Integrand size = 214, antiderivative size = 31 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=x \left (\left (4+x^2\right )^2+\log (x)\right ) \left (-x+\frac {\log \left (\log ^2(x)\right )}{4-x+\log (x)}\right ) \] Output:
((x^2+4)^2+ln(x))*x*(ln(ln(x)^2)/(ln(x)-x+4)-x)
Time = 0.09 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.23 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=-\frac {x \left (\left (4+x^2\right )^2+\log (x)\right ) \left ((-4+x) x-x \log (x)+\log \left (\log ^2(x)\right )\right )}{-4+x-\log (x)} \] Input:
Integrate[(128 - 32*x + 64*x^2 - 16*x^3 + 8*x^4 - 2*x^5 + (40 - 530*x + 28 0*x^2 - 545*x^3 + 258*x^4 - 128*x^5 + 48*x^6 - 6*x^7)*Log[x] + (2 - 296*x + 82*x^2 - 258*x^3 + 64*x^4 - 48*x^5 + 12*x^6)*Log[x]^2 + (-49*x + 4*x^2 - 32*x^3 - 6*x^5)*Log[x]^3 - 2*x*Log[x]^4 + ((52 - x + 88*x^2 - 16*x^3 + 19 *x^4 - 4*x^5)*Log[x] + (20 + 24*x^2 + 5*x^4)*Log[x]^2 + Log[x]^3)*Log[Log[ x]^2])/((16 - 8*x + x^2)*Log[x] + (8 - 2*x)*Log[x]^2 + Log[x]^3),x]
Output:
-((x*((4 + x^2)^2 + Log[x])*((-4 + x)*x - x*Log[x] + Log[Log[x]^2]))/(-4 + x - Log[x]))
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.
| \(\displaystyle \int \frac {-2 x^5+8 x^4-16 x^3+64 x^2+\left (-6 x^5-32 x^3+4 x^2-49 x\right ) \log ^3(x)+\left (\left (5 x^4+24 x^2+20\right ) \log ^2(x)+\left (-4 x^5+19 x^4-16 x^3+88 x^2-x+52\right ) \log (x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )+\left (12 x^6-48 x^5+64 x^4-258 x^3+82 x^2-296 x+2\right ) \log ^2(x)+\left (-6 x^7+48 x^6-128 x^5+258 x^4-545 x^3+280 x^2-530 x+40\right ) \log (x)-32 x-2 x \log ^4(x)+128}{\left (x^2-8 x+16\right ) \log (x)+\log ^3(x)+(8-2 x) \log ^2(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-2 x^5+8 x^4-16 x^3+64 x^2+\left (-6 x^5-32 x^3+4 x^2-49 x\right ) \log ^3(x)+\left (\left (5 x^4+24 x^2+20\right ) \log ^2(x)+\left (-4 x^5+19 x^4-16 x^3+88 x^2-x+52\right ) \log (x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )+\left (12 x^6-48 x^5+64 x^4-258 x^3+82 x^2-296 x+2\right ) \log ^2(x)+\left (-6 x^7+48 x^6-128 x^5+258 x^4-545 x^3+280 x^2-530 x+40\right ) \log (x)-32 x-2 x \log ^4(x)+128}{\log (x) (-x+\log (x)+4)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2 x^5}{(x-\log (x)-4)^2 \log (x)}+\frac {8 x^4}{(x-\log (x)-4)^2 \log (x)}-\frac {16 x^3}{(x-\log (x)-4)^2 \log (x)}+\frac {64 x^2}{(x-\log (x)-4)^2 \log (x)}-\frac {\left (6 x^4+32 x^2-4 x+49\right ) x \log ^2(x)}{(x-\log (x)-4)^2}-\frac {\left (4 x^5-19 x^4-5 x^4 \log (x)+16 x^3-88 x^2-24 x^2 \log (x)+x-\log ^2(x)-20 \log (x)-52\right ) \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}+\frac {2 \left (6 x^6-24 x^5+32 x^4-129 x^3+41 x^2-148 x+1\right ) \log (x)}{(x-\log (x)-4)^2}+\frac {-6 x^7+48 x^6-128 x^5+258 x^4-545 x^3+280 x^2-530 x+40}{(x-\log (x)-4)^2}-\frac {2 x \log ^3(x)}{(x-\log (x)-4)^2}-\frac {32 x}{(x-\log (x)-4)^2 \log (x)}+\frac {128}{\log (x) (-x+\log (x)+4)^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \int \frac {x^5 \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx-2 \int \frac {x^5}{(x-4)^2 \log (x)}dx+19 \int \frac {x^4 \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx+5 \int \frac {x^4 \log (x) \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx+8 \int \frac {x^4}{(x-4)^2 \log (x)}dx-16 \int \frac {x^3 \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx-2 \int \frac {x^3}{x-\log (x)-4}dx-16 \int \frac {x^3}{(x-4)^2 \log (x)}dx+88 \int \frac {x^2 \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx+24 \int \frac {x^2 \log (x) \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx-8 \int \frac {x^2}{x-\log (x)-4}dx+64 \int \frac {x^2}{(x-4)^2 \log (x)}dx+52 \int \frac {\log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx-\int \frac {x \log \left (\log ^2(x)\right )}{(x-\log (x)-4)^2}dx+20 \int \frac {\log (x) \log \left (\log ^2(x)\right )}{(-x+\log (x)+4)^2}dx+\int \frac {\log ^2(x) \log \left (\log ^2(x)\right )}{(-x+\log (x)+4)^2}dx-192 \int \frac {1}{x-\log (x)-4}dx-800 \int \frac {1}{(x-4) (x-\log (x)-4)}dx-48 \int \frac {x}{x-\log (x)-4}dx+128 \int \frac {1}{(x-4)^2 \log (x)}dx-32 \int \frac {x}{(x-4)^2 \log (x)}dx+2 \int \frac {1}{-x+\log (x)+4}dx-x^6-8 x^4-16 x^2-x^2 \log (x)\) |
Input:
Int[(128 - 32*x + 64*x^2 - 16*x^3 + 8*x^4 - 2*x^5 + (40 - 530*x + 280*x^2 - 545*x^3 + 258*x^4 - 128*x^5 + 48*x^6 - 6*x^7)*Log[x] + (2 - 296*x + 82*x ^2 - 258*x^3 + 64*x^4 - 48*x^5 + 12*x^6)*Log[x]^2 + (-49*x + 4*x^2 - 32*x^ 3 - 6*x^5)*Log[x]^3 - 2*x*Log[x]^4 + ((52 - x + 88*x^2 - 16*x^3 + 19*x^4 - 4*x^5)*Log[x] + (20 + 24*x^2 + 5*x^4)*Log[x]^2 + Log[x]^3)*Log[Log[x]^2]) /((16 - 8*x + x^2)*Log[x] + (8 - 2*x)*Log[x]^2 + Log[x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(114\) vs. \(2(31)=62\).
Time = 1.93 (sec) , antiderivative size = 115, normalized size of antiderivative = 3.71
| method | result | size |
| parallelrisch | \(\frac {-x^{3} \ln \left (x \right )+8 x^{4} \ln \left (x \right )+20 x^{2} \ln \left (x \right )+\ln \left (x \right ) x^{6}+x^{2} \ln \left (x \right )^{2}+4 x^{6}-x^{7}+64 x^{2}-16 x^{3}+32 x^{4}-8 x^{5}-\ln \left (x \right ) \ln \left (\ln \left (x \right )^{2}\right ) x -16 x \ln \left (\ln \left (x \right )^{2}\right )-8 \ln \left (\ln \left (x \right )^{2}\right ) x^{3}-\ln \left (\ln \left (x \right )^{2}\right ) x^{5}}{x -\ln \left (x \right )-4}\) | \(115\) |
| risch | \(-\frac {2 x \left (x^{4}+8 x^{2}+\ln \left (x \right )+16\right ) \ln \left (\ln \left (x \right )\right )}{x -\ln \left (x \right )-4}-\frac {x \left (-i \pi \,x^{4} \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{3}-8 i \pi \,x^{2} \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{3}-16 i \pi \operatorname {csgn}\left (i \ln \left (x \right )\right )^{2} \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )-i \pi \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{3} \ln \left (x \right )-i \pi \,x^{4} \operatorname {csgn}\left (i \ln \left (x \right )\right )^{2} \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )+32 i \pi \,\operatorname {csgn}\left (i \ln \left (x \right )\right ) \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{2}-i \pi \operatorname {csgn}\left (i \ln \left (x \right )\right )^{2} \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right ) \ln \left (x \right )-16 i \pi \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{3}+2 i \pi \,\operatorname {csgn}\left (i \ln \left (x \right )\right ) \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{2} \ln \left (x \right )+2 x^{6}-2 x^{5} \ln \left (x \right )+2 i \pi \,x^{4} \operatorname {csgn}\left (i \ln \left (x \right )\right ) \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{2}+16 i \pi \,x^{2} \operatorname {csgn}\left (i \ln \left (x \right )\right ) \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )^{2}-8 i \pi \,x^{2} \operatorname {csgn}\left (i \ln \left (x \right )\right )^{2} \operatorname {csgn}\left (i \ln \left (x \right )^{2}\right )-8 x^{5}+16 x^{4}-16 x^{3} \ln \left (x \right )-64 x^{3}+2 x^{2} \ln \left (x \right )-2 x \ln \left (x \right )^{2}+32 x^{2}-40 x \ln \left (x \right )-128 x \right )}{2 \left (x -\ln \left (x \right )-4\right )}\) | \(343\) |
Input:
int(((ln(x)^3+(5*x^4+24*x^2+20)*ln(x)^2+(-4*x^5+19*x^4-16*x^3+88*x^2-x+52) *ln(x))*ln(ln(x)^2)-2*x*ln(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*ln(x)^3+(12*x^6 -48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*ln(x)^2+(-6*x^7+48*x^6-128*x^5+258* x^4-545*x^3+280*x^2-530*x+40)*ln(x)-2*x^5+8*x^4-16*x^3+64*x^2-32*x+128)/(l n(x)^3+(-2*x+8)*ln(x)^2+(x^2-8*x+16)*ln(x)),x,method=_RETURNVERBOSE)
Output:
(-x^3*ln(x)+8*x^4*ln(x)+20*x^2*ln(x)+ln(x)*x^6+x^2*ln(x)^2+4*x^6-x^7+64*x^ 2-16*x^3+32*x^4-8*x^5-ln(x)*ln(ln(x)^2)*x-16*x*ln(ln(x)^2)-8*ln(ln(x)^2)*x ^3-ln(ln(x)^2)*x^5)/(x-ln(x)-4)
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (30) = 60\).
Time = 0.10 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.03 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=-\frac {x^{7} - 4 \, x^{6} + 8 \, x^{5} - 32 \, x^{4} - x^{2} \log \left (x\right )^{2} + 16 \, x^{3} - 64 \, x^{2} + {\left (x^{5} + 8 \, x^{3} + x \log \left (x\right ) + 16 \, x\right )} \log \left (\log \left (x\right )^{2}\right ) - {\left (x^{6} + 8 \, x^{4} - x^{3} + 20 \, x^{2}\right )} \log \left (x\right )}{x - \log \left (x\right ) - 4} \] Input:
integrate(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x ^2-x+52)*log(x))*log(log(x)^2)-2*x*log(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log (x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*x^ 6-128*x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x ^2-32*x+128)/(log(x)^3+(-2*x+8)*log(x)^2+(x^2-8*x+16)*log(x)),x, algorithm ="fricas")
Output:
-(x^7 - 4*x^6 + 8*x^5 - 32*x^4 - x^2*log(x)^2 + 16*x^3 - 64*x^2 + (x^5 + 8 *x^3 + x*log(x) + 16*x)*log(log(x)^2) - (x^6 + 8*x^4 - x^3 + 20*x^2)*log(x ))/(x - log(x) - 4)
Exception generated. \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((ln(x)**3+(5*x**4+24*x**2+20)*ln(x)**2+(-4*x**5+19*x**4-16*x**3 +88*x**2-x+52)*ln(x))*ln(ln(x)**2)-2*x*ln(x)**4+(-6*x**5-32*x**3+4*x**2-49 *x)*ln(x)**3+(12*x**6-48*x**5+64*x**4-258*x**3+82*x**2-296*x+2)*ln(x)**2+( -6*x**7+48*x**6-128*x**5+258*x**4-545*x**3+280*x**2-530*x+40)*ln(x)-2*x**5 +8*x**4-16*x**3+64*x**2-32*x+128)/(ln(x)**3+(-2*x+8)*ln(x)**2+(x**2-8*x+16 )*ln(x)),x)
Output:
Exception raised: TypeError >> '>' not supported between instances of 'Pol y' and 'int'
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (30) = 60\).
Time = 0.09 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.00 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=-\frac {x^{7} - 4 \, x^{6} + 8 \, x^{5} - 32 \, x^{4} - x^{2} \log \left (x\right )^{2} + 16 \, x^{3} - 64 \, x^{2} - {\left (x^{6} + 8 \, x^{4} - x^{3} + 20 \, x^{2}\right )} \log \left (x\right ) + 2 \, {\left (x^{5} + 8 \, x^{3} + x \log \left (x\right ) + 16 \, x\right )} \log \left (\log \left (x\right )\right )}{x - \log \left (x\right ) - 4} \] Input:
integrate(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x ^2-x+52)*log(x))*log(log(x)^2)-2*x*log(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log (x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*x^ 6-128*x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x ^2-32*x+128)/(log(x)^3+(-2*x+8)*log(x)^2+(x^2-8*x+16)*log(x)),x, algorithm ="maxima")
Output:
-(x^7 - 4*x^6 + 8*x^5 - 32*x^4 - x^2*log(x)^2 + 16*x^3 - 64*x^2 - (x^6 + 8 *x^4 - x^3 + 20*x^2)*log(x) + 2*(x^5 + 8*x^3 + x*log(x) + 16*x)*log(log(x) ))/(x - log(x) - 4)
Time = 0.20 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.84 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=-x^{6} - 8 \, x^{4} - x^{2} \log \left (x\right ) - 16 \, x^{2} + {\left (x - \frac {x^{5} + 8 \, x^{3} + x^{2} + 12 \, x}{x - \log \left (x\right ) - 4}\right )} \log \left (\log \left (x\right )^{2}\right ) \] Input:
integrate(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x ^2-x+52)*log(x))*log(log(x)^2)-2*x*log(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log (x)^3+(12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*x^ 6-128*x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x ^2-32*x+128)/(log(x)^3+(-2*x+8)*log(x)^2+(x^2-8*x+16)*log(x)),x, algorithm ="giac")
Output:
-x^6 - 8*x^4 - x^2*log(x) - 16*x^2 + (x - (x^5 + 8*x^3 + x^2 + 12*x)/(x - log(x) - 4))*log(log(x)^2)
Time = 8.26 (sec) , antiderivative size = 281, normalized size of antiderivative = 9.06 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=-34\,\ln \left (\ln \left (x\right )\right )-x^2\,\ln \left (x\right )-16\,x^2-8\,x^4-x^6-\frac {\ln \left ({\ln \left (x\right )}^2\right )\,\left ({\ln \left (x\right )}^2\,\left (\frac {1}{x-1}-\frac {x}{x-1}+1\right )-\left (x-4\right )\,\left (\frac {1}{x-1}-\frac {20\,x^5-25\,x^4+48\,x^3-72\,x^2+x-18}{x-1}+\frac {x-2}{x-1}-\frac {-25\,x^5+25\,x^4-72\,x^3+72\,x^2}{x-1}\right )-\ln \left (x\right )\,\left (\frac {20\,x^5-25\,x^4+48\,x^3-72\,x^2+x-18}{x-1}-\frac {1}{x-1}-\frac {x-2}{x-1}+\left (\frac {1}{x-1}+1\right )\,\left (x-4\right )+\frac {-25\,x^5+25\,x^4-72\,x^3+72\,x^2}{x-1}+\frac {x\,\left (5\,x^4+24\,x^2+20\right )}{x-1}\right )+\frac {x\,\left (4\,x^5-19\,x^4+16\,x^3-88\,x^2+x-52\right )}{x-1}\right )}{\ln \left (x\right )-x+4} \] Input:
int(-(32*x - log(log(x)^2)*(log(x)^3 + log(x)^2*(24*x^2 + 5*x^4 + 20) - lo g(x)*(x - 88*x^2 + 16*x^3 - 19*x^4 + 4*x^5 - 52)) + 2*x*log(x)^4 + log(x)^ 3*(49*x - 4*x^2 + 32*x^3 + 6*x^5) + log(x)*(530*x - 280*x^2 + 545*x^3 - 25 8*x^4 + 128*x^5 - 48*x^6 + 6*x^7 - 40) - 64*x^2 + 16*x^3 - 8*x^4 + 2*x^5 - log(x)^2*(82*x^2 - 296*x - 258*x^3 + 64*x^4 - 48*x^5 + 12*x^6 + 2) - 128) /(log(x)^3 + log(x)*(x^2 - 8*x + 16) - log(x)^2*(2*x - 8)),x)
Output:
- 34*log(log(x)) - x^2*log(x) - 16*x^2 - 8*x^4 - x^6 - (log(log(x)^2)*(log (x)^2*(1/(x - 1) - x/(x - 1) + 1) - (x - 4)*(1/(x - 1) - (x - 72*x^2 + 48* x^3 - 25*x^4 + 20*x^5 - 18)/(x - 1) + (x - 2)/(x - 1) - (72*x^2 - 72*x^3 + 25*x^4 - 25*x^5)/(x - 1)) - log(x)*((x - 72*x^2 + 48*x^3 - 25*x^4 + 20*x^ 5 - 18)/(x - 1) - 1/(x - 1) - (x - 2)/(x - 1) + (1/(x - 1) + 1)*(x - 4) + (72*x^2 - 72*x^3 + 25*x^4 - 25*x^5)/(x - 1) + (x*(24*x^2 + 5*x^4 + 20))/(x - 1)) + (x*(x - 88*x^2 + 16*x^3 - 19*x^4 + 4*x^5 - 52))/(x - 1)))/(log(x) - x + 4)
Time = 0.19 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.35 \[ \int \frac {128-32 x+64 x^2-16 x^3+8 x^4-2 x^5+\left (40-530 x+280 x^2-545 x^3+258 x^4-128 x^5+48 x^6-6 x^7\right ) \log (x)+\left (2-296 x+82 x^2-258 x^3+64 x^4-48 x^5+12 x^6\right ) \log ^2(x)+\left (-49 x+4 x^2-32 x^3-6 x^5\right ) \log ^3(x)-2 x \log ^4(x)+\left (\left (52-x+88 x^2-16 x^3+19 x^4-4 x^5\right ) \log (x)+\left (20+24 x^2+5 x^4\right ) \log ^2(x)+\log ^3(x)\right ) \log \left (\log ^2(x)\right )}{\left (16-8 x+x^2\right ) \log (x)+(8-2 x) \log ^2(x)+\log ^3(x)} \, dx=\frac {x \left (\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) \mathrm {log}\left (x \right )+\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) x^{4}+8 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) x^{2}+16 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )-\mathrm {log}\left (x \right )^{2} x -\mathrm {log}\left (x \right ) x^{5}-8 \,\mathrm {log}\left (x \right ) x^{3}+\mathrm {log}\left (x \right ) x^{2}-20 \,\mathrm {log}\left (x \right ) x +x^{6}-4 x^{5}+8 x^{4}-32 x^{3}+16 x^{2}-64 x \right )}{\mathrm {log}\left (x \right )-x +4} \] Input:
int(((log(x)^3+(5*x^4+24*x^2+20)*log(x)^2+(-4*x^5+19*x^4-16*x^3+88*x^2-x+5 2)*log(x))*log(log(x)^2)-2*x*log(x)^4+(-6*x^5-32*x^3+4*x^2-49*x)*log(x)^3+ (12*x^6-48*x^5+64*x^4-258*x^3+82*x^2-296*x+2)*log(x)^2+(-6*x^7+48*x^6-128* x^5+258*x^4-545*x^3+280*x^2-530*x+40)*log(x)-2*x^5+8*x^4-16*x^3+64*x^2-32* x+128)/(log(x)^3+(-2*x+8)*log(x)^2+(x^2-8*x+16)*log(x)),x)
Output:
(x*(log(log(x)**2)*log(x) + log(log(x)**2)*x**4 + 8*log(log(x)**2)*x**2 + 16*log(log(x)**2) - log(x)**2*x - log(x)*x**5 - 8*log(x)*x**3 + log(x)*x** 2 - 20*log(x)*x + x**6 - 4*x**5 + 8*x**4 - 32*x**3 + 16*x**2 - 64*x))/(log (x) - x + 4)