Integrand size = 181, antiderivative size = 27 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\left (-1+\frac {5}{x-(-2 x+5 (25+\log (x)))^2}\right ) \log \left (x^3\right ) \]
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\[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-3 \left (244218750-15658755 x+376021 x^2-4008 x^3+16 x^4\right )-75 \left (93755-3002 x+24 x^2\right ) \log ^2(x)+1500 (-125+2 x) \log ^3(x)-1875 \log ^4(x)+5 \left (1250-521 x+8 x^2\right ) \log \left (x^3\right )+10 \log (x) \left (-11720625+563280 x-9012 x^2+48 x^3-5 (-5+2 x) \log \left (x^3\right )\right )}{x \left (15625-501 x+4 x^2+(1250-20 x) \log (x)+25 \log ^2(x)\right )^2} \, dx \\ & = \int \left (-\frac {3 \left (15625-501 x+4 x^2\right ) \left (15630-501 x+4 x^2\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {5632800 \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}-\frac {117206250 \log (x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}-\frac {90120 x \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {480 x^2 \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}-\frac {75 \left (93755-3002 x+24 x^2\right ) \log ^2(x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {1500 (-125+2 x) \log ^3(x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}-\frac {1875 \log ^4(x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {5 \left (1250-521 x+8 x^2+50 \log (x)-20 x \log (x)\right ) \log \left (x^3\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}\right ) \, dx \\ & = -\left (3 \int \frac {\left (15625-501 x+4 x^2\right ) \left (15630-501 x+4 x^2\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx\right )+5 \int \frac {\left (1250-521 x+8 x^2+50 \log (x)-20 x \log (x)\right ) \log \left (x^3\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-75 \int \frac {\left (93755-3002 x+24 x^2\right ) \log ^2(x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+480 \int \frac {x^2 \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+1500 \int \frac {(-125+2 x) \log ^3(x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-1875 \int \frac {\log ^4(x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-90120 \int \frac {x \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+5632800 \int \frac {\log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-117206250 \int \frac {\log (x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx \\ & = -\left (3 \int \left (-\frac {15658755}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {244218750}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {376021 x}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}-\frac {4008 x^2}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {16 x^3}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}\right ) \, dx\right )+5 \int \left (-\frac {521 \log \left (x^3\right )}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {1250 \log \left (x^3\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {8 x \log \left (x^3\right )}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}-\frac {20 \log (x) \log \left (x^3\right )}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {50 \log (x) \log \left (x^3\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}\right ) \, dx-75 \int \left (-\frac {\left (93755-3002 x+24 x^2\right ) \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)\right )}{25 x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {93755-3002 x+24 x^2}{25 x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )}\right ) \, dx+480 \int \frac {x^2 \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+1500 \int \left (-\frac {(-125+2 x) \left (-3906250+187750 x-3004 x^2+16 x^3-234375 \log (x)+7495 x \log (x)-60 x^2 \log (x)\right )}{125 x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {(-125+2 x) (-250+4 x+5 \log (x))}{125 x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )}\right ) \, dx-1875 \int \left (\frac {1}{625 x}+\frac {-732421875+46906250 x-1125999 x^2+12008 x^3-48 x^4-39062500 \log (x)+1872500 x \log (x)-29960 x^2 \log (x)+160 x^3 \log (x)}{625 x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2}+\frac {2 \left (15625-499 x+4 x^2-1250 \log (x)+20 x \log (x)\right )}{625 x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )}\right ) \, dx-90120 \int \frac {x \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+5632800 \int \frac {\log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-117206250 \int \frac {\log (x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx \\ & = -3 \log (x)+3 \int \frac {\left (93755-3002 x+24 x^2\right ) \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-3 \int \frac {-732421875+46906250 x-1125999 x^2+12008 x^3-48 x^4-39062500 \log (x)+1872500 x \log (x)-29960 x^2 \log (x)+160 x^3 \log (x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-3 \int \frac {93755-3002 x+24 x^2}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )} \, dx-6 \int \frac {15625-499 x+4 x^2-1250 \log (x)+20 x \log (x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )} \, dx-12 \int \frac {(-125+2 x) \left (-3906250+187750 x-3004 x^2+16 x^3-234375 \log (x)+7495 x \log (x)-60 x^2 \log (x)\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+12 \int \frac {(-125+2 x) (-250+4 x+5 \log (x))}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )} \, dx+40 \int \frac {x \log \left (x^3\right )}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-48 \int \frac {x^3}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-100 \int \frac {\log (x) \log \left (x^3\right )}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+250 \int \frac {\log (x) \log \left (x^3\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+480 \int \frac {x^2 \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-2605 \int \frac {\log \left (x^3\right )}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+6250 \int \frac {\log \left (x^3\right )}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+12024 \int \frac {x^2}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-90120 \int \frac {x \log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-1128063 \int \frac {x}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+5632800 \int \frac {\log (x)}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx+46976265 \int \frac {1}{\left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-117206250 \int \frac {\log (x)}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx-732656250 \int \frac {1}{x \left (15625-501 x+4 x^2+1250 \log (x)-20 x \log (x)+25 \log ^2(x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=-3 \log (x)-\frac {5 \log \left (x^3\right )}{15625-501 x+4 x^2+(1250-20 x) \log (x)+25 \log ^2(x)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(74\) vs. \(2(26)=52\).
Time = 3.95 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.78
method | result | size |
parallelrisch | \(\frac {58593750-1878750 x +1500 x \ln \left (x \right )^{2}-37425 x \ln \left (x \right )-125 \ln \left (x^{3}\right )-1875 \ln \left (x \right )^{3}+3515625 \ln \left (x \right )+15000 x^{2}-300 x^{2} \ln \left (x \right )}{625 \ln \left (x \right )^{2}-500 x \ln \left (x \right )+100 x^{2}+31250 \ln \left (x \right )-12525 x +390625}\) | \(75\) |
risch | \(-3 \ln \left (x \right )-\frac {5 \left (6 \ln \left (x \right )-i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x^{3}\right )+i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{3}\right )^{2}-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x^{3}\right )^{2}-i \pi \operatorname {csgn}\left (i x^{3}\right )^{3}\right )}{2 \left (25 \ln \left (x \right )^{2}-20 x \ln \left (x \right )+4 x^{2}+1250 \ln \left (x \right )-501 x +15625\right )}\) | \(163\) |
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.26 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\frac {3 \, {\left (10 \, {\left (2 \, x - 125\right )} \log \left (x\right )^{2} - 25 \, \log \left (x\right )^{3} - {\left (4 \, x^{2} - 501 \, x + 15630\right )} \log \left (x\right )\right )}}{4 \, x^{2} - 10 \, {\left (2 \, x - 125\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} - 501 \, x + 15625} \]
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Time = 0.13 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=- 3 \log {\left (x \right )} - \frac {15 \log {\left (x \right )}}{4 x^{2} - 501 x + \left (1250 - 20 x\right ) \log {\left (x \right )} + 25 \log {\left (x \right )}^{2} + 15625} \]
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Time = 0.25 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=-\frac {15 \, \log \left (x\right )}{4 \, x^{2} - 10 \, {\left (2 \, x - 125\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} - 501 \, x + 15625} - 3 \, \log \left (x\right ) \]
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Time = 0.28 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=-\frac {15 \, \log \left (x\right )}{4 \, x^{2} - 20 \, x \log \left (x\right ) + 25 \, \log \left (x\right )^{2} - 501 \, x + 1250 \, \log \left (x\right ) + 15625} - 3 \, \log \left (x\right ) \]
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Timed out. \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\int -\frac {{\ln \left (x\right )}^2\,\left (1800\,x^2-225150\,x+7031625\right )-46976265\,x+1875\,{\ln \left (x\right )}^4+\ln \left (x^3\right )\,\left (2605\,x+\ln \left (x\right )\,\left (100\,x-250\right )-40\,x^2-6250\right )+1128063\,x^2-12024\,x^3+48\,x^4-{\ln \left (x\right )}^3\,\left (3000\,x-187500\right )-\ln \left (x\right )\,\left (480\,x^3-90120\,x^2+5632800\,x-117206250\right )+732656250}{244140625\,x+{\ln \left (x\right )}^3\,\left (62500\,x-1000\,x^2\right )+625\,x\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (-160\,x^4+30040\,x^3-1877500\,x^2+39062500\,x\right )+{\ln \left (x\right )}^2\,\left (600\,x^3-75050\,x^2+2343750\,x\right )-15656250\,x^2+376001\,x^3-4008\,x^4+16\,x^5} \,d x \]
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