\(\int \frac {e^{\frac {-5-3 x+3 (65536-512 x+x^2)^{2 \log ^2(x^2)}}{-x+(65536-512 x+x^2)^{2 \log ^2(x^2)}}} (1280 x-5 x^2+(65536-512 x+x^2)^{2 \log ^2(x^2)} (20 x \log ^2(x^2)+(-10240+40 x) \log (x^2) \log (65536-512 x+x^2)))}{-256 x^3+x^4+(65536-512 x+x^2)^{4 \log ^2(x^2)} (-256 x+x^2)+(65536-512 x+x^2)^{2 \log ^2(x^2)} (512 x^2-2 x^3)} \, dx\) [44]

Optimal result

Integrand size = 172, antiderivative size = 26 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{3+\frac {5}{-\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}+x}} \] Output:

exp(5/(x-exp(ln((x-256)^2)*ln(x^2)^2)^2)+3)
 

Mathematica [A] (verified)

Time = 0.19 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{3-\frac {5}{\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x}} \] Input:

Integrate[(E^((-5 - 3*x + 3*(65536 - 512*x + x^2)^(2*Log[x^2]^2))/(-x + (6 
5536 - 512*x + x^2)^(2*Log[x^2]^2)))*(1280*x - 5*x^2 + (65536 - 512*x + x^ 
2)^(2*Log[x^2]^2)*(20*x*Log[x^2]^2 + (-10240 + 40*x)*Log[x^2]*Log[65536 - 
512*x + x^2])))/(-256*x^3 + x^4 + (65536 - 512*x + x^2)^(4*Log[x^2]^2)*(-2 
56*x + x^2) + (65536 - 512*x + x^2)^(2*Log[x^2]^2)*(512*x^2 - 2*x^3)),x]
 

Output:

E^(3 - 5/(((-256 + x)^2)^(2*Log[x^2]^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.

\(\displaystyle \int \frac {\left (-5 x^2+\left (20 x \log ^2\left (x^2\right )+(40 x-10240) \log \left (x^2-512 x+65536\right ) \log \left (x^2\right )\right ) \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}+1280 x\right ) \exp \left (\frac {3 \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{x^4-256 x^3+\left (x^2-256 x\right ) \left (x^2-512 x+65536\right )^{4 \log ^2\left (x^2\right )}+\left (512 x^2-2 x^3\right ) \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (5 x^2-\left (\left (20 x \log ^2\left (x^2\right )+(40 x-10240) \log \left (x^2-512 x+65536\right ) \log \left (x^2\right )\right ) \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}\right )-1280 x\right ) \exp \left (\frac {3 \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{(256-x) x \left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {20 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (x \log \left (x^2\right )+2 x \log \left ((x-256)^2\right )-512 \log \left ((x-256)^2\right )\right ) \exp \left (\frac {3 \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{(x-256) x \left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}-\frac {5 \exp \left (\frac {3 \left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left (x^2-512 x+65536\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{\left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {20 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-x \log \left (x^2\right )-2 x \log \left ((x-256)^2\right )+512 \log \left ((x-256)^2\right )\right ) \exp \left (\frac {3 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{(256-x) x \left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}-\frac {5 \exp \left (\frac {3 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{\left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle \int \left (\frac {20 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-x \log \left (x^2\right )-2 x \log \left ((x-256)^2\right )+512 \log \left ((x-256)^2\right )\right ) \exp \left (\frac {3 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{(256-x) x \left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}-\frac {5 \exp \left (\frac {3 \left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-3 x-5}{\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x}\right )}{\left (\left ((x-256)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}\right )dx\)

Input:

Int[(E^((-5 - 3*x + 3*(65536 - 512*x + x^2)^(2*Log[x^2]^2))/(-x + (65536 - 
 512*x + x^2)^(2*Log[x^2]^2)))*(1280*x - 5*x^2 + (65536 - 512*x + x^2)^(2* 
Log[x^2]^2)*(20*x*Log[x^2]^2 + (-10240 + 40*x)*Log[x^2]*Log[65536 - 512*x 
+ x^2])))/(-256*x^3 + x^4 + (65536 - 512*x + x^2)^(4*Log[x^2]^2)*(-256*x + 
 x^2) + (65536 - 512*x + x^2)^(2*Log[x^2]^2)*(512*x^2 - 2*x^3)),x]
 

Output:

$Aborted
 

Maple [C] (warning: unable to verify)

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

Time = 0.31 (sec) , antiderivative size = 266, normalized size of antiderivative = 10.23

\[{\mathrm e}^{\frac {-3 \,{\mathrm e}^{-\frac {\left (i \pi \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{3}-2 i \pi \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{2} \operatorname {csgn}\left (i \left (x -256\right )\right )+i \pi \,\operatorname {csgn}\left (i \left (x -256\right )^{2}\right ) \operatorname {csgn}\left (i \left (x -256\right )\right )^{2}-4 \ln \left (x -256\right )\right ) {\left (-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+4 \ln \left (x \right )\right )}^{2}}{4}}+3 x +5}{-{\mathrm e}^{-\frac {\left (i \pi \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{3}-2 i \pi \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{2} \operatorname {csgn}\left (i \left (x -256\right )\right )+i \pi \,\operatorname {csgn}\left (i \left (x -256\right )^{2}\right ) \operatorname {csgn}\left (i \left (x -256\right )\right )^{2}-4 \ln \left (x -256\right )\right ) {\left (-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+4 \ln \left (x \right )\right )}^{2}}{4}}+x}}\]

Input:

int(((20*x*ln(x^2)^2+(40*x-10240)*ln(x^2-512*x+65536)*ln(x^2))*exp(ln(x^2- 
512*x+65536)*ln(x^2)^2)^2-5*x^2+1280*x)*exp((3*exp(ln(x^2-512*x+65536)*ln( 
x^2)^2)^2-3*x-5)/(exp(ln(x^2-512*x+65536)*ln(x^2)^2)^2-x))/((x^2-256*x)*ex 
p(ln(x^2-512*x+65536)*ln(x^2)^2)^4+(-2*x^3+512*x^2)*exp(ln(x^2-512*x+65536 
)*ln(x^2)^2)^2+x^4-256*x^3),x)
 

Output:

exp((-3*exp(-1/4*(I*Pi*csgn(I*(x-256)^2)^3-2*I*Pi*csgn(I*(x-256)^2)^2*csgn 
(I*(x-256))+I*Pi*csgn(I*(x-256)^2)*csgn(I*(x-256))^2-4*ln(x-256))*(-I*Pi*c 
sgn(I*x^2)^3+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi*csgn(I*x^2)*csgn(I*x)^2+4 
*ln(x))^2)+3*x+5)/(-exp(-1/4*(I*Pi*csgn(I*(x-256)^2)^3-2*I*Pi*csgn(I*(x-25 
6)^2)^2*csgn(I*(x-256))+I*Pi*csgn(I*(x-256)^2)*csgn(I*(x-256))^2-4*ln(x-25 
6))*(-I*Pi*csgn(I*x^2)^3+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi*csgn(I*x^2)*c 
sgn(I*x)^2+4*ln(x))^2)+x))
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.88 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{\left (\frac {3 \, {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - 3 \, x - 5}{{\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - x}\right )} \] Input:

integrate(((20*x*log(x^2)^2+(40*x-10240)*log(x^2-512*x+65536)*log(x^2))*ex 
p(log(x^2-512*x+65536)*log(x^2)^2)^2-5*x^2+1280*x)*exp((3*exp(log(x^2-512* 
x+65536)*log(x^2)^2)^2-3*x-5)/(exp(log(x^2-512*x+65536)*log(x^2)^2)^2-x))/ 
((x^2-256*x)*exp(log(x^2-512*x+65536)*log(x^2)^2)^4+(-2*x^3+512*x^2)*exp(l 
og(x^2-512*x+65536)*log(x^2)^2)^2+x^4-256*x^3),x, algorithm="fricas")
 

Output:

e^((3*(x^2 - 512*x + 65536)^(2*log(x^2)^2) - 3*x - 5)/((x^2 - 512*x + 6553 
6)^(2*log(x^2)^2) - x))
 

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=\text {Timed out} \] Input:

integrate(((20*x*ln(x**2)**2+(40*x-10240)*ln(x**2-512*x+65536)*ln(x**2))*e 
xp(ln(x**2-512*x+65536)*ln(x**2)**2)**2-5*x**2+1280*x)*exp((3*exp(ln(x**2- 
512*x+65536)*ln(x**2)**2)**2-3*x-5)/(exp(ln(x**2-512*x+65536)*ln(x**2)**2) 
**2-x))/((x**2-256*x)*exp(ln(x**2-512*x+65536)*ln(x**2)**2)**4+(-2*x**3+51 
2*x**2)*exp(ln(x**2-512*x+65536)*ln(x**2)**2)**2+x**4-256*x**3),x)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{\left (-\frac {5}{{\left (x - 256\right )}^{16 \, \log \left (x\right )^{2}} - x} + 3\right )} \] Input:

integrate(((20*x*log(x^2)^2+(40*x-10240)*log(x^2-512*x+65536)*log(x^2))*ex 
p(log(x^2-512*x+65536)*log(x^2)^2)^2-5*x^2+1280*x)*exp((3*exp(log(x^2-512* 
x+65536)*log(x^2)^2)^2-3*x-5)/(exp(log(x^2-512*x+65536)*log(x^2)^2)^2-x))/ 
((x^2-256*x)*exp(log(x^2-512*x+65536)*log(x^2)^2)^4+(-2*x^3+512*x^2)*exp(l 
og(x^2-512*x+65536)*log(x^2)^2)^2+x^4-256*x^3),x, algorithm="maxima")
 

Output:

e^(-5/((x - 256)^(16*log(x)^2) - x) + 3)
 

Giac [F]

\[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=\int { \frac {5 \, {\left (4 \, {\left (2 \, {\left (x - 256\right )} \log \left (x^{2} - 512 \, x + 65536\right ) \log \left (x^{2}\right ) + x \log \left (x^{2}\right )^{2}\right )} {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - x^{2} + 256 \, x\right )} e^{\left (\frac {3 \, {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - 3 \, x - 5}{{\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - x}\right )}}{x^{4} - 256 \, x^{3} + {\left (x^{2} - 256 \, x\right )} {\left (x^{2} - 512 \, x + 65536\right )}^{4 \, \log \left (x^{2}\right )^{2}} - 2 \, {\left (x^{3} - 256 \, x^{2}\right )} {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}}} \,d x } \] Input:

integrate(((20*x*log(x^2)^2+(40*x-10240)*log(x^2-512*x+65536)*log(x^2))*ex 
p(log(x^2-512*x+65536)*log(x^2)^2)^2-5*x^2+1280*x)*exp((3*exp(log(x^2-512* 
x+65536)*log(x^2)^2)^2-3*x-5)/(exp(log(x^2-512*x+65536)*log(x^2)^2)^2-x))/ 
((x^2-256*x)*exp(log(x^2-512*x+65536)*log(x^2)^2)^4+(-2*x^3+512*x^2)*exp(l 
og(x^2-512*x+65536)*log(x^2)^2)^2+x^4-256*x^3),x, algorithm="giac")
 

Output:

integrate(5*(4*(2*(x - 256)*log(x^2 - 512*x + 65536)*log(x^2) + x*log(x^2) 
^2)*(x^2 - 512*x + 65536)^(2*log(x^2)^2) - x^2 + 256*x)*e^((3*(x^2 - 512*x 
 + 65536)^(2*log(x^2)^2) - 3*x - 5)/((x^2 - 512*x + 65536)^(2*log(x^2)^2) 
- x))/(x^4 - 256*x^3 + (x^2 - 256*x)*(x^2 - 512*x + 65536)^(4*log(x^2)^2) 
- 2*(x^3 - 256*x^2)*(x^2 - 512*x + 65536)^(2*log(x^2)^2)), x)
 

Mupad [B] (verification not implemented)

Time = 4.15 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.73 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx={\mathrm {e}}^{-\frac {3\,{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}{x-{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}}\,{\mathrm {e}}^{\frac {3\,x}{x-{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}}\,{\mathrm {e}}^{\frac {5}{x-{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}} \] Input:

int((exp((3*x - 3*exp(2*log(x^2)^2*log(x^2 - 512*x + 65536)) + 5)/(x - exp 
(2*log(x^2)^2*log(x^2 - 512*x + 65536))))*(1280*x + exp(2*log(x^2)^2*log(x 
^2 - 512*x + 65536))*(20*x*log(x^2)^2 + log(x^2)*log(x^2 - 512*x + 65536)* 
(40*x - 10240)) - 5*x^2))/(exp(2*log(x^2)^2*log(x^2 - 512*x + 65536))*(512 
*x^2 - 2*x^3) - exp(4*log(x^2)^2*log(x^2 - 512*x + 65536))*(256*x - x^2) - 
 256*x^3 + x^4),x)
 

Output:

exp(-(3*(x^2 - 512*x + 65536)^(2*log(x^2)^2))/(x - (x^2 - 512*x + 65536)^( 
2*log(x^2)^2)))*exp((3*x)/(x - (x^2 - 512*x + 65536)^(2*log(x^2)^2)))*exp( 
5/(x - (x^2 - 512*x + 65536)^(2*log(x^2)^2)))
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=\frac {e^{3}}{e^{\frac {5}{e^{2 \mathrm {log}\left (x^{2}\right )^{2} \mathrm {log}\left (x^{2}-512 x +65536\right )}-x}}} \] Input:

int(((20*x*log(x^2)^2+(40*x-10240)*log(x^2-512*x+65536)*log(x^2))*exp(log( 
x^2-512*x+65536)*log(x^2)^2)^2-5*x^2+1280*x)*exp((3*exp(log(x^2-512*x+6553 
6)*log(x^2)^2)^2-3*x-5)/(exp(log(x^2-512*x+65536)*log(x^2)^2)^2-x))/((x^2- 
256*x)*exp(log(x^2-512*x+65536)*log(x^2)^2)^4+(-2*x^3+512*x^2)*exp(log(x^2 
-512*x+65536)*log(x^2)^2)^2+x^4-256*x^3),x)
 

Output:

e**3/e**(5/(e**(2*log(x**2)**2*log(x**2 - 512*x + 65536)) - x))