2)-4*x^4)*log(log(x^2)-25)+x 
*log(2)^2+4*x^3*log(2)+4*x^5+x^2-4)/(log(x^2)-25),x, algorithm="maxima")
 

Output:

e^(4*x^5 - 4*x^4*log(2*log(x) - 25) + x^3*log(2*log(x) - 25)^2 + 4*x^3*log 
(2) - 2*x^2*log(2)*log(2*log(x) - 25) + x*log(2)^2 + x^2 - 4)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (27) = 54\).

Time = 0.76 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=e^{\left (4 \, x^{5} - 4 \, x^{4} \log \left (\log \left (x^{2}\right ) - 25\right ) + x^{3} \log \left (\log \left (x^{2}\right ) - 25\right )^{2} + 4 \, x^{3} \log \left (2\right ) - 2 \, x^{2} \log \left (2\right ) \log \left (\log \left (x^{2}\right ) - 25\right ) + x \log \left (2\right )^{2} + x^{2} - 4\right )} \] Input:

integrate(((3*x^2*log(x^2)-75*x^2)*log(log(x^2)-25)^2+((-4*x*log(2)-16*x^3 
)*log(x^2)+100*x*log(2)+400*x^3+4*x^2)*log(log(x^2)-25)+(log(2)^2+12*x^2*l 
og(2)+20*x^4+2*x)*log(x^2)-25*log(2)^2+(-300*x^2-4*x)*log(2)-500*x^4-8*x^3 
-50*x)*exp(x^3*log(log(x^2)-25)^2+(-2*x^2*log(2)-4*x^4)*log(log(x^2)-25)+x 
*log(2)^2+4*x^3*log(2)+4*x^5+x^2-4)/(log(x^2)-25),x, algorithm="giac")
 

Output:

e^(4*x^5 - 4*x^4*log(log(x^2) - 25) + x^3*log(log(x^2) - 25)^2 + 4*x^3*log 
(2) - 2*x^2*log(2)*log(log(x^2) - 25) + x*log(2)^2 + x^2 - 4)
 

Mupad [B] (verification not implemented)

Time = 1.95 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.18 \[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=\frac {{16}^{x^3}\,{\mathrm {e}}^{x\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{x^3\,{\ln \left (\ln \left (x^2\right )-25\right )}^2}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{4\,x^5}}{{\left (\ln \left (x^2\right )-25\right )}^{4\,x^4+2\,\ln \left (2\right )\,x^2}} \] Input:

int(-(exp(x*log(2)^2 + 4*x^3*log(2) + x^3*log(log(x^2) - 25)^2 - log(log(x 
^2) - 25)*(2*x^2*log(2) + 4*x^4) + x^2 + 4*x^5 - 4)*(50*x + log(2)*(4*x + 
300*x^2) - log(x^2)*(2*x + 12*x^2*log(2) + log(2)^2 + 20*x^4) + 25*log(2)^ 
2 + 8*x^3 + 500*x^4 - log(log(x^2) - 25)^2*(3*x^2*log(x^2) - 75*x^2) - log 
(log(x^2) - 25)*(100*x*log(2) - log(x^2)*(4*x*log(2) + 16*x^3) + 4*x^2 + 4 
00*x^3)))/(log(x^2) - 25),x)
 

Output:

(16^(x^3)*exp(x*log(2)^2)*exp(x^3*log(log(x^2) - 25)^2)*exp(x^2)*exp(-4)*e 
xp(4*x^5))/(log(x^2) - 25)^(2*x^2*log(2) + 4*x^4)
 

Reduce [F]

\[ \int \frac {e^{-4+x^2+4 x^5+4 x^3 \log (2)+x \log ^2(2)+\left (-4 x^4-2 x^2 \log (2)\right ) \log \left (-25+\log \left (x^2\right )\right )+x^3 \log ^2\left (-25+\log \left (x^2\right )\right )} \left (-50 x-8 x^3-500 x^4+\left (-4 x-300 x^2\right ) \log (2)-25 \log ^2(2)+\left (2 x+20 x^4+12 x^2 \log (2)+\log ^2(2)\right ) \log \left (x^2\right )+\left (4 x^2+400 x^3+100 x \log (2)+\left (-16 x^3-4 x \log (2)\right ) \log \left (x^2\right )\right ) \log \left (-25+\log \left (x^2\right )\right )+\left (-75 x^2+3 x^2 \log \left (x^2\right )\right ) \log ^2\left (-25+\log \left (x^2\right )\right )\right )}{-25+\log \left (x^2\right )} \, dx=\text {too large to display} \] Input:

int(((3*x^2*log(x^2)-75*x^2)*log(log(x^2)-25)^2+((-4*x*log(2)-16*x^3)*log( 
x^2)+100*x*log(2)+400*x^3+4*x^2)*log(log(x^2)-25)+(log(2)^2+12*x^2*log(2)+ 
20*x^4+2*x)*log(x^2)-25*log(2)^2+(-300*x^2-4*x)*log(2)-500*x^4-8*x^3-50*x) 
*exp(x^3*log(log(x^2)-25)^2+(-2*x^2*log(2)-4*x^4)*log(log(x^2)-25)+x*log(2 
)^2+4*x^3*log(2)+4*x^5+x^2-4)/(log(x^2)-25),x)
 

Output:

( - 75*int((e**(log(log(x**2) - 25)**2*x**3 + log(2)**2*x + 4*x**5 + x**2) 
*2**(4*x**3)*log(log(x**2) - 25)**2*x**2)/((log(x**2) - 25)**(2*log(2)*x** 
2 + 4*x**4)*log(x**2) - 25*(log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)),x) 
- 500*int((e**(log(log(x**2) - 25)**2*x**3 + log(2)**2*x + 4*x**5 + x**2)* 
2**(4*x**3)*x**4)/((log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)*log(x**2) - 
25*(log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)),x) - 8*int((e**(log(log(x** 
2) - 25)**2*x**3 + log(2)**2*x + 4*x**5 + x**2)*2**(4*x**3)*x**3)/((log(x* 
*2) - 25)**(2*log(2)*x**2 + 4*x**4)*log(x**2) - 25*(log(x**2) - 25)**(2*lo 
g(2)*x**2 + 4*x**4)),x) - 300*int((e**(log(log(x**2) - 25)**2*x**3 + log(2 
)**2*x + 4*x**5 + x**2)*2**(4*x**3)*x**2)/((log(x**2) - 25)**(2*log(2)*x** 
2 + 4*x**4)*log(x**2) - 25*(log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)),x)* 
log(2) + 3*int((e**(log(log(x**2) - 25)**2*x**3 + log(2)**2*x + 4*x**5 + x 
**2)*2**(4*x**3)*log(x**2)*log(log(x**2) - 25)**2*x**2)/((log(x**2) - 25)* 
*(2*log(2)*x**2 + 4*x**4)*log(x**2) - 25*(log(x**2) - 25)**(2*log(2)*x**2 
+ 4*x**4)),x) + 20*int((e**(log(log(x**2) - 25)**2*x**3 + log(2)**2*x + 4* 
x**5 + x**2)*2**(4*x**3)*log(x**2)*x**4)/((log(x**2) - 25)**(2*log(2)*x**2 
 + 4*x**4)*log(x**2) - 25*(log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)),x) + 
 12*int((e**(log(log(x**2) - 25)**2*x**3 + log(2)**2*x + 4*x**5 + x**2)*2* 
*(4*x**3)*log(x**2)*x**2)/((log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)*log( 
x**2) - 25*(log(x**2) - 25)**(2*log(2)*x**2 + 4*x**4)),x)*log(2) - 16*i...