\(\int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+(2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7) \log (x)+(408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+(-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5) \log ^2(x)+(-500 x+1200 x^2-960 x^3+256 x^4) \log ^4(x)} \, dx\) [737]

Optimal result

Integrand size = 201, antiderivative size = 38 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {\left (-2+\frac {1}{2 \left (\frac {5-x}{3}-x\right )}-x^2\right )^2}{1+x+\log ^2(x)} \] Output:

(1/(10/3-8/3*x)-x^2-2)^2/(x+ln(x)^2+1)
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.05 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.97 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {\left (17-16 x+10 x^2-8 x^3\right )^2}{4 (5-4 x)^2 \left (1+x+\log ^2(x)\right )} \] Input:

Integrate[(1853*x - 7252*x^2 + 10252*x^3 - 5952*x^4 + 1508*x^5 + 784*x^6 - 
 1856*x^7 + 768*x^8 + (2890 - 7752*x + 10312*x^2 - 10688*x^3 + 8296*x^4 - 
4448*x^5 + 1920*x^6 - 512*x^7)*Log[x] + (408*x - 3784*x^2 + 8880*x^3 - 948 
8*x^4 + 6848*x^5 - 3840*x^6 + 1024*x^7)*Log[x]^2)/(-500*x + 200*x^2 + 940* 
x^3 - 464*x^4 - 448*x^5 + 256*x^6 + (-1000*x + 1400*x^2 + 480*x^3 - 1408*x 
^4 + 512*x^5)*Log[x]^2 + (-500*x + 1200*x^2 - 960*x^3 + 256*x^4)*Log[x]^4) 
,x]
 

Output:

(17 - 16*x + 10*x^2 - 8*x^3)^2/(4*(5 - 4*x)^2*(1 + x + Log[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.

\(\displaystyle \int \frac {768 x^8-1856 x^7+784 x^6+1508 x^5-5952 x^4+10252 x^3-7252 x^2+\left (1024 x^7-3840 x^6+6848 x^5-9488 x^4+8880 x^3-3784 x^2+408 x\right ) \log ^2(x)+\left (-512 x^7+1920 x^6-4448 x^5+8296 x^4-10688 x^3+10312 x^2-7752 x+2890\right ) \log (x)+1853 x}{256 x^6-448 x^5-464 x^4+940 x^3+200 x^2+\left (256 x^4-960 x^3+1200 x^2-500 x\right ) \log ^4(x)+\left (512 x^5-1408 x^4+480 x^3+1400 x^2-1000 x\right ) \log ^2(x)-500 x} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (-8 x^3+10 x^2-16 x+17\right ) \left (8 x \left (16 x^3-40 x^2+25 x-3\right ) \log ^2(x)+x \left (96 x^4-112 x^3-234 x^2+324 x-109\right )-2 \left (32 x^4-80 x^3+114 x^2-148 x+85\right ) \log (x)\right )}{4 (5-4 x)^3 x \left (x+\log ^2(x)+1\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{4} \int -\frac {\left (-8 x^3+10 x^2-16 x+17\right ) \left (8 x \left (-16 x^3+40 x^2-25 x+3\right ) \log ^2(x)+2 \left (32 x^4-80 x^3+114 x^2-148 x+85\right ) \log (x)+x \left (-96 x^4+112 x^3+234 x^2-324 x+109\right )\right )}{(5-4 x)^3 x \left (\log ^2(x)+x+1\right )^2}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -\frac {1}{4} \int \frac {\left (-8 x^3+10 x^2-16 x+17\right ) \left (8 x \left (-16 x^3+40 x^2-25 x+3\right ) \log ^2(x)+2 \left (32 x^4-80 x^3+114 x^2-148 x+85\right ) \log (x)+x \left (-96 x^4+112 x^3+234 x^2-324 x+109\right )\right )}{(5-4 x)^3 x \left (\log ^2(x)+x+1\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {1}{4} \int \left (\frac {\left (8 x^3-10 x^2+16 x-17\right )^2 (x+2 \log (x))}{x (4 x-5)^2 \left (\log ^2(x)+x+1\right )^2}-\frac {8 \left (128 x^6-480 x^5+856 x^4-1186 x^3+1110 x^2-473 x+51\right )}{(4 x-5)^3 \left (\log ^2(x)+x+1\right )}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {1}{4} \left (-4 \int \frac {x^4}{\left (\log ^2(x)+x+1\right )^2}dx-8 \int \frac {x^3 \log (x)}{\left (\log ^2(x)+x+1\right )^2}dx+16 \int \frac {x^3}{\log ^2(x)+x+1}dx-16 \int \frac {x^2}{\left (\log ^2(x)+x+1\right )^2}dx-\frac {819}{100} \int \frac {1}{\left (\log ^2(x)+x+1\right )^2}dx-3 \int \frac {x}{\left (\log ^2(x)+x+1\right )^2}dx-9 \int \frac {1}{(4 x-5)^2 \left (\log ^2(x)+x+1\right )^2}dx-\frac {171}{4} \int \frac {1}{(4 x-5) \left (\log ^2(x)+x+1\right )^2}dx-6 \int \frac {\log (x)}{\left (\log ^2(x)+x+1\right )^2}dx-32 \int \frac {x \log (x)}{\left (\log ^2(x)+x+1\right )^2}dx-\frac {72}{5} \int \frac {\log (x)}{(4 x-5)^2 \left (\log ^2(x)+x+1\right )^2}dx-\frac {1638}{25} \int \frac {\log (x)}{(4 x-5) \left (\log ^2(x)+x+1\right )^2}dx+3 \int \frac {1}{\log ^2(x)+x+1}dx+32 \int \frac {x}{\log ^2(x)+x+1}dx-72 \int \frac {1}{(4 x-5)^3 \left (\log ^2(x)+x+1\right )}dx-171 \int \frac {1}{(4 x-5)^2 \left (\log ^2(x)+x+1\right )}dx+\frac {289}{25 \left (x+\log ^2(x)+1\right )}\right )\)

Input:

Int[(1853*x - 7252*x^2 + 10252*x^3 - 5952*x^4 + 1508*x^5 + 784*x^6 - 1856* 
x^7 + 768*x^8 + (2890 - 7752*x + 10312*x^2 - 10688*x^3 + 8296*x^4 - 4448*x 
^5 + 1920*x^6 - 512*x^7)*Log[x] + (408*x - 3784*x^2 + 8880*x^3 - 9488*x^4 
+ 6848*x^5 - 3840*x^6 + 1024*x^7)*Log[x]^2)/(-500*x + 200*x^2 + 940*x^3 - 
464*x^4 - 448*x^5 + 256*x^6 + (-1000*x + 1400*x^2 + 480*x^3 - 1408*x^4 + 5 
12*x^5)*Log[x]^2 + (-500*x + 1200*x^2 - 960*x^3 + 256*x^4)*Log[x]^4),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(53\) vs. \(2(26)=52\).

Time = 2.91 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.42

method	result	size
risch	\(\frac {64 x^{6}-160 x^{5}+356 x^{4}-592 x^{3}+596 x^{2}-544 x +289}{4 \left (16 x^{2}-40 x +25\right ) \left (x +\ln \left (x \right )^{2}+1\right )}\)	\(54\)
default	\(\frac {714+272 x^{2} \ln \left (x \right )^{2}-680 x \ln \left (x \right )^{2}-160 x^{5}+188 x^{2}+356 x^{4}-320 x^{3}-799 x +425 \ln \left (x \right )^{2}+64 x^{6}}{4 \left (x +\ln \left (x \right )^{2}+1\right ) \left (-5+4 x \right )^{2}}\)	\(71\)
parallelrisch	\(\frac {1024 x^{6}-2560 x^{5}+5696 x^{4}-9472 x^{3}+9536 x^{2}-8704 x +4624}{1024 x^{2} \ln \left (x \right )^{2}+1024 x^{3}-2560 x \ln \left (x \right )^{2}-1536 x^{2}+1600 \ln \left (x \right )^{2}-960 x +1600}\)	\(72\)

Input:

int(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*ln(x)^2 
+(-512*x^7+1920*x^6-4448*x^5+8296*x^4-10688*x^3+10312*x^2-7752*x+2890)*ln( 
x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2+1853*x)/( 
(256*x^4-960*x^3+1200*x^2-500*x)*ln(x)^4+(512*x^5-1408*x^4+480*x^3+1400*x^ 
2-1000*x)*ln(x)^2+256*x^6-448*x^5-464*x^4+940*x^3+200*x^2-500*x),x,method= 
_RETURNVERBOSE)
 

Output:

1/4*(64*x^6-160*x^5+356*x^4-592*x^3+596*x^2-544*x+289)/(16*x^2-40*x+25)/(x 
+ln(x)^2+1)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (29) = 58\).

Time = 0.08 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.68 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {64 \, x^{6} - 160 \, x^{5} + 356 \, x^{4} - 592 \, x^{3} + 596 \, x^{2} - 544 \, x + 289}{4 \, {\left (16 \, x^{3} + {\left (16 \, x^{2} - 40 \, x + 25\right )} \log \left (x\right )^{2} - 24 \, x^{2} - 15 \, x + 25\right )}} \] Input:

integrate(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*l 
og(x)^2+(-512*x^7+1920*x^6-4448*x^5+8296*x^4-10688*x^3+10312*x^2-7752*x+28 
90)*log(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2+1 
853*x)/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^ 
3+1400*x^2-1000*x)*log(x)^2+256*x^6-448*x^5-464*x^4+940*x^3+200*x^2-500*x) 
,x, algorithm="fricas")
 

Output:

1/4*(64*x^6 - 160*x^5 + 356*x^4 - 592*x^3 + 596*x^2 - 544*x + 289)/(16*x^3 
 + (16*x^2 - 40*x + 25)*log(x)^2 - 24*x^2 - 15*x + 25)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (24) = 48\).

Time = 0.12 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.58 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {64 x^{6} - 160 x^{5} + 356 x^{4} - 592 x^{3} + 596 x^{2} - 544 x + 289}{64 x^{3} - 96 x^{2} - 60 x + \left (64 x^{2} - 160 x + 100\right ) \log {\left (x \right )}^{2} + 100} \] Input:

integrate(((1024*x**7-3840*x**6+6848*x**5-9488*x**4+8880*x**3-3784*x**2+40 
8*x)*ln(x)**2+(-512*x**7+1920*x**6-4448*x**5+8296*x**4-10688*x**3+10312*x* 
*2-7752*x+2890)*ln(x)+768*x**8-1856*x**7+784*x**6+1508*x**5-5952*x**4+1025 
2*x**3-7252*x**2+1853*x)/((256*x**4-960*x**3+1200*x**2-500*x)*ln(x)**4+(51 
2*x**5-1408*x**4+480*x**3+1400*x**2-1000*x)*ln(x)**2+256*x**6-448*x**5-464 
*x**4+940*x**3+200*x**2-500*x),x)
 

Output:

(64*x**6 - 160*x**5 + 356*x**4 - 592*x**3 + 596*x**2 - 544*x + 289)/(64*x* 
*3 - 96*x**2 - 60*x + (64*x**2 - 160*x + 100)*log(x)**2 + 100)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (29) = 58\).

Time = 0.09 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.68 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {64 \, x^{6} - 160 \, x^{5} + 356 \, x^{4} - 592 \, x^{3} + 596 \, x^{2} - 544 \, x + 289}{4 \, {\left (16 \, x^{3} + {\left (16 \, x^{2} - 40 \, x + 25\right )} \log \left (x\right )^{2} - 24 \, x^{2} - 15 \, x + 25\right )}} \] Input:

integrate(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*l 
og(x)^2+(-512*x^7+1920*x^6-4448*x^5+8296*x^4-10688*x^3+10312*x^2-7752*x+28 
90)*log(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2+1 
853*x)/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^ 
3+1400*x^2-1000*x)*log(x)^2+256*x^6-448*x^5-464*x^4+940*x^3+200*x^2-500*x) 
,x, algorithm="maxima")
 

Output:

1/4*(64*x^6 - 160*x^5 + 356*x^4 - 592*x^3 + 596*x^2 - 544*x + 289)/(16*x^3 
 + (16*x^2 - 40*x + 25)*log(x)^2 - 24*x^2 - 15*x + 25)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (29) = 58\).

Time = 0.19 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.87 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {64 \, x^{6} - 160 \, x^{5} + 356 \, x^{4} - 592 \, x^{3} + 596 \, x^{2} - 544 \, x + 289}{4 \, {\left (16 \, x^{2} \log \left (x\right )^{2} + 16 \, x^{3} - 40 \, x \log \left (x\right )^{2} - 24 \, x^{2} + 25 \, \log \left (x\right )^{2} - 15 \, x + 25\right )}} \] Input:

integrate(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*l 
og(x)^2+(-512*x^7+1920*x^6-4448*x^5+8296*x^4-10688*x^3+10312*x^2-7752*x+28 
90)*log(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2+1 
853*x)/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^ 
3+1400*x^2-1000*x)*log(x)^2+256*x^6-448*x^5-464*x^4+940*x^3+200*x^2-500*x) 
,x, algorithm="giac")
 

Output:

1/4*(64*x^6 - 160*x^5 + 356*x^4 - 592*x^3 + 596*x^2 - 544*x + 289)/(16*x^2 
*log(x)^2 + 16*x^3 - 40*x*log(x)^2 - 24*x^2 + 25*log(x)^2 - 15*x + 25)
 

Mupad [B] (verification not implemented)

Time = 4.08 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.13 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=-\frac {-64\,x^{10}-16\,x^9+148\,x^8-227\,x^7+588\,x^6+93\,x^5-1157\,x^4+\frac {6565\,x^3}{4}-2431\,x^2+1445\,x}{{\left (4\,x-5\right )}^3\,\left ({\ln \left (x\right )}^2+x+1\right )\,\left (x^3+4\,x^2+4\,x\right )} \] Input:

int(-(1853*x + log(x)^2*(408*x - 3784*x^2 + 8880*x^3 - 9488*x^4 + 6848*x^5 
 - 3840*x^6 + 1024*x^7) - log(x)*(7752*x - 10312*x^2 + 10688*x^3 - 8296*x^ 
4 + 4448*x^5 - 1920*x^6 + 512*x^7 - 2890) - 7252*x^2 + 10252*x^3 - 5952*x^ 
4 + 1508*x^5 + 784*x^6 - 1856*x^7 + 768*x^8)/(500*x + log(x)^4*(500*x - 12 
00*x^2 + 960*x^3 - 256*x^4) - log(x)^2*(1400*x^2 - 1000*x + 480*x^3 - 1408 
*x^4 + 512*x^5) - 200*x^2 - 940*x^3 + 464*x^4 + 448*x^5 - 256*x^6),x)
 

Output:

-(1445*x - 2431*x^2 + (6565*x^3)/4 - 1157*x^4 + 93*x^5 + 588*x^6 - 227*x^7 
 + 148*x^8 - 16*x^9 - 64*x^10)/((4*x - 5)^3*(x + log(x)^2 + 1)*(4*x + 4*x^ 
2 + x^3))
 

Reduce [B] (verification not implemented)

Time = 0.16 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.34 \[ \int \frac {1853 x-7252 x^2+10252 x^3-5952 x^4+1508 x^5+784 x^6-1856 x^7+768 x^8+\left (2890-7752 x+10312 x^2-10688 x^3+8296 x^4-4448 x^5+1920 x^6-512 x^7\right ) \log (x)+\left (408 x-3784 x^2+8880 x^3-9488 x^4+6848 x^5-3840 x^6+1024 x^7\right ) \log ^2(x)}{-500 x+200 x^2+940 x^3-464 x^4-448 x^5+256 x^6+\left (-1000 x+1400 x^2+480 x^3-1408 x^4+512 x^5\right ) \log ^2(x)+\left (-500 x+1200 x^2-960 x^3+256 x^4\right ) \log ^4(x)} \, dx=\frac {-8704 \mathrm {log}\left (x \right )^{2} x^{2}+21760 \mathrm {log}\left (x \right )^{2} x -13600 \mathrm {log}\left (x \right )^{2}+960 x^{6}-2400 x^{5}+5340 x^{4}-17584 x^{3}+21996 x^{2}-9265}{960 \mathrm {log}\left (x \right )^{2} x^{2}-2400 \mathrm {log}\left (x \right )^{2} x +1500 \mathrm {log}\left (x \right )^{2}+960 x^{3}-1440 x^{2}-900 x +1500} \] Input:

int(((1024*x^7-3840*x^6+6848*x^5-9488*x^4+8880*x^3-3784*x^2+408*x)*log(x)^ 
2+(-512*x^7+1920*x^6-4448*x^5+8296*x^4-10688*x^3+10312*x^2-7752*x+2890)*lo 
g(x)+768*x^8-1856*x^7+784*x^6+1508*x^5-5952*x^4+10252*x^3-7252*x^2+1853*x) 
/((256*x^4-960*x^3+1200*x^2-500*x)*log(x)^4+(512*x^5-1408*x^4+480*x^3+1400 
*x^2-1000*x)*log(x)^2+256*x^6-448*x^5-464*x^4+940*x^3+200*x^2-500*x),x)
 

Output:

( - 8704*log(x)**2*x**2 + 21760*log(x)**2*x - 13600*log(x)**2 + 960*x**6 - 
 2400*x**5 + 5340*x**4 - 17584*x**3 + 21996*x**2 - 9265)/(60*(16*log(x)**2 
*x**2 - 40*log(x)**2*x + 25*log(x)**2 + 16*x**3 - 24*x**2 - 15*x + 25))