Integrand size = 181, antiderivative size = 27 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\left (-1+\frac {5}{x-(-2 x+5 (25+\log (x)))^2}\right ) \log \left (x^3\right ) \] Output:
(5/(x-(5*ln(x)+125-2*x)^2)-1)*ln(x^3)
Time = 0.06 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=-3 \log (x)-\frac {5 \log \left (x^3\right )}{15625-501 x+4 x^2+(1250-20 x) \log (x)+25 \log ^2(x)} \] Input:
Integrate[(-732656250 + 46976265*x - 1128063*x^2 + 12024*x^3 - 48*x^4 + (- 117206250 + 5632800*x - 90120*x^2 + 480*x^3)*Log[x] + (-7031625 + 225150*x - 1800*x^2)*Log[x]^2 + (-187500 + 3000*x)*Log[x]^3 - 1875*Log[x]^4 + (625 0 - 2605*x + 40*x^2 + (250 - 100*x)*Log[x])*Log[x^3])/(244140625*x - 15656 250*x^2 + 376001*x^3 - 4008*x^4 + 16*x^5 + (39062500*x - 1877500*x^2 + 300 40*x^3 - 160*x^4)*Log[x] + (2343750*x - 75050*x^2 + 600*x^3)*Log[x]^2 + (6 2500*x - 1000*x^2)*Log[x]^3 + 625*x*Log[x]^4),x]
Output:
-3*Log[x] - (5*Log[x^3])/(15625 - 501*x + 4*x^2 + (1250 - 20*x)*Log[x] + 2 5*Log[x]^2)
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.
| \(\displaystyle \int \frac {-48 x^4+12024 x^3-1128063 x^2+\left (-1800 x^2+225150 x-7031625\right ) \log ^2(x)+\left (480 x^3-90120 x^2+5632800 x-117206250\right ) \log (x)+\left (40 x^2-2605 x+(250-100 x) \log (x)+6250\right ) \log \left (x^3\right )+46976265 x-1875 \log ^4(x)+(3000 x-187500) \log ^3(x)-732656250}{16 x^5-4008 x^4+376001 x^3-15656250 x^2+\left (62500 x-1000 x^2\right ) \log ^3(x)+\left (600 x^3-75050 x^2+2343750 x\right ) \log ^2(x)+\left (-160 x^4+30040 x^3-1877500 x^2+39062500 x\right ) \log (x)+244140625 x+625 x \log ^4(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-48 x^4+12024 x^3-1128063 x^2+\left (-1800 x^2+225150 x-7031625\right ) \log ^2(x)+\left (480 x^3-90120 x^2+5632800 x-117206250\right ) \log (x)+\left (40 x^2-2605 x+(250-100 x) \log (x)+6250\right ) \log \left (x^3\right )+46976265 x-1875 \log ^4(x)+(3000 x-187500) \log ^3(x)-732656250}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {75 \left (24 x^2-3002 x+93755\right ) \log ^2(x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {30 (2 x-133) (2 x-125) (4 x-235) \log (x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {12024 x^2}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {1128063 x}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {732656250}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {46976265}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {1875 \log ^4(x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {1500 (2 x-125) \log ^3(x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {5 \left (8 x^2-521 x-20 x \log (x)+50 \log (x)+1250\right ) \log \left (x^3\right )}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {48 x^3}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-75 \left (24 x^2-3002 x+93755\right ) \log ^2(x)+10 \left (48 x^3-5 (2 x-5) \log \left (x^3\right )-9012 x^2+563280 x-11720625\right ) \log (x)+5 \left (8 x^2-521 x+1250\right ) \log \left (x^3\right )-3 \left (16 x^4-4008 x^3+376021 x^2-15658755 x+244218750\right )-1875 \log ^4(x)+1500 (2 x-125) \log ^3(x)}{x \left (4 x^2-501 x+25 \log ^2(x)+(1250-20 x) \log (x)+15625\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {75 \left (24 x^2-3002 x+93755\right ) \log ^2(x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {480 x^2 \log (x)}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {90120 x \log (x)}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {117206250 \log (x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {5632800 \log (x)}{\left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {3 \left (4 x^2-501 x+15625\right ) \left (4 x^2-501 x+15630\right )}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}-\frac {1875 \log ^4(x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {1500 (2 x-125) \log ^3(x)}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}+\frac {5 \left (8 x^2-521 x-20 x \log (x)+50 \log (x)+1250\right ) \log \left (x^3\right )}{x \left (4 x^2-501 x+25 \log ^2(x)-20 x \log (x)+1250 \log (x)+15625\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -15 \int \frac {1}{x \left (4 x^2-20 \log (x) x-501 x+25 \log ^2(x)+1250 \log (x)+15625\right )}dx-2605 \int \frac {\log \left (x^3\right )}{\left (4 x^2-20 \log (x) x-501 x+25 \log ^2(x)+1250 \log (x)+15625\right )^2}dx+6250 \int \frac {\log \left (x^3\right )}{x \left (4 x^2-20 \log (x) x-501 x+25 \log ^2(x)+1250 \log (x)+15625\right )^2}dx+40 \int \frac {x \log \left (x^3\right )}{\left (4 x^2-20 \log (x) x-501 x+25 \log ^2(x)+1250 \log (x)+15625\right )^2}dx-100 \int \frac {\log (x) \log \left (x^3\right )}{\left (4 x^2-20 \log (x) x-501 x+25 \log ^2(x)+1250 \log (x)+15625\right )^2}dx+250 \int \frac {\log (x) \log \left (x^3\right )}{x \left (4 x^2-20 \log (x) x-501 x+25 \log ^2(x)+1250 \log (x)+15625\right )^2}dx-3 \log (x)\) |
Input:
Int[(-732656250 + 46976265*x - 1128063*x^2 + 12024*x^3 - 48*x^4 + (-117206 250 + 5632800*x - 90120*x^2 + 480*x^3)*Log[x] + (-7031625 + 225150*x - 180 0*x^2)*Log[x]^2 + (-187500 + 3000*x)*Log[x]^3 - 1875*Log[x]^4 + (6250 - 26 05*x + 40*x^2 + (250 - 100*x)*Log[x])*Log[x^3])/(244140625*x - 15656250*x^ 2 + 376001*x^3 - 4008*x^4 + 16*x^5 + (39062500*x - 1877500*x^2 + 30040*x^3 - 160*x^4)*Log[x] + (2343750*x - 75050*x^2 + 600*x^3)*Log[x]^2 + (62500*x - 1000*x^2)*Log[x]^3 + 625*x*Log[x]^4),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(74\) vs. \(2(26)=52\).
Time = 12.74 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.78
| method | result | size |
| parallelrisch | \(\frac {58593750-1878750 x -125 \ln \left (x^{3}\right )-300 x^{2} \ln \left (x \right )-37425 x \ln \left (x \right )+1500 x \ln \left (x \right )^{2}+3515625 \ln \left (x \right )-1875 \ln \left (x \right )^{3}+15000 x^{2}}{625 \ln \left (x \right )^{2}-500 x \ln \left (x \right )+100 x^{2}+31250 \ln \left (x \right )-12525 x +390625}\) | \(75\) |
| risch | \(-3 \ln \left (x \right )-\frac {5 \left (6 \ln \left (x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )+i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x^{3}\right )^{2}-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{3}\right )-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}-i \pi \operatorname {csgn}\left (i x^{3}\right )^{3}+i \pi \operatorname {csgn}\left (i x^{3}\right )^{2} \operatorname {csgn}\left (i x \right )\right )}{2 \left (25 \ln \left (x \right )^{2}-20 x \ln \left (x \right )+4 x^{2}+1250 \ln \left (x \right )-501 x +15625\right )}\) | \(163\) |
Input:
int((((-100*x+250)*ln(x)+40*x^2-2605*x+6250)*ln(x^3)-1875*ln(x)^4+(3000*x- 187500)*ln(x)^3+(-1800*x^2+225150*x-7031625)*ln(x)^2+(480*x^3-90120*x^2+56 32800*x-117206250)*ln(x)-48*x^4+12024*x^3-1128063*x^2+46976265*x-732656250 )/(625*x*ln(x)^4+(-1000*x^2+62500*x)*ln(x)^3+(600*x^3-75050*x^2+2343750*x) *ln(x)^2+(-160*x^4+30040*x^3-1877500*x^2+39062500*x)*ln(x)+16*x^5-4008*x^4 +376001*x^3-15656250*x^2+244140625*x),x,method=_RETURNVERBOSE)
Output:
1/25*(58593750-1878750*x-125*ln(x^3)-300*x^2*ln(x)-37425*x*ln(x)+1500*x*ln (x)^2+3515625*ln(x)-1875*ln(x)^3+15000*x^2)/(25*ln(x)^2-20*x*ln(x)+4*x^2+1 250*ln(x)-501*x+15625)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (27) = 54\).
Time = 0.13 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.26 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\frac {3 \, {\left (10 \, {\left (2 \, x - 125\right )} \log \left (x\right )^{2} - 25 \, \log \left (x\right )^{3} - {\left (4 \, x^{2} - 501 \, x + 15630\right )} \log \left (x\right )\right )}}{4 \, x^{2} - 10 \, {\left (2 \, x - 125\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} - 501 \, x + 15625} \] Input:
integrate((((-100*x+250)*log(x)+40*x^2-2605*x+6250)*log(x^3)-1875*log(x)^4 +(3000*x-187500)*log(x)^3+(-1800*x^2+225150*x-7031625)*log(x)^2+(480*x^3-9 0120*x^2+5632800*x-117206250)*log(x)-48*x^4+12024*x^3-1128063*x^2+46976265 *x-732656250)/(625*x*log(x)^4+(-1000*x^2+62500*x)*log(x)^3+(600*x^3-75050* x^2+2343750*x)*log(x)^2+(-160*x^4+30040*x^3-1877500*x^2+39062500*x)*log(x) +16*x^5-4008*x^4+376001*x^3-15656250*x^2+244140625*x),x, algorithm="fricas ")
Output:
3*(10*(2*x - 125)*log(x)^2 - 25*log(x)^3 - (4*x^2 - 501*x + 15630)*log(x)) /(4*x^2 - 10*(2*x - 125)*log(x) + 25*log(x)^2 - 501*x + 15625)
Time = 0.11 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=- 3 \log {\left (x \right )} - \frac {15 \log {\left (x \right )}}{4 x^{2} - 501 x + \left (1250 - 20 x\right ) \log {\left (x \right )} + 25 \log {\left (x \right )}^{2} + 15625} \] Input:
integrate((((-100*x+250)*ln(x)+40*x**2-2605*x+6250)*ln(x**3)-1875*ln(x)**4 +(3000*x-187500)*ln(x)**3+(-1800*x**2+225150*x-7031625)*ln(x)**2+(480*x**3 -90120*x**2+5632800*x-117206250)*ln(x)-48*x**4+12024*x**3-1128063*x**2+469 76265*x-732656250)/(625*x*ln(x)**4+(-1000*x**2+62500*x)*ln(x)**3+(600*x**3 -75050*x**2+2343750*x)*ln(x)**2+(-160*x**4+30040*x**3-1877500*x**2+3906250 0*x)*ln(x)+16*x**5-4008*x**4+376001*x**3-15656250*x**2+244140625*x),x)
Output:
-3*log(x) - 15*log(x)/(4*x**2 - 501*x + (1250 - 20*x)*log(x) + 25*log(x)** 2 + 15625)
Time = 0.08 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=-\frac {15 \, \log \left (x\right )}{4 \, x^{2} - 10 \, {\left (2 \, x - 125\right )} \log \left (x\right ) + 25 \, \log \left (x\right )^{2} - 501 \, x + 15625} - 3 \, \log \left (x\right ) \] Input:
integrate((((-100*x+250)*log(x)+40*x^2-2605*x+6250)*log(x^3)-1875*log(x)^4 +(3000*x-187500)*log(x)^3+(-1800*x^2+225150*x-7031625)*log(x)^2+(480*x^3-9 0120*x^2+5632800*x-117206250)*log(x)-48*x^4+12024*x^3-1128063*x^2+46976265 *x-732656250)/(625*x*log(x)^4+(-1000*x^2+62500*x)*log(x)^3+(600*x^3-75050* x^2+2343750*x)*log(x)^2+(-160*x^4+30040*x^3-1877500*x^2+39062500*x)*log(x) +16*x^5-4008*x^4+376001*x^3-15656250*x^2+244140625*x),x, algorithm="maxima ")
Output:
-15*log(x)/(4*x^2 - 10*(2*x - 125)*log(x) + 25*log(x)^2 - 501*x + 15625) - 3*log(x)
Time = 0.13 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=-\frac {15 \, \log \left (x\right )}{4 \, x^{2} - 20 \, x \log \left (x\right ) + 25 \, \log \left (x\right )^{2} - 501 \, x + 1250 \, \log \left (x\right ) + 15625} - 3 \, \log \left (x\right ) \] Input:
integrate((((-100*x+250)*log(x)+40*x^2-2605*x+6250)*log(x^3)-1875*log(x)^4 +(3000*x-187500)*log(x)^3+(-1800*x^2+225150*x-7031625)*log(x)^2+(480*x^3-9 0120*x^2+5632800*x-117206250)*log(x)-48*x^4+12024*x^3-1128063*x^2+46976265 *x-732656250)/(625*x*log(x)^4+(-1000*x^2+62500*x)*log(x)^3+(600*x^3-75050* x^2+2343750*x)*log(x)^2+(-160*x^4+30040*x^3-1877500*x^2+39062500*x)*log(x) +16*x^5-4008*x^4+376001*x^3-15656250*x^2+244140625*x),x, algorithm="giac")
Output:
-15*log(x)/(4*x^2 - 20*x*log(x) + 25*log(x)^2 - 501*x + 1250*log(x) + 1562 5) - 3*log(x)
Timed out. \[ \int \frac {-732656250+46976265 x-1128063 x^2+12024 x^3-48 x^4+\left (-117206250+5632800 x-90120 x^2+480 x^3\right ) \log (x)+\left (-7031625+225150 x-1800 x^2\right ) \log ^2(x)+(-187500+3000 x) \log ^3(x)-1875 \log ^4(x)+\left (6250-2605 x+40 x^2+(250-100 x) \log (x)\right ) \log \left (x^3\right )}{244140625 x-15656250 x^2+376001 x^3-4008 x^4+16 x^5+\left (39062500 x-1877500 x^2+30040 x^3-160 x^4\right ) \log (x)+\left (2343750 x-75050 x^2+600 x^3\right ) \log ^2(x)+\left (62500 x-1000 x^2\right ) \log ^3(x)+625 x \log ^4(x)} \, dx=\int -\frac {{\ln \left (x\right )}^2\,\left (1800\,x^2-225150\,x+7031625\right )-46976265\,x+1875\,{\ln \left (x\right )}^4+\ln \left (x^3\right )\,\left (2605\,x+\ln \left (x\right )\,\left (100\,x-250\right )-40\,x^2-6250\right )+1128063\,x^2-12024\,x^3+48\,x^4-{\ln \left (x\right )}^3\,\left (3000\,x-187500\right )-\ln \left (x\right )\,\left (480\,x^3-90120\,x^2+5632800\,x-117206250\right )+732656250}{244140625\,x+{\ln \left (x\right )}^3\,\left (62500\,x-1000\,x^2\right )+625\,x\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (-160\,x^4+30040\,x^3-1877500\,x^2+39062500\,x\right )+{\ln \left (x\right )}^2\,\left (600\,x^3-75050\,x^2+2343750\,x\right )-15656250\,x^2+376001\,x^3-4008\,x^4+16\,x^5} \,d x \] Input:
int(-(log(x)^2*(1800*x^2 - 225150*x + 7031625) - 46976265*x + 1875*log(x)^ 4 + log(x^3)*(2605*x + log(x)*(100*x - 250) - 40*x^2 - 6250) + 1128063*x^2 - 12024*x^3 + 48*x^4 - log(x)^3*(3000*x - 187500) - log(x)*(5632800*x - 9 0120*x^2 + 480*x^3 - 117206250) + 732656250)/(244140625*x + log(x)^3*(6250 0*x - 1000*x^2) + 625*x*log(x)^4 + log(x)*(39062500*x - 1877500*x^2 + 3004 0*x^3 - 160*x^4) + log(x)^2*(2343750*x - 75050*x^2 + 600*x^3) - 15656250*x ^2 + 376001*x^3 - 4008*x^4 + 16*x^5),x)
Output:
int(-(log(x)^2*(1800*x^2 - 225150*x + 7031625) - 46976265*x + 1875*log(x)^ 4 + log(x^3)*(2605*x + log(x)*(100*x - 250) - 40*x^2 - 6250) + 1128063*x^2 - 12024*x^3 + 48*x^4 - log(x)^3*(3000*x - 187500) - log(x)*(5632800*x - 9 0120*x^2 + 480*x^3 - 117206250) + 732656250)/(244140625*x + log(x)^3*(6250 0*x - 1000*x^2) + 625*x*log(x)^4 + log(x)*(39062500*x - 1877500*x^2 + 3004 0*x^3 - 160*x^4) + log(x)^2*(2343750*x - 75050*x^2 + 600*x^3) - 15656250*x ^2 + 376001*x^3 - 4008*x^4 + 16*x^5), x)
Time = 0.20 (sec) , antiderivative size = 222, normalized size of antiderivative = 8.22 \[ \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 {125000000 \mathrm {log}\left (x^{3}\right )^{2} \mathrm {log}\left (x \right )^{2}-100000000 \mathrm {log}\left (x^{3}\right )^{2} \mathrm {log}\left (x \right ) x +6250000000 \mathrm {log}\left (x^{3}\right )^{2} \mathrm {log}\left (x \right )+20000000 \mathrm {log}\left (x^{3}\right )^{2} x^{2}-2505000000 \mathrm {log}\left (x^{3}\right )^{2} x +78125000000 \mathrm {log}\left (x^{3}\right )^{2}-750000000 \,\mathrm {log}\left (x^{3}\right ) \mathrm {log}\left (x \right )^{3}+600000000 \,\mathrm {log}\left (x^{3}\right ) \mathrm {log}\left (x \right )^{2} x -28068637425 \,\mathrm {log}\left (x^{3}\right ) \mathrm {log}\left (x \right )^{2}-120000000 \,\mathrm {log}\left (x^{3}\right ) \mathrm {log}\left (x \right ) x^{2}+7484909940 \,\mathrm {log}\left (x^{3}\right ) \mathrm {log}\left (x \right ) x +2818128750 \,\mathrm {log}\left (x^{3}\right ) \mathrm {log}\left (x \right )+1509018012 \,\mathrm {log}\left (x^{3}\right ) x^{2}-189004506003 \,\mathrm {log}\left (x^{3}\right ) x +1125000000 \mathrm {log}\left (x \right )^{4}-900000000 \mathrm {log}\left (x \right )^{3} x -88391068228350 \mathrm {log}\left (x \right )^{3}+180000000 \mathrm {log}\left (x \right )^{2} x^{2}+70735309582680 \mathrm {log}\left (x \right )^{2} x -4421662786417500 \mathrm {log}\left (x \right )^{2}-14151570916536 \,\mathrm {log}\left (x \right ) x^{2}+1772484257296134 \,\mathrm {log}\left (x \right ) x -55279573892718750 \,\mathrm {log}\left (x \right )}{29473008046875 \mathrm {log}\left (x \right )^{2}-23578406437500 \,\mathrm {log}\left (x \right ) x +1473650402343750 \,\mathrm {log}\left (x \right )+4715681287500 x^{2}-590639081259375 x +18420630029296875} \] Input:
int((((-100*x+250)*log(x)+40*x^2-2605*x+6250)*log(x^3)-1875*log(x)^4+(3000 *x-187500)*log(x)^3+(-1800*x^2+225150*x-7031625)*log(x)^2+(480*x^3-90120*x ^2+5632800*x-117206250)*log(x)-48*x^4+12024*x^3-1128063*x^2+46976265*x-732 656250)/(625*x*log(x)^4+(-1000*x^2+62500*x)*log(x)^3+(600*x^3-75050*x^2+23 43750*x)*log(x)^2+(-160*x^4+30040*x^3-1877500*x^2+39062500*x)*log(x)+16*x^ 5-4008*x^4+376001*x^3-15656250*x^2+244140625*x),x)
Output:
(125000000*log(x**3)**2*log(x)**2 - 100000000*log(x**3)**2*log(x)*x + 6250 000000*log(x**3)**2*log(x) + 20000000*log(x**3)**2*x**2 - 2505000000*log(x **3)**2*x + 78125000000*log(x**3)**2 - 750000000*log(x**3)*log(x)**3 + 600 000000*log(x**3)*log(x)**2*x - 28068637425*log(x**3)*log(x)**2 - 120000000 *log(x**3)*log(x)*x**2 + 7484909940*log(x**3)*log(x)*x + 2818128750*log(x* *3)*log(x) + 1509018012*log(x**3)*x**2 - 189004506003*log(x**3)*x + 112500 0000*log(x)**4 - 900000000*log(x)**3*x - 88391068228350*log(x)**3 + 180000 000*log(x)**2*x**2 + 70735309582680*log(x)**2*x - 4421662786417500*log(x)* *2 - 14151570916536*log(x)*x**2 + 1772484257296134*log(x)*x - 552795738927 18750*log(x))/(1178920321875*(25*log(x)**2 - 20*log(x)*x + 1250*log(x) + 4 *x**2 - 501*x + 15625))