\(\int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+(768 x-128 x^2+128 x^3-384 x^4) \log (-2+x)+(-512+256 x-1024 x^2+512 x^3) \log ^2(-2+x)+(-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+(-1280 x-128 x^2+256 x^3) \log (-2+x)) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+(-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8) \log (-2+x)+(3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6) \log ^2(-2+x)+(1536 x^2-256 x^3-256 x^4) \log ^3(-2+x)+(-512 x+256 x^2) \log ^4(-2+x)} \, dx\) [2491]

Optimal result

Integrand size = 293, antiderivative size = 31 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {x^2+\log (x)}{-3-x+\left (\frac {1}{4} x (3+x)-\log (-2+x)\right )^2} \] Output:

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

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \left (x^2+\log (x)\right )}{-48-16 x+9 x^2+6 x^3+x^4-8 x (3+x) \log (-2+x)+16 \log ^2(-2+x)} \] Input:

Integrate[(1536 - 256*x + 2528*x^2 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 
 - 32*x^7 + (768*x - 128*x^2 + 128*x^3 - 384*x^4)*Log[-2 + x] + (-512 + 25 
6*x - 1024*x^2 + 512*x^3)*Log[-2 + x]^2 + (-512*x + 1216*x^2 + 416*x^3 - 1 
60*x^4 - 64*x^5 + (-1280*x - 128*x^2 + 256*x^3)*Log[-2 + x])*Log[x])/(-460 
8*x - 768*x^2 + 2752*x^3 + 1120*x^4 - 450*x^5 - 359*x^6 - 32*x^7 + 30*x^8 
+ 10*x^9 + x^10 + (-4608*x^2 - 768*x^3 + 1888*x^4 + 688*x^5 - 144*x^6 - 11 
2*x^7 - 16*x^8)*Log[-2 + x] + (3072*x - 512*x^2 - 2240*x^3 - 288*x^4 + 384 
*x^5 + 96*x^6)*Log[-2 + x]^2 + (1536*x^2 - 256*x^3 - 256*x^4)*Log[-2 + x]^ 
3 + (-512*x + 256*x^2)*Log[-2 + x]^4),x]
 

Output:

(16*(x^2 + Log[x]))/(-48 - 16*x + 9*x^2 + 6*x^3 + x^4 - 8*x*(3 + x)*Log[-2 
 + x] + 16*Log[-2 + x]^2)
 

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.

Failed to integrate

Input:

Int[(1536 - 256*x + 2528*x^2 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32* 
x^7 + (768*x - 128*x^2 + 128*x^3 - 384*x^4)*Log[-2 + x] + (-512 + 256*x - 
1024*x^2 + 512*x^3)*Log[-2 + x]^2 + (-512*x + 1216*x^2 + 416*x^3 - 160*x^4 
 - 64*x^5 + (-1280*x - 128*x^2 + 256*x^3)*Log[-2 + x])*Log[x])/(-4608*x - 
768*x^2 + 2752*x^3 + 1120*x^4 - 450*x^5 - 359*x^6 - 32*x^7 + 30*x^8 + 10*x 
^9 + x^10 + (-4608*x^2 - 768*x^3 + 1888*x^4 + 688*x^5 - 144*x^6 - 112*x^7 
- 16*x^8)*Log[-2 + x] + (3072*x - 512*x^2 - 2240*x^3 - 288*x^4 + 384*x^5 + 
 96*x^6)*Log[-2 + x]^2 + (1536*x^2 - 256*x^3 - 256*x^4)*Log[-2 + x]^3 + (- 
512*x + 256*x^2)*Log[-2 + x]^4),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.78 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.71

\[\frac {16 \ln \left (x \right )+16 x^{2}}{x^{4}-8 \ln \left (-2+x \right ) x^{2}+6 x^{3}+16 \ln \left (-2+x \right )^{2}-24 x \ln \left (-2+x \right )+9 x^{2}-16 x -48}\]

Input:

int((((256*x^3-128*x^2-1280*x)*ln(-2+x)-64*x^5-160*x^4+416*x^3+1216*x^2-51 
2*x)*ln(x)+(512*x^3-1024*x^2+256*x-512)*ln(-2+x)^2+(-384*x^4+128*x^3-128*x 
^2+768*x)*ln(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528*x^2-256*x+1 
536)/((256*x^2-512*x)*ln(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*ln(-2+x)^3+(9 
6*x^6+384*x^5-288*x^4-2240*x^3-512*x^2+3072*x)*ln(-2+x)^2+(-16*x^8-112*x^7 
-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*ln(-2+x)+x^10+10*x^9+30*x^8-32 
*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x)
 

Output:

16*(ln(x)+x^2)/(x^4-8*ln(-2+x)*x^2+6*x^3+16*ln(-2+x)^2-24*x*ln(-2+x)+9*x^2 
-16*x-48)
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.58 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \, {\left (x^{2} + \log \left (x\right )\right )}}{x^{4} + 6 \, x^{3} + 9 \, x^{2} - 8 \, {\left (x^{2} + 3 \, x\right )} \log \left (x - 2\right ) + 16 \, \log \left (x - 2\right )^{2} - 16 \, x - 48} \] Input:

integrate((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216 
*x^2-512*x)*log(x)+(512*x^3-1024*x^2+256*x-512)*log(-2+x)^2+(-384*x^4+128* 
x^3-128*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528*x 
^2-256*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*lo 
g(-2+x)^3+(96*x^6+384*x^5-288*x^4-2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-1 
6*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^10+10 
*x^9+30*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x, al 
gorithm="fricas")
 

Output:

16*(x^2 + log(x))/(x^4 + 6*x^3 + 9*x^2 - 8*(x^2 + 3*x)*log(x - 2) + 16*log 
(x - 2)^2 - 16*x - 48)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (24) = 48\).

Time = 0.22 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.65 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 x^{2} + 16 \log {\left (x \right )}}{x^{4} + 6 x^{3} + 9 x^{2} - 16 x + \left (- 8 x^{2} - 24 x\right ) \log {\left (x - 2 \right )} + 16 \log {\left (x - 2 \right )}^{2} - 48} \] Input:

integrate((((256*x**3-128*x**2-1280*x)*ln(-2+x)-64*x**5-160*x**4+416*x**3+ 
1216*x**2-512*x)*ln(x)+(512*x**3-1024*x**2+256*x-512)*ln(-2+x)**2+(-384*x* 
*4+128*x**3-128*x**2+768*x)*ln(-2+x)-32*x**7-32*x**6+336*x**5+192*x**4-107 
2*x**3+2528*x**2-256*x+1536)/((256*x**2-512*x)*ln(-2+x)**4+(-256*x**4-256* 
x**3+1536*x**2)*ln(-2+x)**3+(96*x**6+384*x**5-288*x**4-2240*x**3-512*x**2+ 
3072*x)*ln(-2+x)**2+(-16*x**8-112*x**7-144*x**6+688*x**5+1888*x**4-768*x** 
3-4608*x**2)*ln(-2+x)+x**10+10*x**9+30*x**8-32*x**7-359*x**6-450*x**5+1120 
*x**4+2752*x**3-768*x**2-4608*x),x)
 

Output:

(16*x**2 + 16*log(x))/(x**4 + 6*x**3 + 9*x**2 - 16*x + (-8*x**2 - 24*x)*lo 
g(x - 2) + 16*log(x - 2)**2 - 48)
 

Maxima [A] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.58 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \, {\left (x^{2} + \log \left (x\right )\right )}}{x^{4} + 6 \, x^{3} + 9 \, x^{2} - 8 \, {\left (x^{2} + 3 \, x\right )} \log \left (x - 2\right ) + 16 \, \log \left (x - 2\right )^{2} - 16 \, x - 48} \] Input:

integrate((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216 
*x^2-512*x)*log(x)+(512*x^3-1024*x^2+256*x-512)*log(-2+x)^2+(-384*x^4+128* 
x^3-128*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528*x 
^2-256*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*lo 
g(-2+x)^3+(96*x^6+384*x^5-288*x^4-2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-1 
6*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^10+10 
*x^9+30*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x, al 
gorithm="maxima")
 

Output:

16*(x^2 + log(x))/(x^4 + 6*x^3 + 9*x^2 - 8*(x^2 + 3*x)*log(x - 2) + 16*log 
(x - 2)^2 - 16*x - 48)
 

Giac [A] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.68 \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\frac {16 \, {\left (x^{2} + \log \left (x\right )\right )}}{x^{4} + 6 \, x^{3} - 8 \, x^{2} \log \left (x - 2\right ) + 9 \, x^{2} - 24 \, x \log \left (x - 2\right ) + 16 \, \log \left (x - 2\right )^{2} - 16 \, x - 48} \] Input:

integrate((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216 
*x^2-512*x)*log(x)+(512*x^3-1024*x^2+256*x-512)*log(-2+x)^2+(-384*x^4+128* 
x^3-128*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528*x 
^2-256*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*lo 
g(-2+x)^3+(96*x^6+384*x^5-288*x^4-2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-1 
6*x^8-112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^10+10 
*x^9+30*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x, al 
gorithm="giac")
 

Output:

16*(x^2 + log(x))/(x^4 + 6*x^3 - 8*x^2*log(x - 2) + 9*x^2 - 24*x*log(x - 2 
) + 16*log(x - 2)^2 - 16*x - 48)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=-\int \frac {\ln \left (x-2\right )\,\left (-384\,x^4+128\,x^3-128\,x^2+768\,x\right )-256\,x-\ln \left (x\right )\,\left (512\,x+\ln \left (x-2\right )\,\left (-256\,x^3+128\,x^2+1280\,x\right )-1216\,x^2-416\,x^3+160\,x^4+64\,x^5\right )+{\ln \left (x-2\right )}^2\,\left (512\,x^3-1024\,x^2+256\,x-512\right )+2528\,x^2-1072\,x^3+192\,x^4+336\,x^5-32\,x^6-32\,x^7+1536}{4608\,x+{\ln \left (x-2\right )}^3\,\left (256\,x^4+256\,x^3-1536\,x^2\right )-{\ln \left (x-2\right )}^2\,\left (96\,x^6+384\,x^5-288\,x^4-2240\,x^3-512\,x^2+3072\,x\right )+{\ln \left (x-2\right )}^4\,\left (512\,x-256\,x^2\right )+\ln \left (x-2\right )\,\left (16\,x^8+112\,x^7+144\,x^6-688\,x^5-1888\,x^4+768\,x^3+4608\,x^2\right )+768\,x^2-2752\,x^3-1120\,x^4+450\,x^5+359\,x^6+32\,x^7-30\,x^8-10\,x^9-x^{10}} \,d x \] Input:

int(-(log(x - 2)*(768*x - 128*x^2 + 128*x^3 - 384*x^4) - 256*x - log(x)*(5 
12*x + log(x - 2)*(1280*x + 128*x^2 - 256*x^3) - 1216*x^2 - 416*x^3 + 160* 
x^4 + 64*x^5) + log(x - 2)^2*(256*x - 1024*x^2 + 512*x^3 - 512) + 2528*x^2 
 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32*x^7 + 1536)/(4608*x + log(x 
- 2)^3*(256*x^3 - 1536*x^2 + 256*x^4) - log(x - 2)^2*(3072*x - 512*x^2 - 2 
240*x^3 - 288*x^4 + 384*x^5 + 96*x^6) + log(x - 2)^4*(512*x - 256*x^2) + l 
og(x - 2)*(4608*x^2 + 768*x^3 - 1888*x^4 - 688*x^5 + 144*x^6 + 112*x^7 + 1 
6*x^8) + 768*x^2 - 2752*x^3 - 1120*x^4 + 450*x^5 + 359*x^6 + 32*x^7 - 30*x 
^8 - 10*x^9 - x^10),x)
 

Output:

-int((log(x - 2)*(768*x - 128*x^2 + 128*x^3 - 384*x^4) - 256*x - log(x)*(5 
12*x + log(x - 2)*(1280*x + 128*x^2 - 256*x^3) - 1216*x^2 - 416*x^3 + 160* 
x^4 + 64*x^5) + log(x - 2)^2*(256*x - 1024*x^2 + 512*x^3 - 512) + 2528*x^2 
 - 1072*x^3 + 192*x^4 + 336*x^5 - 32*x^6 - 32*x^7 + 1536)/(4608*x + log(x 
- 2)^3*(256*x^3 - 1536*x^2 + 256*x^4) - log(x - 2)^2*(3072*x - 512*x^2 - 2 
240*x^3 - 288*x^4 + 384*x^5 + 96*x^6) + log(x - 2)^4*(512*x - 256*x^2) + l 
og(x - 2)*(4608*x^2 + 768*x^3 - 1888*x^4 - 688*x^5 + 144*x^6 + 112*x^7 + 1 
6*x^8) + 768*x^2 - 2752*x^3 - 1120*x^4 + 450*x^5 + 359*x^6 + 32*x^7 - 30*x 
^8 - 10*x^9 - x^10), x)
 

Reduce [F]

\[ \int \frac {1536-256 x+2528 x^2-1072 x^3+192 x^4+336 x^5-32 x^6-32 x^7+\left (768 x-128 x^2+128 x^3-384 x^4\right ) \log (-2+x)+\left (-512+256 x-1024 x^2+512 x^3\right ) \log ^2(-2+x)+\left (-512 x+1216 x^2+416 x^3-160 x^4-64 x^5+\left (-1280 x-128 x^2+256 x^3\right ) \log (-2+x)\right ) \log (x)}{-4608 x-768 x^2+2752 x^3+1120 x^4-450 x^5-359 x^6-32 x^7+30 x^8+10 x^9+x^{10}+\left (-4608 x^2-768 x^3+1888 x^4+688 x^5-144 x^6-112 x^7-16 x^8\right ) \log (-2+x)+\left (3072 x-512 x^2-2240 x^3-288 x^4+384 x^5+96 x^6\right ) \log ^2(-2+x)+\left (1536 x^2-256 x^3-256 x^4\right ) \log ^3(-2+x)+\left (-512 x+256 x^2\right ) \log ^4(-2+x)} \, dx=\text {too large to display} \] Input:

int((((256*x^3-128*x^2-1280*x)*log(-2+x)-64*x^5-160*x^4+416*x^3+1216*x^2-5 
12*x)*log(x)+(512*x^3-1024*x^2+256*x-512)*log(-2+x)^2+(-384*x^4+128*x^3-12 
8*x^2+768*x)*log(-2+x)-32*x^7-32*x^6+336*x^5+192*x^4-1072*x^3+2528*x^2-256 
*x+1536)/((256*x^2-512*x)*log(-2+x)^4+(-256*x^4-256*x^3+1536*x^2)*log(-2+x 
)^3+(96*x^6+384*x^5-288*x^4-2240*x^3-512*x^2+3072*x)*log(-2+x)^2+(-16*x^8- 
112*x^7-144*x^6+688*x^5+1888*x^4-768*x^3-4608*x^2)*log(-2+x)+x^10+10*x^9+3 
0*x^8-32*x^7-359*x^6-450*x^5+1120*x^4+2752*x^3-768*x^2-4608*x),x)
 

Output:

16*( - 32*int(log(x - 2)**2/(256*log(x - 2)**4*x**2 - 512*log(x - 2)**4*x 
- 256*log(x - 2)**3*x**4 - 256*log(x - 2)**3*x**3 + 1536*log(x - 2)**3*x** 
2 + 96*log(x - 2)**2*x**6 + 384*log(x - 2)**2*x**5 - 288*log(x - 2)**2*x** 
4 - 2240*log(x - 2)**2*x**3 - 512*log(x - 2)**2*x**2 + 3072*log(x - 2)**2* 
x - 16*log(x - 2)*x**8 - 112*log(x - 2)*x**7 - 144*log(x - 2)*x**6 + 688*l 
og(x - 2)*x**5 + 1888*log(x - 2)*x**4 - 768*log(x - 2)*x**3 - 4608*log(x - 
 2)*x**2 + x**10 + 10*x**9 + 30*x**8 - 32*x**7 - 359*x**6 - 450*x**5 + 112 
0*x**4 + 2752*x**3 - 768*x**2 - 4608*x),x) + 16*int(log(x - 2)**2/(256*log 
(x - 2)**4*x - 512*log(x - 2)**4 - 256*log(x - 2)**3*x**3 - 256*log(x - 2) 
**3*x**2 + 1536*log(x - 2)**3*x + 96*log(x - 2)**2*x**5 + 384*log(x - 2)** 
2*x**4 - 288*log(x - 2)**2*x**3 - 2240*log(x - 2)**2*x**2 - 512*log(x - 2) 
**2*x + 3072*log(x - 2)**2 - 16*log(x - 2)*x**7 - 112*log(x - 2)*x**6 - 14 
4*log(x - 2)*x**5 + 688*log(x - 2)*x**4 + 1888*log(x - 2)*x**3 - 768*log(x 
 - 2)*x**2 - 4608*log(x - 2)*x + x**9 + 10*x**8 + 30*x**7 - 32*x**6 - 359* 
x**5 - 450*x**4 + 1120*x**3 + 2752*x**2 - 768*x - 4608),x) - 2*int(x**6/(2 
56*log(x - 2)**4*x - 512*log(x - 2)**4 - 256*log(x - 2)**3*x**3 - 256*log( 
x - 2)**3*x**2 + 1536*log(x - 2)**3*x + 96*log(x - 2)**2*x**5 + 384*log(x 
- 2)**2*x**4 - 288*log(x - 2)**2*x**3 - 2240*log(x - 2)**2*x**2 - 512*log( 
x - 2)**2*x + 3072*log(x - 2)**2 - 16*log(x - 2)*x**7 - 112*log(x - 2)*x** 
6 - 144*log(x - 2)*x**5 + 688*log(x - 2)*x**4 + 1888*log(x - 2)*x**3 - ...