Integrand size = 165, antiderivative size = 23 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=6 \left (2+x-\frac {4-\frac {x}{(5+x)^2}}{\log (x)}\right )^2 \] Output:
6*(2+x-(4-x/(5+x)^2)/ln(x))^2
Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(23)=46\).
Time = 0.05 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.74 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=12 \left (2 x+\frac {x^2}{2}+\frac {\left (100+39 x+4 x^2\right )^2}{2 (5+x)^4 \log ^2(x)}+\frac {-200-178 x-47 x^2-4 x^3}{(5+x)^2 \log (x)}\right ) \] Input:
Integrate[(-600000 - 588000*x - 232860*x^2 - 46572*x^3 - 4704*x^4 - 192*x^ 5 + (300000 + 441000*x + 265560*x^2 + 82968*x^3 + 14244*x^4 + 1284*x^5 + 4 8*x^6)*Log[x] + (-147000*x - 146400*x^2 - 58920*x^3 - 11904*x^4 - 1200*x^5 - 48*x^6)*Log[x]^2 + (75000*x + 112500*x^2 + 67500*x^3 + 21000*x^4 + 3600 *x^5 + 324*x^6 + 12*x^7)*Log[x]^3)/((3125*x + 3125*x^2 + 1250*x^3 + 250*x^ 4 + 25*x^5 + x^6)*Log[x]^3),x]
Output:
12*(2*x + x^2/2 + (100 + 39*x + 4*x^2)^2/(2*(5 + x)^4*Log[x]^2) + (-200 - 178*x - 47*x^2 - 4*x^3)/((5 + x)^2*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.
| \(\displaystyle \int \frac {-192 x^5-4704 x^4-46572 x^3-232860 x^2+\left (-48 x^6-1200 x^5-11904 x^4-58920 x^3-146400 x^2-147000 x\right ) \log ^2(x)+\left (48 x^6+1284 x^5+14244 x^4+82968 x^3+265560 x^2+441000 x+300000\right ) \log (x)+\left (12 x^7+324 x^6+3600 x^5+21000 x^4+67500 x^3+112500 x^2+75000 x\right ) \log ^3(x)-588000 x-600000}{\left (x^6+25 x^5+250 x^4+1250 x^3+3125 x^2+3125 x\right ) \log ^3(x)} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-192 x^5-4704 x^4-46572 x^3-232860 x^2+\left (-48 x^6-1200 x^5-11904 x^4-58920 x^3-146400 x^2-147000 x\right ) \log ^2(x)+\left (48 x^6+1284 x^5+14244 x^4+82968 x^3+265560 x^2+441000 x+300000\right ) \log (x)+\left (12 x^7+324 x^6+3600 x^5+21000 x^4+67500 x^3+112500 x^2+75000 x\right ) \log ^3(x)-588000 x-600000}{x \left (x^5+25 x^4+250 x^3+1250 x^2+3125 x+3125\right ) \log ^3(x)}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {-192 x^5-4704 x^4-46572 x^3-232860 x^2+\left (-48 x^6-1200 x^5-11904 x^4-58920 x^3-146400 x^2-147000 x\right ) \log ^2(x)+\left (48 x^6+1284 x^5+14244 x^4+82968 x^3+265560 x^2+441000 x+300000\right ) \log (x)+\left (12 x^7+324 x^6+3600 x^5+21000 x^4+67500 x^3+112500 x^2+75000 x\right ) \log ^3(x)-588000 x-600000}{x (x+5)^5 \log ^3(x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {12 \left (4 x^2+39 x+100\right )^2}{x (x+5)^4 \log ^3(x)}-\frac {24 \left (2 x^3+30 x^2+146 x+245\right )}{(x+5)^3 \log (x)}+\frac {12 \left (x^4+17 x^3+106 x^2+270 x+250\right ) \left (4 x^2+39 x+100\right )}{x (x+5)^5 \log ^2(x)}+12 (x+2)\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -12 \int \frac {\left (4 x^2+39 x+100\right )^2}{x (x+5)^4 \log ^3(x)}dx-24 \int \frac {2 x^3+30 x^2+146 x+245}{(x+5)^3 \log (x)}dx+12 \int \frac {\left (4 x^2+39 x+100\right ) \left (x^4+17 x^3+106 x^2+270 x+250\right )}{x (x+5)^5 \log ^2(x)}dx+6 (x+2)^2\) |
Input:
Int[(-600000 - 588000*x - 232860*x^2 - 46572*x^3 - 4704*x^4 - 192*x^5 + (3 00000 + 441000*x + 265560*x^2 + 82968*x^3 + 14244*x^4 + 1284*x^5 + 48*x^6) *Log[x] + (-147000*x - 146400*x^2 - 58920*x^3 - 11904*x^4 - 1200*x^5 - 48* x^6)*Log[x]^2 + (75000*x + 112500*x^2 + 67500*x^3 + 21000*x^4 + 3600*x^5 + 324*x^6 + 12*x^7)*Log[x]^3)/((3125*x + 3125*x^2 + 1250*x^3 + 250*x^4 + 25 *x^5 + x^6)*Log[x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(77\) vs. \(2(23)=46\).
Time = 15.21 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.39
| method | result | size |
| default | \(\frac {-84 \ln \left (x \right )+96}{\ln \left (x \right )^{2}}+6 x^{2}+\frac {24 \left (\ln \left (x \right )-2\right ) x}{\ln \left (x \right )}-\frac {6 \left (16 x^{3} \ln \left (x \right )+210 x^{2} \ln \left (x \right )+8 x^{3}+900 x \ln \left (x \right )+79 x^{2}+1250 \ln \left (x \right )+200 x \right )}{\ln \left (x \right )^{2} \left (5+x \right )^{4}}\) | \(78\) |
| risch | \(6 x^{2}+24 x -\frac {6 \left (8 x^{5} \ln \left (x \right )+174 x^{4} \ln \left (x \right )-16 x^{4}+1496 x^{3} \ln \left (x \right )-312 x^{3}+6310 x^{2} \ln \left (x \right )-2321 x^{2}+12900 x \ln \left (x \right )-7800 x +10000 \ln \left (x \right )-10000\right )}{\left (5+x \right ) \left (x^{3}+15 x^{2}+75 x +125\right ) \ln \left (x \right )^{2}}\) | \(93\) |
| parallelrisch | \(-\frac {-9000000-7020000 x +7200 x^{5} \ln \left (x \right )-191250 x^{4} \ln \left (x \right )^{2}+156600 x^{4} \ln \left (x \right )+5625000 x \ln \left (x \right )^{2}+11610000 x \ln \left (x \right )-900 \ln \left (x \right )^{2} x^{6}-21600 x^{5} \ln \left (x \right )^{2}-675000 x^{3} \ln \left (x \right )^{2}+1346400 x^{3} \ln \left (x \right )+5679000 x^{2} \ln \left (x \right )+9000000 \ln \left (x \right )+9843750 \ln \left (x \right )^{2}-14400 x^{4}-280800 x^{3}-2088900 x^{2}}{150 \ln \left (x \right )^{2} \left (x^{4}+20 x^{3}+150 x^{2}+500 x +625\right )}\) | \(133\) |
Input:
int(((12*x^7+324*x^6+3600*x^5+21000*x^4+67500*x^3+112500*x^2+75000*x)*ln(x )^3+(-48*x^6-1200*x^5-11904*x^4-58920*x^3-146400*x^2-147000*x)*ln(x)^2+(48 *x^6+1284*x^5+14244*x^4+82968*x^3+265560*x^2+441000*x+300000)*ln(x)-192*x^ 5-4704*x^4-46572*x^3-232860*x^2-588000*x-600000)/(x^6+25*x^5+250*x^4+1250* x^3+3125*x^2+3125*x)/ln(x)^3,x,method=_RETURNVERBOSE)
Output:
12*(-7*ln(x)+8)/ln(x)^2+6*x^2+24*(ln(x)-2)/ln(x)*x-6/ln(x)^2*(16*x^3*ln(x) +210*x^2*ln(x)+8*x^3+900*x*ln(x)+79*x^2+1250*ln(x)+200*x)/(5+x)^4
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (21) = 42\).
Time = 0.08 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.65 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=\frac {6 \, {\left (16 \, x^{4} + 312 \, x^{3} + {\left (x^{6} + 24 \, x^{5} + 230 \, x^{4} + 1100 \, x^{3} + 2625 \, x^{2} + 2500 \, x\right )} \log \left (x\right )^{2} + 2321 \, x^{2} - 2 \, {\left (4 \, x^{5} + 87 \, x^{4} + 748 \, x^{3} + 3155 \, x^{2} + 6450 \, x + 5000\right )} \log \left (x\right ) + 7800 \, x + 10000\right )}}{{\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} \log \left (x\right )^{2}} \] Input:
integrate(((12*x^7+324*x^6+3600*x^5+21000*x^4+67500*x^3+112500*x^2+75000*x )*log(x)^3+(-48*x^6-1200*x^5-11904*x^4-58920*x^3-146400*x^2-147000*x)*log( x)^2+(48*x^6+1284*x^5+14244*x^4+82968*x^3+265560*x^2+441000*x+300000)*log( x)-192*x^5-4704*x^4-46572*x^3-232860*x^2-588000*x-600000)/(x^6+25*x^5+250* x^4+1250*x^3+3125*x^2+3125*x)/log(x)^3,x, algorithm="fricas")
Output:
6*(16*x^4 + 312*x^3 + (x^6 + 24*x^5 + 230*x^4 + 1100*x^3 + 2625*x^2 + 2500 *x)*log(x)^2 + 2321*x^2 - 2*(4*x^5 + 87*x^4 + 748*x^3 + 3155*x^2 + 6450*x + 5000)*log(x) + 7800*x + 10000)/((x^4 + 20*x^3 + 150*x^2 + 500*x + 625)*l og(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (17) = 34\).
Time = 0.14 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.57 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=6 x^{2} + 24 x + \frac {96 x^{4} + 1872 x^{3} + 13926 x^{2} + 46800 x + \left (- 48 x^{5} - 1044 x^{4} - 8976 x^{3} - 37860 x^{2} - 77400 x - 60000\right ) \log {\left (x \right )} + 60000}{\left (x^{4} + 20 x^{3} + 150 x^{2} + 500 x + 625\right ) \log {\left (x \right )}^{2}} \] Input:
integrate(((12*x**7+324*x**6+3600*x**5+21000*x**4+67500*x**3+112500*x**2+7 5000*x)*ln(x)**3+(-48*x**6-1200*x**5-11904*x**4-58920*x**3-146400*x**2-147 000*x)*ln(x)**2+(48*x**6+1284*x**5+14244*x**4+82968*x**3+265560*x**2+44100 0*x+300000)*ln(x)-192*x**5-4704*x**4-46572*x**3-232860*x**2-588000*x-60000 0)/(x**6+25*x**5+250*x**4+1250*x**3+3125*x**2+3125*x)/ln(x)**3,x)
Output:
6*x**2 + 24*x + (96*x**4 + 1872*x**3 + 13926*x**2 + 46800*x + (-48*x**5 - 1044*x**4 - 8976*x**3 - 37860*x**2 - 77400*x - 60000)*log(x) + 60000)/((x* *4 + 20*x**3 + 150*x**2 + 500*x + 625)*log(x)**2)
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (21) = 42\).
Time = 0.07 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.65 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=\frac {6 \, {\left (16 \, x^{4} + 312 \, x^{3} + {\left (x^{6} + 24 \, x^{5} + 230 \, x^{4} + 1100 \, x^{3} + 2625 \, x^{2} + 2500 \, x\right )} \log \left (x\right )^{2} + 2321 \, x^{2} - 2 \, {\left (4 \, x^{5} + 87 \, x^{4} + 748 \, x^{3} + 3155 \, x^{2} + 6450 \, x + 5000\right )} \log \left (x\right ) + 7800 \, x + 10000\right )}}{{\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} \log \left (x\right )^{2}} \] Input:
integrate(((12*x^7+324*x^6+3600*x^5+21000*x^4+67500*x^3+112500*x^2+75000*x )*log(x)^3+(-48*x^6-1200*x^5-11904*x^4-58920*x^3-146400*x^2-147000*x)*log( x)^2+(48*x^6+1284*x^5+14244*x^4+82968*x^3+265560*x^2+441000*x+300000)*log( x)-192*x^5-4704*x^4-46572*x^3-232860*x^2-588000*x-600000)/(x^6+25*x^5+250* x^4+1250*x^3+3125*x^2+3125*x)/log(x)^3,x, algorithm="maxima")
Output:
6*(16*x^4 + 312*x^3 + (x^6 + 24*x^5 + 230*x^4 + 1100*x^3 + 2625*x^2 + 2500 *x)*log(x)^2 + 2321*x^2 - 2*(4*x^5 + 87*x^4 + 748*x^3 + 3155*x^2 + 6450*x + 5000)*log(x) + 7800*x + 10000)/((x^4 + 20*x^3 + 150*x^2 + 500*x + 625)*l og(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (21) = 42\).
Time = 0.13 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.78 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=6 \, x^{2} + 24 \, x - \frac {6 \, {\left (8 \, x^{5} \log \left (x\right ) + 174 \, x^{4} \log \left (x\right ) - 16 \, x^{4} + 1496 \, x^{3} \log \left (x\right ) - 312 \, x^{3} + 6310 \, x^{2} \log \left (x\right ) - 2321 \, x^{2} + 12900 \, x \log \left (x\right ) - 7800 \, x + 10000 \, \log \left (x\right ) - 10000\right )}}{x^{4} \log \left (x\right )^{2} + 20 \, x^{3} \log \left (x\right )^{2} + 150 \, x^{2} \log \left (x\right )^{2} + 500 \, x \log \left (x\right )^{2} + 625 \, \log \left (x\right )^{2}} \] Input:
integrate(((12*x^7+324*x^6+3600*x^5+21000*x^4+67500*x^3+112500*x^2+75000*x )*log(x)^3+(-48*x^6-1200*x^5-11904*x^4-58920*x^3-146400*x^2-147000*x)*log( x)^2+(48*x^6+1284*x^5+14244*x^4+82968*x^3+265560*x^2+441000*x+300000)*log( x)-192*x^5-4704*x^4-46572*x^3-232860*x^2-588000*x-600000)/(x^6+25*x^5+250* x^4+1250*x^3+3125*x^2+3125*x)/log(x)^3,x, algorithm="giac")
Output:
6*x^2 + 24*x - 6*(8*x^5*log(x) + 174*x^4*log(x) - 16*x^4 + 1496*x^3*log(x) - 312*x^3 + 6310*x^2*log(x) - 2321*x^2 + 12900*x*log(x) - 7800*x + 10000* log(x) - 10000)/(x^4*log(x)^2 + 20*x^3*log(x)^2 + 150*x^2*log(x)^2 + 500*x *log(x)^2 + 625*log(x)^2)
Time = 0.85 (sec) , antiderivative size = 314, normalized size of antiderivative = 13.65 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=\frac {\frac {6\,{\left (4\,x^2+39\,x+100\right )}^2}{{\left (x+5\right )}^4}-\frac {6\,\ln \left (x\right )\,\left (4\,x^6+107\,x^5+1187\,x^4+6914\,x^3+22130\,x^2+36750\,x+25000\right )}{{\left (x+5\right )}^5}+\frac {12\,x\,{\ln \left (x\right )}^2\,\left (2\,x^3+30\,x^2+146\,x+245\right )}{{\left (x+5\right )}^3}}{{\ln \left (x\right )}^2}-480\,\ln \left (x\right )-24\,x+\frac {\frac {12\,x\,{\ln \left (x\right )}^2\,\left (2\,x^4+40\,x^3+304\,x^2+970\,x+1225\right )}{{\left (x+5\right )}^4}-\frac {6\,\left (4\,x^6+107\,x^5+1179\,x^4+6876\,x^3+22320\,x^2+37750\,x+25000\right )}{{\left (x+5\right )}^5}+\frac {12\,x\,\ln \left (x\right )\,\left (2\,x^6+60\,x^5+748\,x^4+4914\,x^3+18090\,x^2+36100\,x+31875\right )}{{\left (x+5\right )}^6}}{\ln \left (x\right )}+6\,x^2+\frac {72\,x^5+1812\,x^4+12420\,x^3+27300\,x^2}{x^6+30\,x^5+375\,x^4+2500\,x^3+9375\,x^2+18750\,x+15625}+\frac {\ln \left (x\right )\,\left (-24\,x^5+5952\,x^3+60360\,x^2+225300\,x+300000\right )}{x^4+20\,x^3+150\,x^2+500\,x+625} \] Input:
int(-(588000*x - log(x)^3*(75000*x + 112500*x^2 + 67500*x^3 + 21000*x^4 + 3600*x^5 + 324*x^6 + 12*x^7) - log(x)*(441000*x + 265560*x^2 + 82968*x^3 + 14244*x^4 + 1284*x^5 + 48*x^6 + 300000) + 232860*x^2 + 46572*x^3 + 4704*x ^4 + 192*x^5 + log(x)^2*(147000*x + 146400*x^2 + 58920*x^3 + 11904*x^4 + 1 200*x^5 + 48*x^6) + 600000)/(log(x)^3*(3125*x + 3125*x^2 + 1250*x^3 + 250* x^4 + 25*x^5 + x^6)),x)
Output:
((6*(39*x + 4*x^2 + 100)^2)/(x + 5)^4 - (6*log(x)*(36750*x + 22130*x^2 + 6 914*x^3 + 1187*x^4 + 107*x^5 + 4*x^6 + 25000))/(x + 5)^5 + (12*x*log(x)^2* (146*x + 30*x^2 + 2*x^3 + 245))/(x + 5)^3)/log(x)^2 - 480*log(x) - 24*x + ((12*x*log(x)^2*(970*x + 304*x^2 + 40*x^3 + 2*x^4 + 1225))/(x + 5)^4 - (6* (37750*x + 22320*x^2 + 6876*x^3 + 1179*x^4 + 107*x^5 + 4*x^6 + 25000))/(x + 5)^5 + (12*x*log(x)*(36100*x + 18090*x^2 + 4914*x^3 + 748*x^4 + 60*x^5 + 2*x^6 + 31875))/(x + 5)^6)/log(x) + 6*x^2 + (27300*x^2 + 12420*x^3 + 1812 *x^4 + 72*x^5)/(18750*x + 9375*x^2 + 2500*x^3 + 375*x^4 + 30*x^5 + x^6 + 1 5625) + (log(x)*(225300*x + 60360*x^2 + 5952*x^3 - 24*x^5 + 300000))/(500* x + 150*x^2 + 20*x^3 + x^4 + 625)
Time = 0.23 (sec) , antiderivative size = 134, normalized size of antiderivative = 5.83 \[ \int \frac {-600000-588000 x-232860 x^2-46572 x^3-4704 x^4-192 x^5+\left (300000+441000 x+265560 x^2+82968 x^3+14244 x^4+1284 x^5+48 x^6\right ) \log (x)+\left (-147000 x-146400 x^2-58920 x^3-11904 x^4-1200 x^5-48 x^6\right ) \log ^2(x)+\left (75000 x+112500 x^2+67500 x^3+21000 x^4+3600 x^5+324 x^6+12 x^7\right ) \log ^3(x)}{\left (3125 x+3125 x^2+1250 x^3+250 x^4+25 x^5+x^6\right ) \log ^3(x)} \, dx=\frac {6 \mathrm {log}\left (x \right )^{2} x^{6}+144 \mathrm {log}\left (x \right )^{2} x^{5}+1380 \mathrm {log}\left (x \right )^{2} x^{4}+6600 \mathrm {log}\left (x \right )^{2} x^{3}+15750 \mathrm {log}\left (x \right )^{2} x^{2}+15000 \mathrm {log}\left (x \right )^{2} x -48 \,\mathrm {log}\left (x \right ) x^{5}-1044 \,\mathrm {log}\left (x \right ) x^{4}-8976 \,\mathrm {log}\left (x \right ) x^{3}-37860 \,\mathrm {log}\left (x \right ) x^{2}-77400 \,\mathrm {log}\left (x \right ) x -60000 \,\mathrm {log}\left (x \right )+96 x^{4}+1872 x^{3}+13926 x^{2}+46800 x +60000}{\mathrm {log}\left (x \right )^{2} \left (x^{4}+20 x^{3}+150 x^{2}+500 x +625\right )} \] Input:
int(((12*x^7+324*x^6+3600*x^5+21000*x^4+67500*x^3+112500*x^2+75000*x)*log( x)^3+(-48*x^6-1200*x^5-11904*x^4-58920*x^3-146400*x^2-147000*x)*log(x)^2+( 48*x^6+1284*x^5+14244*x^4+82968*x^3+265560*x^2+441000*x+300000)*log(x)-192 *x^5-4704*x^4-46572*x^3-232860*x^2-588000*x-600000)/(x^6+25*x^5+250*x^4+12 50*x^3+3125*x^2+3125*x)/log(x)^3,x)
Output:
(6*(log(x)**2*x**6 + 24*log(x)**2*x**5 + 230*log(x)**2*x**4 + 1100*log(x)* *2*x**3 + 2625*log(x)**2*x**2 + 2500*log(x)**2*x - 8*log(x)*x**5 - 174*log (x)*x**4 - 1496*log(x)*x**3 - 6310*log(x)*x**2 - 12900*log(x)*x - 10000*lo g(x) + 16*x**4 + 312*x**3 + 2321*x**2 + 7800*x + 10000))/(log(x)**2*(x**4 + 20*x**3 + 150*x**2 + 500*x + 625))