Integrand size = 147, antiderivative size = 28 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=1-2 x-\frac {4}{\left (-4-\frac {5 x}{3}-\frac {e^2 x}{2 \log (x)}\right )^2} \] Output:
1-2*x-4/(-5/3*x-1/2*exp(2)/ln(x)*x-4)^2
Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(28)=56\).
Time = 0.04 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.32 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=-\frac {2 \left (9 e^4 x^3+12 e^2 x^2 (12+5 x) \log (x)+4 \left (18+144 x+120 x^2+25 x^3\right ) \log ^2(x)\right )}{\left (3 e^2 x+2 (12+5 x) \log (x)\right )^2} \] Input:
Integrate[(-54*E^6*x^3 + (-864*E^2 + E^4*(-1296*x^2 - 540*x^3))*Log[x] + E ^2*(864 - 10368*x - 8640*x^2 - 1800*x^3)*Log[x]^2 + (-24768 - 34560*x - 14 400*x^2 - 2000*x^3)*Log[x]^3)/(27*E^6*x^3 + E^4*(648*x^2 + 270*x^3)*Log[x] + E^2*(5184*x + 4320*x^2 + 900*x^3)*Log[x]^2 + (13824 + 17280*x + 7200*x^ 2 + 1000*x^3)*Log[x]^3),x]
Output:
(-2*(9*E^4*x^3 + 12*E^2*x^2*(12 + 5*x)*Log[x] + 4*(18 + 144*x + 120*x^2 + 25*x^3)*Log[x]^2))/(3*E^2*x + 2*(12 + 5*x)*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.
| \(\displaystyle \int \frac {-54 e^6 x^3+\left (-2000 x^3-14400 x^2-34560 x-24768\right ) \log ^3(x)+e^2 \left (-1800 x^3-8640 x^2-10368 x+864\right ) \log ^2(x)+\left (e^4 \left (-540 x^3-1296 x^2\right )-864 e^2\right ) \log (x)}{27 e^6 x^3+\left (1000 x^3+7200 x^2+17280 x+13824\right ) \log ^3(x)+e^2 \left (900 x^3+4320 x^2+5184 x\right ) \log ^2(x)+e^4 \left (270 x^3+648 x^2\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-54 e^6 x^3+\left (-2000 x^3-14400 x^2-34560 x-24768\right ) \log ^3(x)+e^2 \left (-1800 x^3-8640 x^2-10368 x+864\right ) \log ^2(x)+\left (e^4 \left (-540 x^3-1296 x^2\right )-864 e^2\right ) \log (x)}{\left (3 e^2 x+10 x \log (x)+24 \log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {216 e^2 \left (-5 \left (10-3 e^2\right ) x^2-24 \left (10+3 e^2\right ) x-288\right )}{(5 x+12)^3 \left (3 e^2 x+10 x \log (x)+24 \log (x)\right )^2}+\frac {1296 e^4 x \left (25 x^2+6 \left (20+3 e^2\right ) x+144\right )}{(5 x+12)^3 \left (3 e^2 x+10 x \log (x)+24 \log (x)\right )^3}-\frac {2 \left (125 x^3+900 x^2+2160 x+1548\right )}{(5 x+12)^3}-\frac {432 e^2 (5 x-6)}{(5 x+12)^3 \left (3 e^2 x+10 x \log (x)+24 \log (x)\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1296}{5} e^4 \int \frac {1}{\left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^3}dx+\frac {3359232}{25} e^6 \int \frac {1}{(5 x+12)^3 \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^3}dx-\frac {559872}{25} e^6 \int \frac {1}{(5 x+12)^2 \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^3}dx-\frac {7776}{25} e^4 \left (10-3 e^2\right ) \int \frac {1}{(5 x+12) \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^3}dx+\frac {279936}{5} e^4 \int \frac {1}{(5 x+12)^3 \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^2}dx-\frac {31104}{5} e^4 \int \frac {1}{(5 x+12)^2 \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^2}dx-\frac {216}{5} e^2 \left (10-3 e^2\right ) \int \frac {1}{(5 x+12) \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )^2}dx+7776 e^2 \int \frac {1}{(5 x+12)^3 \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )}dx-432 e^2 \int \frac {1}{(5 x+12)^2 \left (10 \log (x) x+3 e^2 x+24 \log (x)\right )}dx-2 x-\frac {36}{(5 x+12)^2}\) |
Input:
Int[(-54*E^6*x^3 + (-864*E^2 + E^4*(-1296*x^2 - 540*x^3))*Log[x] + E^2*(86 4 - 10368*x - 8640*x^2 - 1800*x^3)*Log[x]^2 + (-24768 - 34560*x - 14400*x^ 2 - 2000*x^3)*Log[x]^3)/(27*E^6*x^3 + E^4*(648*x^2 + 270*x^3)*Log[x] + E^2 *(5184*x + 4320*x^2 + 900*x^3)*Log[x]^2 + (13824 + 17280*x + 7200*x^2 + 10 00*x^3)*Log[x]^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs. \(2(23)=46\).
Time = 11.94 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.86
| method | result | size |
| risch | \(-\frac {2 \left (25 x^{3}+120 x^{2}+144 x +18\right )}{25 x^{2}+120 x +144}+\frac {108 \left (3 \,{\mathrm e}^{2} x +20 x \ln \left (x \right )+48 \ln \left (x \right )\right ) {\mathrm e}^{2} x}{\left (25 x^{2}+120 x +144\right ) \left (10 x \ln \left (x \right )+3 \,{\mathrm e}^{2} x +24 \ln \left (x \right )\right )^{2}}\) | \(80\) |
| norman | \(\frac {\frac {26928 \ln \left (x \right )^{2}}{5}+\frac {432 x^{2} {\mathrm e}^{4}}{5}+3456 x \ln \left (x \right )^{2}+\frac {6912 x \,{\mathrm e}^{2} \ln \left (x \right )}{5}+288 \ln \left (x \right ) {\mathrm e}^{2} x^{2}-18 x^{3} {\mathrm e}^{4}-200 x^{3} \ln \left (x \right )^{2}-120 \ln \left (x \right ) {\mathrm e}^{2} x^{3}}{\left (10 x \ln \left (x \right )+3 \,{\mathrm e}^{2} x +24 \ln \left (x \right )\right )^{2}}\) | \(85\) |
| default | \(-\frac {2 \left (-\frac {13464 \ln \left (x \right )^{2}}{5}-\frac {216 x^{2} {\mathrm e}^{4}}{5}-1728 x \ln \left (x \right )^{2}-\frac {3456 x \,{\mathrm e}^{2} \ln \left (x \right )}{5}-144 \ln \left (x \right ) {\mathrm e}^{2} x^{2}+100 x^{3} \ln \left (x \right )^{2}+9 x^{3} {\mathrm e}^{4}+60 \ln \left (x \right ) {\mathrm e}^{2} x^{3}\right )}{\left (10 x \ln \left (x \right )+3 \,{\mathrm e}^{2} x +24 \ln \left (x \right )\right )^{2}}\) | \(86\) |
| parallelrisch | \(\frac {28800 \ln \left (x \right ) {\mathrm e}^{2} x^{2}+138240 x \,{\mathrm e}^{2} \ln \left (x \right )-20000 x^{3} \ln \left (x \right )^{2}+345600 x \ln \left (x \right )^{2}-1800 x^{3} {\mathrm e}^{4}+8640 x^{2} {\mathrm e}^{4}+538560 \ln \left (x \right )^{2}-12000 \ln \left (x \right ) {\mathrm e}^{2} x^{3}}{900 x^{2} {\mathrm e}^{4}+6000 \ln \left (x \right ) {\mathrm e}^{2} x^{2}+10000 x^{2} \ln \left (x \right )^{2}+14400 x \,{\mathrm e}^{2} \ln \left (x \right )+48000 x \ln \left (x \right )^{2}+57600 \ln \left (x \right )^{2}}\) | \(119\) |
Input:
int(((-2000*x^3-14400*x^2-34560*x-24768)*ln(x)^3+(-1800*x^3-8640*x^2-10368 *x+864)*exp(2)*ln(x)^2+((-540*x^3-1296*x^2)*exp(2)^2-864*exp(2))*ln(x)-54* x^3*exp(2)^3)/((1000*x^3+7200*x^2+17280*x+13824)*ln(x)^3+(900*x^3+4320*x^2 +5184*x)*exp(2)*ln(x)^2+(270*x^3+648*x^2)*exp(2)^2*ln(x)+27*x^3*exp(2)^3), x,method=_RETURNVERBOSE)
Output:
-2*(25*x^3+120*x^2+144*x+18)/(25*x^2+120*x+144)+108*(3*exp(2)*x+20*x*ln(x) +48*ln(x))*exp(2)*x/(25*x^2+120*x+144)/(10*x*ln(x)+3*exp(2)*x+24*ln(x))^2
Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (23) = 46\).
Time = 0.10 (sec) , antiderivative size = 89, normalized size of antiderivative = 3.18 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=-\frac {2 \, {\left (9 \, x^{3} e^{4} + 12 \, {\left (5 \, x^{3} + 12 \, x^{2}\right )} e^{2} \log \left (x\right ) + 4 \, {\left (25 \, x^{3} + 120 \, x^{2} + 144 \, x + 18\right )} \log \left (x\right )^{2}\right )}}{9 \, x^{2} e^{4} + 12 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{2} \log \left (x\right ) + 4 \, {\left (25 \, x^{2} + 120 \, x + 144\right )} \log \left (x\right )^{2}} \] Input:
integrate(((-2000*x^3-14400*x^2-34560*x-24768)*log(x)^3+(-1800*x^3-8640*x^ 2-10368*x+864)*exp(2)*log(x)^2+((-540*x^3-1296*x^2)*exp(2)^2-864*exp(2))*l og(x)-54*x^3*exp(2)^3)/((1000*x^3+7200*x^2+17280*x+13824)*log(x)^3+(900*x^ 3+4320*x^2+5184*x)*exp(2)*log(x)^2+(270*x^3+648*x^2)*exp(2)^2*log(x)+27*x^ 3*exp(2)^3),x, algorithm="fricas")
Output:
-2*(9*x^3*e^4 + 12*(5*x^3 + 12*x^2)*e^2*log(x) + 4*(25*x^3 + 120*x^2 + 144 *x + 18)*log(x)^2)/(9*x^2*e^4 + 12*(5*x^2 + 12*x)*e^2*log(x) + 4*(25*x^2 + 120*x + 144)*log(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (26) = 52\).
Time = 0.29 (sec) , antiderivative size = 128, normalized size of antiderivative = 4.57 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=- 2 x + \frac {324 x^{2} e^{4} + \left (2160 x^{2} e^{2} + 5184 x e^{2}\right ) \log {\left (x \right )}}{225 x^{4} e^{4} + 1080 x^{3} e^{4} + 1296 x^{2} e^{4} + \left (1500 x^{4} e^{2} + 10800 x^{3} e^{2} + 25920 x^{2} e^{2} + 20736 x e^{2}\right ) \log {\left (x \right )} + \left (2500 x^{4} + 24000 x^{3} + 86400 x^{2} + 138240 x + 82944\right ) \log {\left (x \right )}^{2}} - \frac {36}{25 x^{2} + 120 x + 144} \] Input:
integrate(((-2000*x**3-14400*x**2-34560*x-24768)*ln(x)**3+(-1800*x**3-8640 *x**2-10368*x+864)*exp(2)*ln(x)**2+((-540*x**3-1296*x**2)*exp(2)**2-864*ex p(2))*ln(x)-54*x**3*exp(2)**3)/((1000*x**3+7200*x**2+17280*x+13824)*ln(x)* *3+(900*x**3+4320*x**2+5184*x)*exp(2)*ln(x)**2+(270*x**3+648*x**2)*exp(2)* *2*ln(x)+27*x**3*exp(2)**3),x)
Output:
-2*x + (324*x**2*exp(4) + (2160*x**2*exp(2) + 5184*x*exp(2))*log(x))/(225* x**4*exp(4) + 1080*x**3*exp(4) + 1296*x**2*exp(4) + (1500*x**4*exp(2) + 10 800*x**3*exp(2) + 25920*x**2*exp(2) + 20736*x*exp(2))*log(x) + (2500*x**4 + 24000*x**3 + 86400*x**2 + 138240*x + 82944)*log(x)**2) - 36/(25*x**2 + 1 20*x + 144)
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (23) = 46\).
Time = 0.10 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.32 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=-\frac {2 \, {\left (9 \, x^{3} e^{4} + 4 \, {\left (25 \, x^{3} + 120 \, x^{2} + 144 \, x + 18\right )} \log \left (x\right )^{2} + 12 \, {\left (5 \, x^{3} e^{2} + 12 \, x^{2} e^{2}\right )} \log \left (x\right )\right )}}{9 \, x^{2} e^{4} + 4 \, {\left (25 \, x^{2} + 120 \, x + 144\right )} \log \left (x\right )^{2} + 12 \, {\left (5 \, x^{2} e^{2} + 12 \, x e^{2}\right )} \log \left (x\right )} \] Input:
integrate(((-2000*x^3-14400*x^2-34560*x-24768)*log(x)^3+(-1800*x^3-8640*x^ 2-10368*x+864)*exp(2)*log(x)^2+((-540*x^3-1296*x^2)*exp(2)^2-864*exp(2))*l og(x)-54*x^3*exp(2)^3)/((1000*x^3+7200*x^2+17280*x+13824)*log(x)^3+(900*x^ 3+4320*x^2+5184*x)*exp(2)*log(x)^2+(270*x^3+648*x^2)*exp(2)^2*log(x)+27*x^ 3*exp(2)^3),x, algorithm="maxima")
Output:
-2*(9*x^3*e^4 + 4*(25*x^3 + 120*x^2 + 144*x + 18)*log(x)^2 + 12*(5*x^3*e^2 + 12*x^2*e^2)*log(x))/(9*x^2*e^4 + 4*(25*x^2 + 120*x + 144)*log(x)^2 + 12 *(5*x^2*e^2 + 12*x*e^2)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (23) = 46\).
Time = 0.23 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.82 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=-\frac {2 \, {\left (60 \, x^{3} e^{2} \log \left (x\right ) + 100 \, x^{3} \log \left (x\right )^{2} + 9 \, x^{3} e^{4} + 144 \, x^{2} e^{2} \log \left (x\right ) + 480 \, x^{2} \log \left (x\right )^{2} + 576 \, x \log \left (x\right )^{2} + 72 \, \log \left (x\right )^{2}\right )}}{60 \, x^{2} e^{2} \log \left (x\right ) + 100 \, x^{2} \log \left (x\right )^{2} + 9 \, x^{2} e^{4} + 144 \, x e^{2} \log \left (x\right ) + 480 \, x \log \left (x\right )^{2} + 576 \, \log \left (x\right )^{2}} \] Input:
integrate(((-2000*x^3-14400*x^2-34560*x-24768)*log(x)^3+(-1800*x^3-8640*x^ 2-10368*x+864)*exp(2)*log(x)^2+((-540*x^3-1296*x^2)*exp(2)^2-864*exp(2))*l og(x)-54*x^3*exp(2)^3)/((1000*x^3+7200*x^2+17280*x+13824)*log(x)^3+(900*x^ 3+4320*x^2+5184*x)*exp(2)*log(x)^2+(270*x^3+648*x^2)*exp(2)^2*log(x)+27*x^ 3*exp(2)^3),x, algorithm="giac")
Output:
-2*(60*x^3*e^2*log(x) + 100*x^3*log(x)^2 + 9*x^3*e^4 + 144*x^2*e^2*log(x) + 480*x^2*log(x)^2 + 576*x*log(x)^2 + 72*log(x)^2)/(60*x^2*e^2*log(x) + 10 0*x^2*log(x)^2 + 9*x^2*e^4 + 144*x*e^2*log(x) + 480*x*log(x)^2 + 576*log(x )^2)
Timed out. \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=\int -\frac {{\ln \left (x\right )}^3\,\left (2000\,x^3+14400\,x^2+34560\,x+24768\right )+54\,x^3\,{\mathrm {e}}^6+\ln \left (x\right )\,\left (864\,{\mathrm {e}}^2+{\mathrm {e}}^4\,\left (540\,x^3+1296\,x^2\right )\right )+{\mathrm {e}}^2\,{\ln \left (x\right )}^2\,\left (1800\,x^3+8640\,x^2+10368\,x-864\right )}{{\ln \left (x\right )}^3\,\left (1000\,x^3+7200\,x^2+17280\,x+13824\right )+27\,x^3\,{\mathrm {e}}^6+{\mathrm {e}}^4\,\ln \left (x\right )\,\left (270\,x^3+648\,x^2\right )+{\mathrm {e}}^2\,{\ln \left (x\right )}^2\,\left (900\,x^3+4320\,x^2+5184\,x\right )} \,d x \] Input:
int(-(log(x)^3*(34560*x + 14400*x^2 + 2000*x^3 + 24768) + 54*x^3*exp(6) + log(x)*(864*exp(2) + exp(4)*(1296*x^2 + 540*x^3)) + exp(2)*log(x)^2*(10368 *x + 8640*x^2 + 1800*x^3 - 864))/(log(x)^3*(17280*x + 7200*x^2 + 1000*x^3 + 13824) + 27*x^3*exp(6) + exp(4)*log(x)*(648*x^2 + 270*x^3) + exp(2)*log( x)^2*(5184*x + 4320*x^2 + 900*x^3)),x)
Output:
int(-(log(x)^3*(34560*x + 14400*x^2 + 2000*x^3 + 24768) + 54*x^3*exp(6) + log(x)*(864*exp(2) + exp(4)*(1296*x^2 + 540*x^3)) + exp(2)*log(x)^2*(10368 *x + 8640*x^2 + 1800*x^3 - 864))/(log(x)^3*(17280*x + 7200*x^2 + 1000*x^3 + 13824) + 27*x^3*exp(6) + exp(4)*log(x)*(648*x^2 + 270*x^3) + exp(2)*log( x)^2*(5184*x + 4320*x^2 + 900*x^3)), x)
Time = 0.21 (sec) , antiderivative size = 113, normalized size of antiderivative = 4.04 \[ \int \frac {-54 e^6 x^3+\left (-864 e^2+e^4 \left (-1296 x^2-540 x^3\right )\right ) \log (x)+e^2 \left (864-10368 x-8640 x^2-1800 x^3\right ) \log ^2(x)+\left (-24768-34560 x-14400 x^2-2000 x^3\right ) \log ^3(x)}{27 e^6 x^3+e^4 \left (648 x^2+270 x^3\right ) \log (x)+e^2 \left (5184 x+4320 x^2+900 x^3\right ) \log ^2(x)+\left (13824+17280 x+7200 x^2+1000 x^3\right ) \log ^3(x)} \, dx=\frac {-200 \mathrm {log}\left (x \right )^{2} x^{3}-960 \mathrm {log}\left (x \right )^{2} x^{2}-1152 \mathrm {log}\left (x \right )^{2} x -144 \mathrm {log}\left (x \right )^{2}-120 \,\mathrm {log}\left (x \right ) e^{2} x^{3}-288 \,\mathrm {log}\left (x \right ) e^{2} x^{2}-18 e^{4} x^{3}}{100 \mathrm {log}\left (x \right )^{2} x^{2}+480 \mathrm {log}\left (x \right )^{2} x +576 \mathrm {log}\left (x \right )^{2}+60 \,\mathrm {log}\left (x \right ) e^{2} x^{2}+144 \,\mathrm {log}\left (x \right ) e^{2} x +9 e^{4} x^{2}} \] Input:
int(((-2000*x^3-14400*x^2-34560*x-24768)*log(x)^3+(-1800*x^3-8640*x^2-1036 8*x+864)*exp(2)*log(x)^2+((-540*x^3-1296*x^2)*exp(2)^2-864*exp(2))*log(x)- 54*x^3*exp(2)^3)/((1000*x^3+7200*x^2+17280*x+13824)*log(x)^3+(900*x^3+4320 *x^2+5184*x)*exp(2)*log(x)^2+(270*x^3+648*x^2)*exp(2)^2*log(x)+27*x^3*exp( 2)^3),x)
Output:
(2*( - 100*log(x)**2*x**3 - 480*log(x)**2*x**2 - 576*log(x)**2*x - 72*log( x)**2 - 60*log(x)*e**2*x**3 - 144*log(x)*e**2*x**2 - 9*e**4*x**3))/(100*lo g(x)**2*x**2 + 480*log(x)**2*x + 576*log(x)**2 + 60*log(x)*e**2*x**2 + 144 *log(x)*e**2*x + 9*e**4*x**2)