\(\int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5)+8 x^4 \log (x)+(160 x+120 x^3-4 x^4+e^x (160 x-160 x^2+120 x^3-120 x^4)) \log ^2(x)+(-5 x^2+e^x (-5 x^2+5 x^3)) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+(-160 x^3-120 x^5) \log ^2(x)+5 x^4 \log ^4(x)} \, dx\) [937]

Optimal result

Integrand size = 165, antiderivative size = 39 \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=\frac {1+e^x+2 x-\frac {x}{5 \left (-3+\frac {-\frac {4}{x}+\frac {\log ^2(x)}{4}}{x}\right )}}{x} \] Output:

(exp(x)+2*x+1-1/5*x/((1/4*ln(x)^2-4/x)/x-3))/x
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.08 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.97 \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=\frac {1}{5} \left (\frac {5}{x}+\frac {5 e^x}{x}-\frac {4 x^2}{-16-12 x^2+x \log ^2(x)}\right ) \] Input:

Integrate[(-1280 - 1920*x^2 + 128*x^3 - 720*x^4 + E^x*(-1280 + 1280*x - 19 
20*x^2 + 1920*x^3 - 720*x^4 + 720*x^5) + 8*x^4*Log[x] + (160*x + 120*x^3 - 
 4*x^4 + E^x*(160*x - 160*x^2 + 120*x^3 - 120*x^4))*Log[x]^2 + (-5*x^2 + E 
^x*(-5*x^2 + 5*x^3))*Log[x]^4)/(1280*x^2 + 1920*x^4 + 720*x^6 + (-160*x^3 
- 120*x^5)*Log[x]^2 + 5*x^4*Log[x]^4),x]
 

Output:

(5/x + (5*E^x)/x - (4*x^2)/(-16 - 12*x^2 + x*Log[x]^2))/5
 

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.

\(\displaystyle \int \frac {-720 x^4+8 x^4 \log (x)+128 x^3-1920 x^2+\left (e^x \left (5 x^3-5 x^2\right )-5 x^2\right ) \log ^4(x)+\left (-4 x^4+120 x^3+e^x \left (-120 x^4+120 x^3-160 x^2+160 x\right )+160 x\right ) \log ^2(x)+e^x \left (720 x^5-720 x^4+1920 x^3-1920 x^2+1280 x-1280\right )-1280}{720 x^6+1920 x^4+5 x^4 \log ^4(x)+1280 x^2+\left (-120 x^5-160 x^3\right ) \log ^2(x)} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {-720 x^4+8 x^4 \log (x)+128 x^3-1920 x^2+\left (e^x \left (5 x^3-5 x^2\right )-5 x^2\right ) \log ^4(x)+\left (-4 x^4+120 x^3+e^x \left (-120 x^4+120 x^3-160 x^2+160 x\right )+160 x\right ) \log ^2(x)+e^x \left (720 x^5-720 x^4+1920 x^3-1920 x^2+1280 x-1280\right )-1280}{5 x^2 \left (12 x^2-x \log ^2(x)+16\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{5} \int -\frac {-8 \log (x) x^4+720 x^4-128 x^3+1920 x^2+5 \left (x^2+e^x \left (x^2-x^3\right )\right ) \log ^4(x)-4 \left (-x^4+30 x^3+40 x+10 e^x \left (-3 x^4+3 x^3-4 x^2+4 x\right )\right ) \log ^2(x)+80 e^x \left (-9 x^5+9 x^4-24 x^3+24 x^2-16 x+16\right )+1280}{x^2 \left (12 x^2-\log ^2(x) x+16\right )^2}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -\frac {1}{5} \int \frac {-8 \log (x) x^4+720 x^4-128 x^3+1920 x^2+5 \left (x^2+e^x \left (x^2-x^3\right )\right ) \log ^4(x)-4 \left (-x^4+30 x^3+40 x+10 e^x \left (-3 x^4+3 x^3-4 x^2+4 x\right )\right ) \log ^2(x)+80 e^x \left (-9 x^5+9 x^4-24 x^3+24 x^2-16 x+16\right )+1280}{x^2 \left (12 x^2-\log ^2(x) x+16\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {1}{5} \int \left (\frac {5 \log ^4(x)}{\left (-12 x^2+\log ^2(x) x-16\right )^2}+\frac {4 x^2 \log ^2(x)}{\left (12 x^2-\log ^2(x) x+16\right )^2}-\frac {120 x \log ^2(x)}{\left (12 x^2-\log ^2(x) x+16\right )^2}-\frac {160 \log ^2(x)}{x \left (12 x^2-\log ^2(x) x+16\right )^2}-\frac {8 x^2 \log (x)}{\left (12 x^2-\log ^2(x) x+16\right )^2}-\frac {5 e^x (x-1)}{x^2}+\frac {720 x^2}{\left (12 x^2-\log ^2(x) x+16\right )^2}-\frac {128 x}{\left (12 x^2-\log ^2(x) x+16\right )^2}+\frac {1280}{x^2 \left (12 x^2-\log ^2(x) x+16\right )^2}+\frac {1920}{\left (12 x^2-\log ^2(x) x+16\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {1}{5} \left (64 \int \frac {x}{\left (12 x^2-\log ^2(x) x+16\right )^2}dx+8 \int \frac {x^2 \log (x)}{\left (12 x^2-\log ^2(x) x+16\right )^2}dx+4 \int \frac {x}{12 x^2-\log ^2(x) x+16}dx-48 \int \frac {x^3}{\left (12 x^2-\log ^2(x) x+16\right )^2}dx+\frac {5 e^x}{x}+\frac {5}{x}\right )\)

Input:

Int[(-1280 - 1920*x^2 + 128*x^3 - 720*x^4 + E^x*(-1280 + 1280*x - 1920*x^2 
 + 1920*x^3 - 720*x^4 + 720*x^5) + 8*x^4*Log[x] + (160*x + 120*x^3 - 4*x^4 
 + E^x*(160*x - 160*x^2 + 120*x^3 - 120*x^4))*Log[x]^2 + (-5*x^2 + E^x*(-5 
*x^2 + 5*x^3))*Log[x]^4)/(1280*x^2 + 1920*x^4 + 720*x^6 + (-160*x^3 - 120* 
x^5)*Log[x]^2 + 5*x^4*Log[x]^4),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 1.12 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.79

\[\frac {{\mathrm e}^{x}+1}{x}+\frac {4 x^{2}}{5 \left (-x \ln \left (x \right )^{2}+12 x^{2}+16\right )}\]

Input:

int((((5*x^3-5*x^2)*exp(x)-5*x^2)*ln(x)^4+((-120*x^4+120*x^3-160*x^2+160*x 
)*exp(x)-4*x^4+120*x^3+160*x)*ln(x)^2+8*x^4*ln(x)+(720*x^5-720*x^4+1920*x^ 
3-1920*x^2+1280*x-1280)*exp(x)-720*x^4+128*x^3-1920*x^2-1280)/(5*x^4*ln(x) 
^4+(-120*x^5-160*x^3)*ln(x)^2+720*x^6+1920*x^4+1280*x^2),x)
 

Output:

(exp(x)+1)/x+4/5*x^2/(-x*ln(x)^2+12*x^2+16)
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.44 \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=-\frac {4 \, x^{3} - 5 \, {\left (x e^{x} + x\right )} \log \left (x\right )^{2} + 60 \, x^{2} + 20 \, {\left (3 \, x^{2} + 4\right )} e^{x} + 80}{5 \, {\left (x^{2} \log \left (x\right )^{2} - 12 \, x^{3} - 16 \, x\right )}} \] Input:

integrate((((5*x^3-5*x^2)*exp(x)-5*x^2)*log(x)^4+((-120*x^4+120*x^3-160*x^ 
2+160*x)*exp(x)-4*x^4+120*x^3+160*x)*log(x)^2+8*x^4*log(x)+(720*x^5-720*x^ 
4+1920*x^3-1920*x^2+1280*x-1280)*exp(x)-720*x^4+128*x^3-1920*x^2-1280)/(5* 
x^4*log(x)^4+(-120*x^5-160*x^3)*log(x)^2+720*x^6+1920*x^4+1280*x^2),x, alg 
orithm="fricas")
 

Output:

-1/5*(4*x^3 - 5*(x*e^x + x)*log(x)^2 + 60*x^2 + 20*(3*x^2 + 4)*e^x + 80)/( 
x^2*log(x)^2 - 12*x^3 - 16*x)
 

Sympy [A] (verification not implemented)

Time = 0.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.69 \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=- \frac {4 x^{2}}{- 60 x^{2} + 5 x \log {\left (x \right )}^{2} - 80} + \frac {e^{x}}{x} + \frac {1}{x} \] Input:

integrate((((5*x**3-5*x**2)*exp(x)-5*x**2)*ln(x)**4+((-120*x**4+120*x**3-1 
60*x**2+160*x)*exp(x)-4*x**4+120*x**3+160*x)*ln(x)**2+8*x**4*ln(x)+(720*x* 
*5-720*x**4+1920*x**3-1920*x**2+1280*x-1280)*exp(x)-720*x**4+128*x**3-1920 
*x**2-1280)/(5*x**4*ln(x)**4+(-120*x**5-160*x**3)*ln(x)**2+720*x**6+1920*x 
**4+1280*x**2),x)
 

Output:

-4*x**2/(-60*x**2 + 5*x*log(x)**2 - 80) + exp(x)/x + 1/x
 

Maxima [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.46 \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=-\frac {4 \, x^{3} - 5 \, x \log \left (x\right )^{2} + 60 \, x^{2} - 5 \, {\left (x \log \left (x\right )^{2} - 12 \, x^{2} - 16\right )} e^{x} + 80}{5 \, {\left (x^{2} \log \left (x\right )^{2} - 12 \, x^{3} - 16 \, x\right )}} \] Input:

integrate((((5*x^3-5*x^2)*exp(x)-5*x^2)*log(x)^4+((-120*x^4+120*x^3-160*x^ 
2+160*x)*exp(x)-4*x^4+120*x^3+160*x)*log(x)^2+8*x^4*log(x)+(720*x^5-720*x^ 
4+1920*x^3-1920*x^2+1280*x-1280)*exp(x)-720*x^4+128*x^3-1920*x^2-1280)/(5* 
x^4*log(x)^4+(-120*x^5-160*x^3)*log(x)^2+720*x^6+1920*x^4+1280*x^2),x, alg 
orithm="maxima")
 

Output:

-1/5*(4*x^3 - 5*x*log(x)^2 + 60*x^2 - 5*(x*log(x)^2 - 12*x^2 - 16)*e^x + 8 
0)/(x^2*log(x)^2 - 12*x^3 - 16*x)
 

Giac [A] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.54 \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=\frac {5 \, x e^{x} \log \left (x\right )^{2} - 4 \, x^{3} - 60 \, x^{2} e^{x} + 5 \, x \log \left (x\right )^{2} - 60 \, x^{2} - 80 \, e^{x} - 80}{5 \, {\left (x^{2} \log \left (x\right )^{2} - 12 \, x^{3} - 16 \, x\right )}} \] Input:

integrate((((5*x^3-5*x^2)*exp(x)-5*x^2)*log(x)^4+((-120*x^4+120*x^3-160*x^ 
2+160*x)*exp(x)-4*x^4+120*x^3+160*x)*log(x)^2+8*x^4*log(x)+(720*x^5-720*x^ 
4+1920*x^3-1920*x^2+1280*x-1280)*exp(x)-720*x^4+128*x^3-1920*x^2-1280)/(5* 
x^4*log(x)^4+(-120*x^5-160*x^3)*log(x)^2+720*x^6+1920*x^4+1280*x^2),x, alg 
orithm="giac")
 

Output:

1/5*(5*x*e^x*log(x)^2 - 4*x^3 - 60*x^2*e^x + 5*x*log(x)^2 - 60*x^2 - 80*e^ 
x - 80)/(x^2*log(x)^2 - 12*x^3 - 16*x)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=\int \frac {8\,x^4\,\ln \left (x\right )-{\ln \left (x\right )}^4\,\left ({\mathrm {e}}^x\,\left (5\,x^2-5\,x^3\right )+5\,x^2\right )+{\mathrm {e}}^x\,\left (720\,x^5-720\,x^4+1920\,x^3-1920\,x^2+1280\,x-1280\right )+{\ln \left (x\right )}^2\,\left (160\,x+{\mathrm {e}}^x\,\left (-120\,x^4+120\,x^3-160\,x^2+160\,x\right )+120\,x^3-4\,x^4\right )-1920\,x^2+128\,x^3-720\,x^4-1280}{5\,x^4\,{\ln \left (x\right )}^4-{\ln \left (x\right )}^2\,\left (120\,x^5+160\,x^3\right )+1280\,x^2+1920\,x^4+720\,x^6} \,d x \] Input:

int((8*x^4*log(x) - log(x)^4*(exp(x)*(5*x^2 - 5*x^3) + 5*x^2) + exp(x)*(12 
80*x - 1920*x^2 + 1920*x^3 - 720*x^4 + 720*x^5 - 1280) + log(x)^2*(160*x + 
 exp(x)*(160*x - 160*x^2 + 120*x^3 - 120*x^4) + 120*x^3 - 4*x^4) - 1920*x^ 
2 + 128*x^3 - 720*x^4 - 1280)/(5*x^4*log(x)^4 - log(x)^2*(160*x^3 + 120*x^ 
5) + 1280*x^2 + 1920*x^4 + 720*x^6),x)
 

Output:

int((8*x^4*log(x) - log(x)^4*(exp(x)*(5*x^2 - 5*x^3) + 5*x^2) + exp(x)*(12 
80*x - 1920*x^2 + 1920*x^3 - 720*x^4 + 720*x^5 - 1280) + log(x)^2*(160*x + 
 exp(x)*(160*x - 160*x^2 + 120*x^3 - 120*x^4) + 120*x^3 - 4*x^4) - 1920*x^ 
2 + 128*x^3 - 720*x^4 - 1280)/(5*x^4*log(x)^4 - log(x)^2*(160*x^3 + 120*x^ 
5) + 1280*x^2 + 1920*x^4 + 720*x^6), x)
 

Reduce [F]

\[ \int \frac {-1280-1920 x^2+128 x^3-720 x^4+e^x \left (-1280+1280 x-1920 x^2+1920 x^3-720 x^4+720 x^5\right )+8 x^4 \log (x)+\left (160 x+120 x^3-4 x^4+e^x \left (160 x-160 x^2+120 x^3-120 x^4\right )\right ) \log ^2(x)+\left (-5 x^2+e^x \left (-5 x^2+5 x^3\right )\right ) \log ^4(x)}{1280 x^2+1920 x^4+720 x^6+\left (-160 x^3-120 x^5\right ) \log ^2(x)+5 x^4 \log ^4(x)} \, dx=\frac {5 e^{x}-5 \left (\int \frac {\mathrm {log}\left (x \right )^{4}}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x +160 \left (\int \frac {\mathrm {log}\left (x \right )^{2}}{\mathrm {log}\left (x \right )^{4} x^{3}-24 \mathrm {log}\left (x \right )^{2} x^{4}-32 \mathrm {log}\left (x \right )^{2} x^{2}+144 x^{5}+384 x^{3}+256 x}d x \right ) x -720 \left (\int \frac {x^{2}}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x -4 \left (\int \frac {\mathrm {log}\left (x \right )^{2} x^{2}}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x +120 \left (\int \frac {\mathrm {log}\left (x \right )^{2} x}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x +8 \left (\int \frac {\mathrm {log}\left (x \right ) x^{2}}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x +128 \left (\int \frac {x}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x -1280 \left (\int \frac {1}{\mathrm {log}\left (x \right )^{4} x^{4}-24 \mathrm {log}\left (x \right )^{2} x^{5}-32 \mathrm {log}\left (x \right )^{2} x^{3}+144 x^{6}+384 x^{4}+256 x^{2}}d x \right ) x -1920 \left (\int \frac {1}{\mathrm {log}\left (x \right )^{4} x^{2}-24 \mathrm {log}\left (x \right )^{2} x^{3}-32 \mathrm {log}\left (x \right )^{2} x +144 x^{4}+384 x^{2}+256}d x \right ) x}{5 x} \] Input:

int((((5*x^3-5*x^2)*exp(x)-5*x^2)*log(x)^4+((-120*x^4+120*x^3-160*x^2+160* 
x)*exp(x)-4*x^4+120*x^3+160*x)*log(x)^2+8*x^4*log(x)+(720*x^5-720*x^4+1920 
*x^3-1920*x^2+1280*x-1280)*exp(x)-720*x^4+128*x^3-1920*x^2-1280)/(5*x^4*lo 
g(x)^4+(-120*x^5-160*x^3)*log(x)^2+720*x^6+1920*x^4+1280*x^2),x)
 

Output:

(5*e**x - 5*int(log(x)**4/(log(x)**4*x**2 - 24*log(x)**2*x**3 - 32*log(x)* 
*2*x + 144*x**4 + 384*x**2 + 256),x)*x + 160*int(log(x)**2/(log(x)**4*x**3 
 - 24*log(x)**2*x**4 - 32*log(x)**2*x**2 + 144*x**5 + 384*x**3 + 256*x),x) 
*x - 720*int(x**2/(log(x)**4*x**2 - 24*log(x)**2*x**3 - 32*log(x)**2*x + 1 
44*x**4 + 384*x**2 + 256),x)*x - 4*int((log(x)**2*x**2)/(log(x)**4*x**2 - 
24*log(x)**2*x**3 - 32*log(x)**2*x + 144*x**4 + 384*x**2 + 256),x)*x + 120 
*int((log(x)**2*x)/(log(x)**4*x**2 - 24*log(x)**2*x**3 - 32*log(x)**2*x + 
144*x**4 + 384*x**2 + 256),x)*x + 8*int((log(x)*x**2)/(log(x)**4*x**2 - 24 
*log(x)**2*x**3 - 32*log(x)**2*x + 144*x**4 + 384*x**2 + 256),x)*x + 128*i 
nt(x/(log(x)**4*x**2 - 24*log(x)**2*x**3 - 32*log(x)**2*x + 144*x**4 + 384 
*x**2 + 256),x)*x - 1280*int(1/(log(x)**4*x**4 - 24*log(x)**2*x**5 - 32*lo 
g(x)**2*x**3 + 144*x**6 + 384*x**4 + 256*x**2),x)*x - 1920*int(1/(log(x)** 
4*x**2 - 24*log(x)**2*x**3 - 32*log(x)**2*x + 144*x**4 + 384*x**2 + 256),x 
)*x)/(5*x)