Integrand size = 303, antiderivative size = 28 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\log \left (\log \left (\frac {\left (x-\frac {x^4}{(-x+5 (4+x+\log (x)))^2}\right )^2}{x}\right )\right ) \] Output:
ln(ln((x-x^4/(4*x+20+5*ln(x))^2)^2/x))
Time = 0.08 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\log \left (\log \left (\frac {x \left (400+160 x+16 x^2-x^3+40 (5+x) \log (x)+25 \log ^2(x)\right )^2}{(4 (5+x)+5 \log (x))^4}\right )\right ) \] Input:
Integrate[(8000 + 4800*x + 960*x^2 - 56*x^3 - 12*x^4 + (6000 + 2400*x + 24 0*x^2 - 35*x^3)*Log[x] + (1500 + 300*x)*Log[x]^2 + 125*Log[x]^3)/((8000*x + 4800*x^2 + 960*x^3 + 44*x^4 - 4*x^5 + (6000*x + 2400*x^2 + 240*x^3 - 5*x ^4)*Log[x] + (1500*x + 300*x^2)*Log[x]^2 + 125*x*Log[x]^3)*Log[(160000*x + 128000*x^2 + 38400*x^3 + 4320*x^4 - 64*x^5 - 32*x^6 + x^7 + (160000*x + 9 6000*x^2 + 19200*x^3 + 880*x^4 - 80*x^5)*Log[x] + (60000*x + 24000*x^2 + 2 400*x^3 - 50*x^4)*Log[x]^2 + (10000*x + 2000*x^2)*Log[x]^3 + 625*x*Log[x]^ 4)/(160000 + 128000*x + 38400*x^2 + 5120*x^3 + 256*x^4 + (160000 + 96000*x + 19200*x^2 + 1280*x^3)*Log[x] + (60000 + 24000*x + 2400*x^2)*Log[x]^2 + (10000 + 2000*x)*Log[x]^3 + 625*Log[x]^4)]),x]
Output:
Log[Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^ 2)/(4*(5 + x) + 5*Log[x])^4]]
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.
| \(\displaystyle \int \frac {-12 x^4-56 x^3+960 x^2+\left (-35 x^3+240 x^2+2400 x+6000\right ) \log (x)+4800 x+125 \log ^3(x)+(300 x+1500) \log ^2(x)+8000}{\left (-4 x^5+44 x^4+960 x^3+4800 x^2+\left (300 x^2+1500 x\right ) \log ^2(x)+\left (-5 x^4+240 x^3+2400 x^2+6000 x\right ) \log (x)+8000 x+125 x \log ^3(x)\right ) \log \left (\frac {x^7-32 x^6-64 x^5+4320 x^4+38400 x^3+128000 x^2+\left (2000 x^2+10000 x\right ) \log ^3(x)+\left (-50 x^4+2400 x^3+24000 x^2+60000 x\right ) \log ^2(x)+\left (-80 x^5+880 x^4+19200 x^3+96000 x^2+160000 x\right ) \log (x)+160000 x+625 x \log ^4(x)}{256 x^4+5120 x^3+38400 x^2+\left (2400 x^2+24000 x+60000\right ) \log ^2(x)+\left (1280 x^3+19200 x^2+96000 x+160000\right ) \log (x)+128000 x+625 \log ^4(x)+(2000 x+10000) \log ^3(x)+160000}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {12 x^4+56 x^3-960 x^2+5 \left (7 x^3-48 x^2-480 x-1200\right ) \log (x)-4800 x-125 \log ^3(x)-300 (x+5) \log ^2(x)-8000}{x \left (5 \left (x^3-48 x^2-480 x-1200\right ) \log (x)+4 \left (x^4-11 x^3-240 x^2-1200 x-2000\right )-125 \log ^3(x)-300 (x+5) \log ^2(x)\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {12 x^3}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}+\frac {35 \log (x) x^2}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}+\frac {56 x^2}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}-\frac {240 \log (x) x}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}-\frac {960 x}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}-\frac {4800}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}+\frac {300 \log ^2(x)}{\left (-4 x^4-5 \log (x) x^3+44 x^3+240 \log (x) x^2+960 x^2+300 \log ^2(x) x+2400 \log (x) x+4800 x+125 \log ^3(x)+1500 \log ^2(x)+6000 \log (x)+8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}+\frac {2400 \log (x)}{\left (-4 x^4-5 \log (x) x^3+44 x^3+240 \log (x) x^2+960 x^2+300 \log ^2(x) x+2400 \log (x) x+4800 x+125 \log ^3(x)+1500 \log ^2(x)+6000 \log (x)+8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}-\frac {125 \log ^3(x)}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right ) x}-\frac {1500 \log ^2(x)}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right ) x}-\frac {6000 \log (x)}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right ) x}-\frac {8000}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right ) x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4800 \int \frac {1}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx-8000 \int \frac {1}{x \left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx-960 \int \frac {x}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx+56 \int \frac {x^2}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx+12 \int \frac {x^3}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx-6000 \int \frac {\log (x)}{x \left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx-240 \int \frac {x \log (x)}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx+35 \int \frac {x^2 \log (x)}{\left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx-1500 \int \frac {\log ^2(x)}{x \left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx-125 \int \frac {\log ^3(x)}{x \left (4 x^4+5 \log (x) x^3-44 x^3-240 \log (x) x^2-960 x^2-300 \log ^2(x) x-2400 \log (x) x-4800 x-125 \log ^3(x)-1500 \log ^2(x)-6000 \log (x)-8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx+2400 \int \frac {\log (x)}{\left (-4 x^4-5 \log (x) x^3+44 x^3+240 \log (x) x^2+960 x^2+300 \log ^2(x) x+2400 \log (x) x+4800 x+125 \log ^3(x)+1500 \log ^2(x)+6000 \log (x)+8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx+300 \int \frac {\log ^2(x)}{\left (-4 x^4-5 \log (x) x^3+44 x^3+240 \log (x) x^2+960 x^2+300 \log ^2(x) x+2400 \log (x) x+4800 x+125 \log ^3(x)+1500 \log ^2(x)+6000 \log (x)+8000\right ) \log \left (\frac {x \left (-x^3+16 x^2+160 x+25 \log ^2(x)+40 (x+5) \log (x)+400\right )^2}{(4 (x+5)+5 \log (x))^4}\right )}dx\) |
Input:
Int[(8000 + 4800*x + 960*x^2 - 56*x^3 - 12*x^4 + (6000 + 2400*x + 240*x^2 - 35*x^3)*Log[x] + (1500 + 300*x)*Log[x]^2 + 125*Log[x]^3)/((8000*x + 4800 *x^2 + 960*x^3 + 44*x^4 - 4*x^5 + (6000*x + 2400*x^2 + 240*x^3 - 5*x^4)*Lo g[x] + (1500*x + 300*x^2)*Log[x]^2 + 125*x*Log[x]^3)*Log[(160000*x + 12800 0*x^2 + 38400*x^3 + 4320*x^4 - 64*x^5 - 32*x^6 + x^7 + (160000*x + 96000*x ^2 + 19200*x^3 + 880*x^4 - 80*x^5)*Log[x] + (60000*x + 24000*x^2 + 2400*x^ 3 - 50*x^4)*Log[x]^2 + (10000*x + 2000*x^2)*Log[x]^3 + 625*x*Log[x]^4)/(16 0000 + 128000*x + 38400*x^2 + 5120*x^3 + 256*x^4 + (160000 + 96000*x + 192 00*x^2 + 1280*x^3)*Log[x] + (60000 + 24000*x + 2400*x^2)*Log[x]^2 + (10000 + 2000*x)*Log[x]^3 + 625*Log[x]^4)]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(193\) vs. \(2(26)=52\).
Time = 8.33 (sec) , antiderivative size = 194, normalized size of antiderivative = 6.93
| method | result | size |
| parallelrisch | \(\ln \left (\ln \left (\frac {625 x \ln \left (x \right )^{4}+\left (2000 x^{2}+10000 x \right ) \ln \left (x \right )^{3}+\left (-50 x^{4}+2400 x^{3}+24000 x^{2}+60000 x \right ) \ln \left (x \right )^{2}+\left (-80 x^{5}+880 x^{4}+19200 x^{3}+96000 x^{2}+160000 x \right ) \ln \left (x \right )+x^{7}-32 x^{6}-64 x^{5}+4320 x^{4}+38400 x^{3}+128000 x^{2}+160000 x}{625 \ln \left (x \right )^{4}+2000 x \ln \left (x \right )^{3}+2400 x^{2} \ln \left (x \right )^{2}+1280 x^{3} \ln \left (x \right )+256 x^{4}+10000 \ln \left (x \right )^{3}+24000 x \ln \left (x \right )^{2}+19200 x^{2} \ln \left (x \right )+5120 x^{3}+60000 \ln \left (x \right )^{2}+96000 x \ln \left (x \right )+38400 x^{2}+160000 \ln \left (x \right )+128000 x +160000}\right )\right )\) | \(194\) |
| default | \(\text {Expression too large to display}\) | \(1091\) |
| risch | \(\text {Expression too large to display}\) | \(1190\) |
Input:
int((125*ln(x)^3+(300*x+1500)*ln(x)^2+(-35*x^3+240*x^2+2400*x+6000)*ln(x)- 12*x^4-56*x^3+960*x^2+4800*x+8000)/(125*x*ln(x)^3+(300*x^2+1500*x)*ln(x)^2 +(-5*x^4+240*x^3+2400*x^2+6000*x)*ln(x)-4*x^5+44*x^4+960*x^3+4800*x^2+8000 *x)/ln((625*x*ln(x)^4+(2000*x^2+10000*x)*ln(x)^3+(-50*x^4+2400*x^3+24000*x ^2+60000*x)*ln(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000*x)*ln(x)+x ^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/(625*ln(x)^4+(200 0*x+10000)*ln(x)^3+(2400*x^2+24000*x+60000)*ln(x)^2+(1280*x^3+19200*x^2+96 000*x+160000)*ln(x)+256*x^4+5120*x^3+38400*x^2+128000*x+160000)),x,method= _RETURNVERBOSE)
Output:
ln(ln((625*x*ln(x)^4+(2000*x^2+10000*x)*ln(x)^3+(-50*x^4+2400*x^3+24000*x^ 2+60000*x)*ln(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000*x)*ln(x)+x^ 7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/(625*ln(x)^4+2000* x*ln(x)^3+2400*x^2*ln(x)^2+1280*x^3*ln(x)+256*x^4+10000*ln(x)^3+24000*x*ln (x)^2+19200*x^2*ln(x)+5120*x^3+60000*ln(x)^2+96000*x*ln(x)+38400*x^2+16000 0*ln(x)+128000*x+160000)))
Leaf count of result is larger than twice the leaf count of optimal. 172 vs. \(2 (27) = 54\).
Time = 0.09 (sec) , antiderivative size = 172, normalized size of antiderivative = 6.14 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\log \left (\log \left (\frac {x^{7} - 32 \, x^{6} - 64 \, x^{5} + 625 \, x \log \left (x\right )^{4} + 4320 \, x^{4} + 2000 \, {\left (x^{2} + 5 \, x\right )} \log \left (x\right )^{3} + 38400 \, x^{3} - 50 \, {\left (x^{4} - 48 \, x^{3} - 480 \, x^{2} - 1200 \, x\right )} \log \left (x\right )^{2} + 128000 \, x^{2} - 80 \, {\left (x^{5} - 11 \, x^{4} - 240 \, x^{3} - 1200 \, x^{2} - 2000 \, x\right )} \log \left (x\right ) + 160000 \, x}{256 \, x^{4} + 2000 \, {\left (x + 5\right )} \log \left (x\right )^{3} + 625 \, \log \left (x\right )^{4} + 5120 \, x^{3} + 2400 \, {\left (x^{2} + 10 \, x + 25\right )} \log \left (x\right )^{2} + 38400 \, x^{2} + 1280 \, {\left (x^{3} + 15 \, x^{2} + 75 \, x + 125\right )} \log \left (x\right ) + 128000 \, x + 160000}\right )\right ) \] Input:
integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000 )*log(x)-12*x^4-56*x^3+960*x^2+4800*x+8000)/(125*x*log(x)^3+(300*x^2+1500* x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3+4 800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2 400*x^3+24000*x^2+60000*x)*log(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+1 60000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/ (625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1 280*x^3+19200*x^2+96000*x+160000)*log(x)+256*x^4+5120*x^3+38400*x^2+128000 *x+160000)),x, algorithm="fricas")
Output:
log(log((x^7 - 32*x^6 - 64*x^5 + 625*x*log(x)^4 + 4320*x^4 + 2000*(x^2 + 5 *x)*log(x)^3 + 38400*x^3 - 50*(x^4 - 48*x^3 - 480*x^2 - 1200*x)*log(x)^2 + 128000*x^2 - 80*(x^5 - 11*x^4 - 240*x^3 - 1200*x^2 - 2000*x)*log(x) + 160 000*x)/(256*x^4 + 2000*(x + 5)*log(x)^3 + 625*log(x)^4 + 5120*x^3 + 2400*( x^2 + 10*x + 25)*log(x)^2 + 38400*x^2 + 1280*(x^3 + 15*x^2 + 75*x + 125)*l og(x) + 128000*x + 160000)))
Leaf count of result is larger than twice the leaf count of optimal. 178 vs. \(2 (22) = 44\).
Time = 3.02 (sec) , antiderivative size = 178, normalized size of antiderivative = 6.36 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\log {\left (\log {\left (\frac {x^{7} - 32 x^{6} - 64 x^{5} + 4320 x^{4} + 38400 x^{3} + 128000 x^{2} + 625 x \log {\left (x \right )}^{4} + 160000 x + \left (2000 x^{2} + 10000 x\right ) \log {\left (x \right )}^{3} + \left (- 50 x^{4} + 2400 x^{3} + 24000 x^{2} + 60000 x\right ) \log {\left (x \right )}^{2} + \left (- 80 x^{5} + 880 x^{4} + 19200 x^{3} + 96000 x^{2} + 160000 x\right ) \log {\left (x \right )}}{256 x^{4} + 5120 x^{3} + 38400 x^{2} + 128000 x + \left (2000 x + 10000\right ) \log {\left (x \right )}^{3} + \left (2400 x^{2} + 24000 x + 60000\right ) \log {\left (x \right )}^{2} + \left (1280 x^{3} + 19200 x^{2} + 96000 x + 160000\right ) \log {\left (x \right )} + 625 \log {\left (x \right )}^{4} + 160000} \right )} \right )} \] Input:
integrate((125*ln(x)**3+(300*x+1500)*ln(x)**2+(-35*x**3+240*x**2+2400*x+60 00)*ln(x)-12*x**4-56*x**3+960*x**2+4800*x+8000)/(125*x*ln(x)**3+(300*x**2+ 1500*x)*ln(x)**2+(-5*x**4+240*x**3+2400*x**2+6000*x)*ln(x)-4*x**5+44*x**4+ 960*x**3+4800*x**2+8000*x)/ln((625*x*ln(x)**4+(2000*x**2+10000*x)*ln(x)**3 +(-50*x**4+2400*x**3+24000*x**2+60000*x)*ln(x)**2+(-80*x**5+880*x**4+19200 *x**3+96000*x**2+160000*x)*ln(x)+x**7-32*x**6-64*x**5+4320*x**4+38400*x**3 +128000*x**2+160000*x)/(625*ln(x)**4+(2000*x+10000)*ln(x)**3+(2400*x**2+24 000*x+60000)*ln(x)**2+(1280*x**3+19200*x**2+96000*x+160000)*ln(x)+256*x**4 +5120*x**3+38400*x**2+128000*x+160000)),x)
Output:
log(log((x**7 - 32*x**6 - 64*x**5 + 4320*x**4 + 38400*x**3 + 128000*x**2 + 625*x*log(x)**4 + 160000*x + (2000*x**2 + 10000*x)*log(x)**3 + (-50*x**4 + 2400*x**3 + 24000*x**2 + 60000*x)*log(x)**2 + (-80*x**5 + 880*x**4 + 192 00*x**3 + 96000*x**2 + 160000*x)*log(x))/(256*x**4 + 5120*x**3 + 38400*x** 2 + 128000*x + (2000*x + 10000)*log(x)**3 + (2400*x**2 + 24000*x + 60000)* log(x)**2 + (1280*x**3 + 19200*x**2 + 96000*x + 160000)*log(x) + 625*log(x )**4 + 160000)))
Time = 9.98 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.68 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\log \left (\log \left (-x^{3} + 16 \, x^{2} + 40 \, {\left (x + 5\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} + 160 \, x + 400\right ) - 2 \, \log \left (4 \, x + 5 \, \log \left (x\right ) + 20\right ) + \frac {1}{2} \, \log \left (x\right )\right ) \] Input:
integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000 )*log(x)-12*x^4-56*x^3+960*x^2+4800*x+8000)/(125*x*log(x)^3+(300*x^2+1500* x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3+4 800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2 400*x^3+24000*x^2+60000*x)*log(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+1 60000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/ (625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1 280*x^3+19200*x^2+96000*x+160000)*log(x)+256*x^4+5120*x^3+38400*x^2+128000 *x+160000)),x, algorithm="maxima")
Output:
log(log(-x^3 + 16*x^2 + 40*(x + 5)*log(x) + 25*log(x)^2 + 160*x + 400) - 2 *log(4*x + 5*log(x) + 20) + 1/2*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 202 vs. \(2 (27) = 54\).
Time = 3.38 (sec) , antiderivative size = 202, normalized size of antiderivative = 7.21 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\log \left (-\log \left (x^{6} - 32 \, x^{5} - 80 \, x^{4} \log \left (x\right ) - 50 \, x^{3} \log \left (x\right )^{2} - 64 \, x^{4} + 880 \, x^{3} \log \left (x\right ) + 2400 \, x^{2} \log \left (x\right )^{2} + 2000 \, x \log \left (x\right )^{3} + 625 \, \log \left (x\right )^{4} + 4320 \, x^{3} + 19200 \, x^{2} \log \left (x\right ) + 24000 \, x \log \left (x\right )^{2} + 10000 \, \log \left (x\right )^{3} + 38400 \, x^{2} + 96000 \, x \log \left (x\right ) + 60000 \, \log \left (x\right )^{2} + 128000 \, x + 160000 \, \log \left (x\right ) + 160000\right ) + \log \left (256 \, x^{4} + 1280 \, x^{3} \log \left (x\right ) + 2400 \, x^{2} \log \left (x\right )^{2} + 2000 \, x \log \left (x\right )^{3} + 625 \, \log \left (x\right )^{4} + 5120 \, x^{3} + 19200 \, x^{2} \log \left (x\right ) + 24000 \, x \log \left (x\right )^{2} + 10000 \, \log \left (x\right )^{3} + 38400 \, x^{2} + 96000 \, x \log \left (x\right ) + 60000 \, \log \left (x\right )^{2} + 128000 \, x + 160000 \, \log \left (x\right ) + 160000\right ) - \log \left (x\right )\right ) \] Input:
integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000 )*log(x)-12*x^4-56*x^3+960*x^2+4800*x+8000)/(125*x*log(x)^3+(300*x^2+1500* x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3+4 800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2 400*x^3+24000*x^2+60000*x)*log(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+1 60000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/ (625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1 280*x^3+19200*x^2+96000*x+160000)*log(x)+256*x^4+5120*x^3+38400*x^2+128000 *x+160000)),x, algorithm="giac")
Output:
log(-log(x^6 - 32*x^5 - 80*x^4*log(x) - 50*x^3*log(x)^2 - 64*x^4 + 880*x^3 *log(x) + 2400*x^2*log(x)^2 + 2000*x*log(x)^3 + 625*log(x)^4 + 4320*x^3 + 19200*x^2*log(x) + 24000*x*log(x)^2 + 10000*log(x)^3 + 38400*x^2 + 96000*x *log(x) + 60000*log(x)^2 + 128000*x + 160000*log(x) + 160000) + log(256*x^ 4 + 1280*x^3*log(x) + 2400*x^2*log(x)^2 + 2000*x*log(x)^3 + 625*log(x)^4 + 5120*x^3 + 19200*x^2*log(x) + 24000*x*log(x)^2 + 10000*log(x)^3 + 38400*x ^2 + 96000*x*log(x) + 60000*log(x)^2 + 128000*x + 160000*log(x) + 160000) - log(x))
Time = 8.80 (sec) , antiderivative size = 178, normalized size of antiderivative = 6.36 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\ln \left (\ln \left (\frac {160000\,x+{\ln \left (x\right )}^3\,\left (2000\,x^2+10000\,x\right )+625\,x\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (-80\,x^5+880\,x^4+19200\,x^3+96000\,x^2+160000\,x\right )+{\ln \left (x\right )}^2\,\left (-50\,x^4+2400\,x^3+24000\,x^2+60000\,x\right )+128000\,x^2+38400\,x^3+4320\,x^4-64\,x^5-32\,x^6+x^7}{128000\,x+{\ln \left (x\right )}^2\,\left (2400\,x^2+24000\,x+60000\right )+625\,{\ln \left (x\right )}^4+38400\,x^2+5120\,x^3+256\,x^4+{\ln \left (x\right )}^3\,\left (2000\,x+10000\right )+\ln \left (x\right )\,\left (1280\,x^3+19200\,x^2+96000\,x+160000\right )+160000}\right )\right ) \] Input:
int((4800*x + 125*log(x)^3 + 960*x^2 - 56*x^3 - 12*x^4 + log(x)^2*(300*x + 1500) + log(x)*(2400*x + 240*x^2 - 35*x^3 + 6000) + 8000)/(log((160000*x + log(x)^3*(10000*x + 2000*x^2) + 625*x*log(x)^4 + log(x)*(160000*x + 9600 0*x^2 + 19200*x^3 + 880*x^4 - 80*x^5) + log(x)^2*(60000*x + 24000*x^2 + 24 00*x^3 - 50*x^4) + 128000*x^2 + 38400*x^3 + 4320*x^4 - 64*x^5 - 32*x^6 + x ^7)/(128000*x + log(x)^2*(24000*x + 2400*x^2 + 60000) + 625*log(x)^4 + 384 00*x^2 + 5120*x^3 + 256*x^4 + log(x)^3*(2000*x + 10000) + log(x)*(96000*x + 19200*x^2 + 1280*x^3 + 160000) + 160000))*(8000*x + log(x)^2*(1500*x + 3 00*x^2) + 125*x*log(x)^3 + log(x)*(6000*x + 2400*x^2 + 240*x^3 - 5*x^4) + 4800*x^2 + 960*x^3 + 44*x^4 - 4*x^5)),x)
Output:
log(log((160000*x + log(x)^3*(10000*x + 2000*x^2) + 625*x*log(x)^4 + log(x )*(160000*x + 96000*x^2 + 19200*x^3 + 880*x^4 - 80*x^5) + log(x)^2*(60000* x + 24000*x^2 + 2400*x^3 - 50*x^4) + 128000*x^2 + 38400*x^3 + 4320*x^4 - 6 4*x^5 - 32*x^6 + x^7)/(128000*x + log(x)^2*(24000*x + 2400*x^2 + 60000) + 625*log(x)^4 + 38400*x^2 + 5120*x^3 + 256*x^4 + log(x)^3*(2000*x + 10000) + log(x)*(96000*x + 19200*x^2 + 1280*x^3 + 160000) + 160000)))
Time = 0.17 (sec) , antiderivative size = 211, normalized size of antiderivative = 7.54 \[ \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx=\mathrm {log}\left (\mathrm {log}\left (\frac {625 \mathrm {log}\left (x \right )^{4} x +2000 \mathrm {log}\left (x \right )^{3} x^{2}+10000 \mathrm {log}\left (x \right )^{3} x -50 \mathrm {log}\left (x \right )^{2} x^{4}+2400 \mathrm {log}\left (x \right )^{2} x^{3}+24000 \mathrm {log}\left (x \right )^{2} x^{2}+60000 \mathrm {log}\left (x \right )^{2} x -80 \,\mathrm {log}\left (x \right ) x^{5}+880 \,\mathrm {log}\left (x \right ) x^{4}+19200 \,\mathrm {log}\left (x \right ) x^{3}+96000 \,\mathrm {log}\left (x \right ) x^{2}+160000 \,\mathrm {log}\left (x \right ) x +x^{7}-32 x^{6}-64 x^{5}+4320 x^{4}+38400 x^{3}+128000 x^{2}+160000 x}{625 \mathrm {log}\left (x \right )^{4}+2000 \mathrm {log}\left (x \right )^{3} x +10000 \mathrm {log}\left (x \right )^{3}+2400 \mathrm {log}\left (x \right )^{2} x^{2}+24000 \mathrm {log}\left (x \right )^{2} x +60000 \mathrm {log}\left (x \right )^{2}+1280 \,\mathrm {log}\left (x \right ) x^{3}+19200 \,\mathrm {log}\left (x \right ) x^{2}+96000 \,\mathrm {log}\left (x \right ) x +160000 \,\mathrm {log}\left (x \right )+256 x^{4}+5120 x^{3}+38400 x^{2}+128000 x +160000}\right )\right ) \] Input:
int((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000)*log( x)-12*x^4-56*x^3+960*x^2+4800*x+8000)/(125*x*log(x)^3+(300*x^2+1500*x)*log (x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3+4800*x^ 2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2400*x^ 3+24000*x^2+60000*x)*log(x)^2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000* x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/(625*l og(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1280*x^ 3+19200*x^2+96000*x+160000)*log(x)+256*x^4+5120*x^3+38400*x^2+128000*x+160 000)),x)
Output:
log(log((625*log(x)**4*x + 2000*log(x)**3*x**2 + 10000*log(x)**3*x - 50*lo g(x)**2*x**4 + 2400*log(x)**2*x**3 + 24000*log(x)**2*x**2 + 60000*log(x)** 2*x - 80*log(x)*x**5 + 880*log(x)*x**4 + 19200*log(x)*x**3 + 96000*log(x)* x**2 + 160000*log(x)*x + x**7 - 32*x**6 - 64*x**5 + 4320*x**4 + 38400*x**3 + 128000*x**2 + 160000*x)/(625*log(x)**4 + 2000*log(x)**3*x + 10000*log(x )**3 + 2400*log(x)**2*x**2 + 24000*log(x)**2*x + 60000*log(x)**2 + 1280*lo g(x)*x**3 + 19200*log(x)*x**2 + 96000*log(x)*x + 160000*log(x) + 256*x**4 + 5120*x**3 + 38400*x**2 + 128000*x + 160000)))