Integrand size = 280, antiderivative size = 23 \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=2 \left (-x+\frac {3 e^4}{x (3+2 x+\log (x))^4}\right ) \]
Time = 0.10 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=-2 \left (x-\frac {3 e^4}{x (3+2 x+\log (x))^4}\right ) \]
Integrate[(E^4*(-42 - 60*x) - 486*x^2 - 1620*x^3 - 2160*x^4 - 1440*x^5 - 4 80*x^6 - 64*x^7 + (-6*E^4 - 810*x^2 - 2160*x^3 - 2160*x^4 - 960*x^5 - 160* x^6)*Log[x] + (-540*x^2 - 1080*x^3 - 720*x^4 - 160*x^5)*Log[x]^2 + (-180*x ^2 - 240*x^3 - 80*x^4)*Log[x]^3 + (-30*x^2 - 20*x^3)*Log[x]^4 - 2*x^2*Log[ x]^5)/(243*x^2 + 810*x^3 + 1080*x^4 + 720*x^5 + 240*x^6 + 32*x^7 + (405*x^ 2 + 1080*x^3 + 1080*x^4 + 480*x^5 + 80*x^6)*Log[x] + (270*x^2 + 540*x^3 + 360*x^4 + 80*x^5)*Log[x]^2 + (90*x^2 + 120*x^3 + 40*x^4)*Log[x]^3 + (15*x^ 2 + 10*x^3)*Log[x]^4 + x^2*Log[x]^5),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.
| \(\displaystyle \int \frac {-64 x^7-480 x^6-1440 x^5-2160 x^4-1620 x^3-486 x^2-2 x^2 \log ^5(x)+\left (-20 x^3-30 x^2\right ) \log ^4(x)+\left (-80 x^4-240 x^3-180 x^2\right ) \log ^3(x)+\left (-160 x^5-720 x^4-1080 x^3-540 x^2\right ) \log ^2(x)+\left (-160 x^6-960 x^5-2160 x^4-2160 x^3-810 x^2-6 e^4\right ) \log (x)+e^4 (-60 x-42)}{32 x^7+240 x^6+720 x^5+1080 x^4+810 x^3+243 x^2+x^2 \log ^5(x)+\left (10 x^3+15 x^2\right ) \log ^4(x)+\left (40 x^4+120 x^3+90 x^2\right ) \log ^3(x)+\left (80 x^5+360 x^4+540 x^3+270 x^2\right ) \log ^2(x)+\left (80 x^6+480 x^5+1080 x^4+1080 x^3+405 x^2\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (-x^2 (2 x+3)^5-x^2 \log ^5(x)-5 x^2 (2 x+3) \log ^4(x)-10 x^2 (2 x+3)^2 \log ^3(x)-10 x^2 (2 x+3)^3 \log ^2(x)-\left (5 x^2 (2 x+3)^4+3 e^4\right ) \log (x)-3 e^4 (10 x+7)\right )}{x^2 (2 x+\log (x)+3)^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {x^2 (2 x+3)^5+10 x^2 \log ^2(x) (2 x+3)^3+10 x^2 \log ^3(x) (2 x+3)^2+5 x^2 \log ^4(x) (2 x+3)+x^2 \log ^5(x)+3 e^4 (10 x+7)+\left (5 x^2 (2 x+3)^4+3 e^4\right ) \log (x)}{x^2 (2 x+\log (x)+3)^5}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {x^2 (2 x+3)^5+10 x^2 \log ^2(x) (2 x+3)^3+10 x^2 \log ^3(x) (2 x+3)^2+5 x^2 \log ^4(x) (2 x+3)+x^2 \log ^5(x)+3 e^4 (10 x+7)+\left (5 x^2 (2 x+3)^4+3 e^4\right ) \log (x)}{x^2 (2 x+\log (x)+3)^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {12 e^4 (2 x+1)}{x^2 (2 x+\log (x)+3)^5}+\frac {3 e^4}{x^2 (2 x+\log (x)+3)^4}+1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (12 e^4 \int \frac {1}{x^2 (2 x+\log (x)+3)^5}dx+3 e^4 \int \frac {1}{x^2 (2 x+\log (x)+3)^4}dx+24 e^4 \int \frac {1}{x (2 x+\log (x)+3)^5}dx+x\right )\) |
Int[(E^4*(-42 - 60*x) - 486*x^2 - 1620*x^3 - 2160*x^4 - 1440*x^5 - 480*x^6 - 64*x^7 + (-6*E^4 - 810*x^2 - 2160*x^3 - 2160*x^4 - 960*x^5 - 160*x^6)*L og[x] + (-540*x^2 - 1080*x^3 - 720*x^4 - 160*x^5)*Log[x]^2 + (-180*x^2 - 2 40*x^3 - 80*x^4)*Log[x]^3 + (-30*x^2 - 20*x^3)*Log[x]^4 - 2*x^2*Log[x]^5)/ (243*x^2 + 810*x^3 + 1080*x^4 + 720*x^5 + 240*x^6 + 32*x^7 + (405*x^2 + 10 80*x^3 + 1080*x^4 + 480*x^5 + 80*x^6)*Log[x] + (270*x^2 + 540*x^3 + 360*x^ 4 + 80*x^5)*Log[x]^2 + (90*x^2 + 120*x^3 + 40*x^4)*Log[x]^3 + (15*x^2 + 10 *x^3)*Log[x]^4 + x^2*Log[x]^5),x]
3.19.51.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 0.38 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91
| method | result | size |
| risch | \(\frac {6 \,{\mathrm e}^{4}}{x \left (\ln \left (x \right )+3+2 x \right )^{4}}-2 x\) | \(21\) |
| default | \(-2 x +\frac {6 \,{\mathrm e}^{-\ln \left (x \right )+4}}{\left (3+\ln \left (x \right )\right )^{4}}-\frac {48 \,{\mathrm e}^{4} \left (\ln \left (x \right )^{3}+3 x \ln \left (x \right )^{2}+4 x^{2} \ln \left (x \right )+2 x^{3}+9 \ln \left (x \right )^{2}+18 x \ln \left (x \right )+12 x^{2}+27 \ln \left (x \right )+27 x +27\right )}{\left (\ln \left (x \right )^{2}+6 \ln \left (x \right )+9\right )^{2} \left (\ln \left (x \right )+3+2 x \right )^{4}}\) | \(93\) |
| parallelrisch | \(\frac {-16 x^{3} \ln \left (x \right )^{3}-64 x^{5} \ln \left (x \right )-48 x^{4} \ln \left (x \right )^{2}-288 x^{4} \ln \left (x \right )-24 x^{2} \ln \left (x \right )^{3}-144 x^{3} \ln \left (x \right )^{2}-108 x^{2} \ln \left (x \right )^{2}-2 x^{2} \ln \left (x \right )^{4}+6 \,{\mathrm e}^{4}-32 x^{6}-192 x^{5}-432 x^{4}-432 x^{3}-162 x^{2}-432 x^{3} \ln \left (x \right )-216 x^{2} \ln \left (x \right )}{x \left (16 x^{4}+32 x^{3} \ln \left (x \right )+24 x^{2} \ln \left (x \right )^{2}+8 x \ln \left (x \right )^{3}+\ln \left (x \right )^{4}+96 x^{3}+144 x^{2} \ln \left (x \right )+72 x \ln \left (x \right )^{2}+12 \ln \left (x \right )^{3}+216 x^{2}+216 x \ln \left (x \right )+54 \ln \left (x \right )^{2}+216 x +108 \ln \left (x \right )+81\right )}\) | \(203\) |
int((-2*x^2*ln(x)^5+(-20*x^3-30*x^2)*ln(x)^4+(-80*x^4-240*x^3-180*x^2)*ln( x)^3+(-160*x^5-720*x^4-1080*x^3-540*x^2)*ln(x)^2+(-6*exp(2)^2-160*x^6-960* x^5-2160*x^4-2160*x^3-810*x^2)*ln(x)+(-60*x-42)*exp(2)^2-64*x^7-480*x^6-14 40*x^5-2160*x^4-1620*x^3-486*x^2)/(x^2*ln(x)^5+(10*x^3+15*x^2)*ln(x)^4+(40 *x^4+120*x^3+90*x^2)*ln(x)^3+(80*x^5+360*x^4+540*x^3+270*x^2)*ln(x)^2+(80* x^6+480*x^5+1080*x^4+1080*x^3+405*x^2)*ln(x)+32*x^7+240*x^6+720*x^5+1080*x ^4+810*x^3+243*x^2),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 194 vs. \(2 (20) = 40\).
Time = 0.26 (sec) , antiderivative size = 194, normalized size of antiderivative = 8.43 \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=-\frac {2 \, {\left (16 \, x^{6} + x^{2} \log \left (x\right )^{4} + 96 \, x^{5} + 216 \, x^{4} + 4 \, {\left (2 \, x^{3} + 3 \, x^{2}\right )} \log \left (x\right )^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2}\right )} \log \left (x\right )^{2} + 81 \, x^{2} + 4 \, {\left (8 \, x^{5} + 36 \, x^{4} + 54 \, x^{3} + 27 \, x^{2}\right )} \log \left (x\right ) - 3 \, e^{4}\right )}}{16 \, x^{5} + x \log \left (x\right )^{4} + 96 \, x^{4} + 4 \, {\left (2 \, x^{2} + 3 \, x\right )} \log \left (x\right )^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{3} + 12 \, x^{2} + 9 \, x\right )} \log \left (x\right )^{2} + 216 \, x^{2} + 4 \, {\left (8 \, x^{4} + 36 \, x^{3} + 54 \, x^{2} + 27 \, x\right )} \log \left (x\right ) + 81 \, x} \]
integrate((-2*x^2*log(x)^5+(-20*x^3-30*x^2)*log(x)^4+(-80*x^4-240*x^3-180* x^2)*log(x)^3+(-160*x^5-720*x^4-1080*x^3-540*x^2)*log(x)^2+(-6*exp(2)^2-16 0*x^6-960*x^5-2160*x^4-2160*x^3-810*x^2)*log(x)+(-60*x-42)*exp(2)^2-64*x^7 -480*x^6-1440*x^5-2160*x^4-1620*x^3-486*x^2)/(x^2*log(x)^5+(10*x^3+15*x^2) *log(x)^4+(40*x^4+120*x^3+90*x^2)*log(x)^3+(80*x^5+360*x^4+540*x^3+270*x^2 )*log(x)^2+(80*x^6+480*x^5+1080*x^4+1080*x^3+405*x^2)*log(x)+32*x^7+240*x^ 6+720*x^5+1080*x^4+810*x^3+243*x^2),x, algorithm=\
-2*(16*x^6 + x^2*log(x)^4 + 96*x^5 + 216*x^4 + 4*(2*x^3 + 3*x^2)*log(x)^3 + 216*x^3 + 6*(4*x^4 + 12*x^3 + 9*x^2)*log(x)^2 + 81*x^2 + 4*(8*x^5 + 36*x ^4 + 54*x^3 + 27*x^2)*log(x) - 3*e^4)/(16*x^5 + x*log(x)^4 + 96*x^4 + 4*(2 *x^2 + 3*x)*log(x)^3 + 216*x^3 + 6*(4*x^3 + 12*x^2 + 9*x)*log(x)^2 + 216*x ^2 + 4*(8*x^4 + 36*x^3 + 54*x^2 + 27*x)*log(x) + 81*x)
Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (19) = 38\).
Time = 0.15 (sec) , antiderivative size = 92, normalized size of antiderivative = 4.00 \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=- 2 x + \frac {6 e^{4}}{16 x^{5} + 96 x^{4} + 216 x^{3} + 216 x^{2} + x \log {\left (x \right )}^{4} + 81 x + \left (8 x^{2} + 12 x\right ) \log {\left (x \right )}^{3} + \left (24 x^{3} + 72 x^{2} + 54 x\right ) \log {\left (x \right )}^{2} + \left (32 x^{4} + 144 x^{3} + 216 x^{2} + 108 x\right ) \log {\left (x \right )}} \]
integrate((-2*x**2*ln(x)**5+(-20*x**3-30*x**2)*ln(x)**4+(-80*x**4-240*x**3 -180*x**2)*ln(x)**3+(-160*x**5-720*x**4-1080*x**3-540*x**2)*ln(x)**2+(-6*e xp(2)**2-160*x**6-960*x**5-2160*x**4-2160*x**3-810*x**2)*ln(x)+(-60*x-42)* exp(2)**2-64*x**7-480*x**6-1440*x**5-2160*x**4-1620*x**3-486*x**2)/(x**2*l n(x)**5+(10*x**3+15*x**2)*ln(x)**4+(40*x**4+120*x**3+90*x**2)*ln(x)**3+(80 *x**5+360*x**4+540*x**3+270*x**2)*ln(x)**2+(80*x**6+480*x**5+1080*x**4+108 0*x**3+405*x**2)*ln(x)+32*x**7+240*x**6+720*x**5+1080*x**4+810*x**3+243*x* *2),x)
-2*x + 6*exp(4)/(16*x**5 + 96*x**4 + 216*x**3 + 216*x**2 + x*log(x)**4 + 8 1*x + (8*x**2 + 12*x)*log(x)**3 + (24*x**3 + 72*x**2 + 54*x)*log(x)**2 + ( 32*x**4 + 144*x**3 + 216*x**2 + 108*x)*log(x))
Leaf count of result is larger than twice the leaf count of optimal. 194 vs. \(2 (20) = 40\).
Time = 0.25 (sec) , antiderivative size = 194, normalized size of antiderivative = 8.43 \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=-\frac {2 \, {\left (16 \, x^{6} + x^{2} \log \left (x\right )^{4} + 96 \, x^{5} + 216 \, x^{4} + 4 \, {\left (2 \, x^{3} + 3 \, x^{2}\right )} \log \left (x\right )^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2}\right )} \log \left (x\right )^{2} + 81 \, x^{2} + 4 \, {\left (8 \, x^{5} + 36 \, x^{4} + 54 \, x^{3} + 27 \, x^{2}\right )} \log \left (x\right ) - 3 \, e^{4}\right )}}{16 \, x^{5} + x \log \left (x\right )^{4} + 96 \, x^{4} + 4 \, {\left (2 \, x^{2} + 3 \, x\right )} \log \left (x\right )^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{3} + 12 \, x^{2} + 9 \, x\right )} \log \left (x\right )^{2} + 216 \, x^{2} + 4 \, {\left (8 \, x^{4} + 36 \, x^{3} + 54 \, x^{2} + 27 \, x\right )} \log \left (x\right ) + 81 \, x} \]
integrate((-2*x^2*log(x)^5+(-20*x^3-30*x^2)*log(x)^4+(-80*x^4-240*x^3-180* x^2)*log(x)^3+(-160*x^5-720*x^4-1080*x^3-540*x^2)*log(x)^2+(-6*exp(2)^2-16 0*x^6-960*x^5-2160*x^4-2160*x^3-810*x^2)*log(x)+(-60*x-42)*exp(2)^2-64*x^7 -480*x^6-1440*x^5-2160*x^4-1620*x^3-486*x^2)/(x^2*log(x)^5+(10*x^3+15*x^2) *log(x)^4+(40*x^4+120*x^3+90*x^2)*log(x)^3+(80*x^5+360*x^4+540*x^3+270*x^2 )*log(x)^2+(80*x^6+480*x^5+1080*x^4+1080*x^3+405*x^2)*log(x)+32*x^7+240*x^ 6+720*x^5+1080*x^4+810*x^3+243*x^2),x, algorithm=\
-2*(16*x^6 + x^2*log(x)^4 + 96*x^5 + 216*x^4 + 4*(2*x^3 + 3*x^2)*log(x)^3 + 216*x^3 + 6*(4*x^4 + 12*x^3 + 9*x^2)*log(x)^2 + 81*x^2 + 4*(8*x^5 + 36*x ^4 + 54*x^3 + 27*x^2)*log(x) - 3*e^4)/(16*x^5 + x*log(x)^4 + 96*x^4 + 4*(2 *x^2 + 3*x)*log(x)^3 + 216*x^3 + 6*(4*x^3 + 12*x^2 + 9*x)*log(x)^2 + 216*x ^2 + 4*(8*x^4 + 36*x^3 + 54*x^2 + 27*x)*log(x) + 81*x)
Leaf count of result is larger than twice the leaf count of optimal. 212 vs. \(2 (20) = 40\).
Time = 0.31 (sec) , antiderivative size = 212, normalized size of antiderivative = 9.22 \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=-\frac {2 \, {\left (16 \, x^{6} + 32 \, x^{5} \log \left (x\right ) + 24 \, x^{4} \log \left (x\right )^{2} + 8 \, x^{3} \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4} + 96 \, x^{5} + 144 \, x^{4} \log \left (x\right ) + 72 \, x^{3} \log \left (x\right )^{2} + 12 \, x^{2} \log \left (x\right )^{3} + 216 \, x^{4} + 216 \, x^{3} \log \left (x\right ) + 54 \, x^{2} \log \left (x\right )^{2} + 216 \, x^{3} + 108 \, x^{2} \log \left (x\right ) + 81 \, x^{2} - 3 \, e^{4}\right )}}{16 \, x^{5} + 32 \, x^{4} \log \left (x\right ) + 24 \, x^{3} \log \left (x\right )^{2} + 8 \, x^{2} \log \left (x\right )^{3} + x \log \left (x\right )^{4} + 96 \, x^{4} + 144 \, x^{3} \log \left (x\right ) + 72 \, x^{2} \log \left (x\right )^{2} + 12 \, x \log \left (x\right )^{3} + 216 \, x^{3} + 216 \, x^{2} \log \left (x\right ) + 54 \, x \log \left (x\right )^{2} + 216 \, x^{2} + 108 \, x \log \left (x\right ) + 81 \, x} \]
integrate((-2*x^2*log(x)^5+(-20*x^3-30*x^2)*log(x)^4+(-80*x^4-240*x^3-180* x^2)*log(x)^3+(-160*x^5-720*x^4-1080*x^3-540*x^2)*log(x)^2+(-6*exp(2)^2-16 0*x^6-960*x^5-2160*x^4-2160*x^3-810*x^2)*log(x)+(-60*x-42)*exp(2)^2-64*x^7 -480*x^6-1440*x^5-2160*x^4-1620*x^3-486*x^2)/(x^2*log(x)^5+(10*x^3+15*x^2) *log(x)^4+(40*x^4+120*x^3+90*x^2)*log(x)^3+(80*x^5+360*x^4+540*x^3+270*x^2 )*log(x)^2+(80*x^6+480*x^5+1080*x^4+1080*x^3+405*x^2)*log(x)+32*x^7+240*x^ 6+720*x^5+1080*x^4+810*x^3+243*x^2),x, algorithm=\
-2*(16*x^6 + 32*x^5*log(x) + 24*x^4*log(x)^2 + 8*x^3*log(x)^3 + x^2*log(x) ^4 + 96*x^5 + 144*x^4*log(x) + 72*x^3*log(x)^2 + 12*x^2*log(x)^3 + 216*x^4 + 216*x^3*log(x) + 54*x^2*log(x)^2 + 216*x^3 + 108*x^2*log(x) + 81*x^2 - 3*e^4)/(16*x^5 + 32*x^4*log(x) + 24*x^3*log(x)^2 + 8*x^2*log(x)^3 + x*log( x)^4 + 96*x^4 + 144*x^3*log(x) + 72*x^2*log(x)^2 + 12*x*log(x)^3 + 216*x^3 + 216*x^2*log(x) + 54*x*log(x)^2 + 216*x^2 + 108*x*log(x) + 81*x)
Timed out. \[ \int \frac {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(x)} \, dx=\int -\frac {{\ln \left (x\right )}^4\,\left (20\,x^3+30\,x^2\right )+\ln \left (x\right )\,\left (160\,x^6+960\,x^5+2160\,x^4+2160\,x^3+810\,x^2+6\,{\mathrm {e}}^4\right )+2\,x^2\,{\ln \left (x\right )}^5+{\ln \left (x\right )}^3\,\left (80\,x^4+240\,x^3+180\,x^2\right )+486\,x^2+1620\,x^3+2160\,x^4+1440\,x^5+480\,x^6+64\,x^7+{\ln \left (x\right )}^2\,\left (160\,x^5+720\,x^4+1080\,x^3+540\,x^2\right )+{\mathrm {e}}^4\,\left (60\,x+42\right )}{{\ln \left (x\right )}^4\,\left (10\,x^3+15\,x^2\right )+x^2\,{\ln \left (x\right )}^5+{\ln \left (x\right )}^3\,\left (40\,x^4+120\,x^3+90\,x^2\right )+\ln \left (x\right )\,\left (80\,x^6+480\,x^5+1080\,x^4+1080\,x^3+405\,x^2\right )+243\,x^2+810\,x^3+1080\,x^4+720\,x^5+240\,x^6+32\,x^7+{\ln \left (x\right )}^2\,\left (80\,x^5+360\,x^4+540\,x^3+270\,x^2\right )} \,d x \]
int(-(log(x)^4*(30*x^2 + 20*x^3) + log(x)*(6*exp(4) + 810*x^2 + 2160*x^3 + 2160*x^4 + 960*x^5 + 160*x^6) + 2*x^2*log(x)^5 + log(x)^3*(180*x^2 + 240* x^3 + 80*x^4) + 486*x^2 + 1620*x^3 + 2160*x^4 + 1440*x^5 + 480*x^6 + 64*x^ 7 + log(x)^2*(540*x^2 + 1080*x^3 + 720*x^4 + 160*x^5) + exp(4)*(60*x + 42) )/(log(x)^4*(15*x^2 + 10*x^3) + x^2*log(x)^5 + log(x)^3*(90*x^2 + 120*x^3 + 40*x^4) + log(x)*(405*x^2 + 1080*x^3 + 1080*x^4 + 480*x^5 + 80*x^6) + 24 3*x^2 + 810*x^3 + 1080*x^4 + 720*x^5 + 240*x^6 + 32*x^7 + log(x)^2*(270*x^ 2 + 540*x^3 + 360*x^4 + 80*x^5)),x)
int(-(log(x)^4*(30*x^2 + 20*x^3) + log(x)*(6*exp(4) + 810*x^2 + 2160*x^3 + 2160*x^4 + 960*x^5 + 160*x^6) + 2*x^2*log(x)^5 + log(x)^3*(180*x^2 + 240* x^3 + 80*x^4) + 486*x^2 + 1620*x^3 + 2160*x^4 + 1440*x^5 + 480*x^6 + 64*x^ 7 + log(x)^2*(540*x^2 + 1080*x^3 + 720*x^4 + 160*x^5) + exp(4)*(60*x + 42) )/(log(x)^4*(15*x^2 + 10*x^3) + x^2*log(x)^5 + log(x)^3*(90*x^2 + 120*x^3 + 40*x^4) + log(x)*(405*x^2 + 1080*x^3 + 1080*x^4 + 480*x^5 + 80*x^6) + 24 3*x^2 + 810*x^3 + 1080*x^4 + 720*x^5 + 240*x^6 + 32*x^7 + log(x)^2*(270*x^ 2 + 540*x^3 + 360*x^4 + 80*x^5)), x)