Integrand size = 407, antiderivative size = 22 \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\frac {x^5}{\left (e^x+x-x^2-\log ^2(x)\right )^4} \]
Time = 0.48 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\frac {x^5}{\left (-e^x-x+x^2+\log ^2(x)\right )^4} \]
Integrate[(-x^5 - 3*x^6 + E^x*(-5*x^4 + 4*x^5) - 8*x^4*Log[x] + 5*x^4*Log[ x]^2)/(-E^(5*x) - x^5 + 5*x^6 - 10*x^7 + 10*x^8 - 5*x^9 + x^10 + E^(4*x)*( -5*x + 5*x^2) + E^(3*x)*(-10*x^2 + 20*x^3 - 10*x^4) + E^(2*x)*(-10*x^3 + 3 0*x^4 - 30*x^5 + 10*x^6) + E^x*(-5*x^4 + 20*x^5 - 30*x^6 + 20*x^7 - 5*x^8) + (5*E^(4*x) + 5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8 + E^(3*x)*(20*x - 20*x^2) + E^(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + E^x*(20*x^3 - 60*x^4 + 60* x^5 - 20*x^6))*Log[x]^2 + (-10*E^(3*x) - 10*x^3 + 30*x^4 - 30*x^5 + 10*x^6 + E^(2*x)*(-30*x + 30*x^2) + E^x*(-30*x^2 + 60*x^3 - 30*x^4))*Log[x]^4 + (10*E^(2*x) + 10*x^2 - 20*x^3 + 10*x^4 + E^x*(20*x - 20*x^2))*Log[x]^6 + ( -5*E^x - 5*x + 5*x^2)*Log[x]^8 + Log[x]^10),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.
| \(\displaystyle \int \frac {-3 x^6-x^5+5 x^4 \log ^2(x)-8 x^4 \log (x)+e^x \left (4 x^5-5 x^4\right )}{x^{10}-5 x^9+10 x^8-10 x^7+5 x^6-x^5+e^{4 x} \left (5 x^2-5 x\right )+\left (5 x^2-5 x-5 e^x\right ) \log ^8(x)+e^{3 x} \left (-10 x^4+20 x^3-10 x^2\right )+\left (10 x^4-20 x^3+10 x^2+e^x \left (20 x-20 x^2\right )+10 e^{2 x}\right ) \log ^6(x)+e^{2 x} \left (10 x^6-30 x^5+30 x^4-10 x^3\right )+e^x \left (-5 x^8+20 x^7-30 x^6+20 x^5-5 x^4\right )+\left (10 x^6-30 x^5+30 x^4-10 x^3+e^{2 x} \left (30 x^2-30 x\right )+e^x \left (-30 x^4+60 x^3-30 x^2\right )-10 e^{3 x}\right ) \log ^4(x)+\left (5 x^8-20 x^7+30 x^6-20 x^5+5 x^4+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^4-60 x^3+30 x^2\right )+e^x \left (-20 x^6+60 x^5-60 x^4+20 x^3\right )+5 e^{4 x}\right ) \log ^2(x)-e^{5 x}+\log ^{10}(x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^4 \left (e^x (5-4 x)+x (3 x+1)-5 \log ^2(x)+8 \log (x)\right )}{\left (e^x-(x-1) x-\log ^2(x)\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {4 x^4 \left (x^3-3 x^2+x+x \log ^2(x)-2 \log (x)\right )}{\left (x^2-x-e^x+\log ^2(x)\right )^5}-\frac {x^4 (4 x-5)}{\left (x^2-x-e^x+\log ^2(x)\right )^4}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \int \frac {x^7}{\left (x^2-x-e^x+\log ^2(x)\right )^5}dx-12 \int \frac {x^6}{\left (x^2-x-e^x+\log ^2(x)\right )^5}dx+4 \int \frac {x^5}{\left (x^2-x-e^x+\log ^2(x)\right )^5}dx+4 \int \frac {x^5 \log ^2(x)}{\left (x^2-x-e^x+\log ^2(x)\right )^5}dx-4 \int \frac {x^5}{\left (x^2-x-e^x+\log ^2(x)\right )^4}dx-8 \int \frac {x^4 \log (x)}{\left (x^2-x-e^x+\log ^2(x)\right )^5}dx+5 \int \frac {x^4}{\left (x^2-x-e^x+\log ^2(x)\right )^4}dx\) |
Int[(-x^5 - 3*x^6 + E^x*(-5*x^4 + 4*x^5) - 8*x^4*Log[x] + 5*x^4*Log[x]^2)/ (-E^(5*x) - x^5 + 5*x^6 - 10*x^7 + 10*x^8 - 5*x^9 + x^10 + E^(4*x)*(-5*x + 5*x^2) + E^(3*x)*(-10*x^2 + 20*x^3 - 10*x^4) + E^(2*x)*(-10*x^3 + 30*x^4 - 30*x^5 + 10*x^6) + E^x*(-5*x^4 + 20*x^5 - 30*x^6 + 20*x^7 - 5*x^8) + (5* E^(4*x) + 5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8 + E^(3*x)*(20*x - 20*x^ 2) + E^(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + E^x*(20*x^3 - 60*x^4 + 60*x^5 - 20*x^6))*Log[x]^2 + (-10*E^(3*x) - 10*x^3 + 30*x^4 - 30*x^5 + 10*x^6 + E^( 2*x)*(-30*x + 30*x^2) + E^x*(-30*x^2 + 60*x^3 - 30*x^4))*Log[x]^4 + (10*E^ (2*x) + 10*x^2 - 20*x^3 + 10*x^4 + E^x*(20*x - 20*x^2))*Log[x]^6 + (-5*E^x - 5*x + 5*x^2)*Log[x]^8 + Log[x]^10),x]
3.7.95.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 11.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
| method | result | size |
| risch | \(\frac {x^{5}}{\left (\ln \left (x \right )^{2}+x^{2}-{\mathrm e}^{x}-x \right )^{4}}\) | \(22\) |
| parallelrisch | \(\frac {x^{5}}{-4 x^{2} {\mathrm e}^{3 x}-12 \,{\mathrm e}^{2 x} x^{3}+4 x^{6} \ln \left (x \right )^{2}-12 \ln \left (x \right )^{4} {\mathrm e}^{x} x^{2}-12 x^{3} \ln \left (x \right )^{4}+12 x^{4} \ln \left (x \right )^{2}+4 x \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{2 x} x^{2}-4 x^{6} {\mathrm e}^{x}-12 \,{\mathrm e}^{x} x^{4}+4 \,{\mathrm e}^{x} x^{3}+4 x^{2} \ln \left (x \right )^{6}-4 x \ln \left (x \right )^{6}+6 x^{4} \ln \left (x \right )^{4}+\ln \left (x \right )^{8}-12 x^{5} \ln \left (x \right )^{2}+{\mathrm e}^{4 x}-4 x^{3} \ln \left (x \right )^{2}+12 x^{5} {\mathrm e}^{x}+6 x^{2} \ln \left (x \right )^{4}-12 x^{4} {\mathrm e}^{x} \ln \left (x \right )^{2}-12 x^{2} {\mathrm e}^{x} \ln \left (x \right )^{2}-4 x^{7}+x^{8}+x^{4}+6 x^{6}-4 x^{5}+24 \,{\mathrm e}^{x} \ln \left (x \right )^{2} x^{3}+12 \,{\mathrm e}^{2 x} \ln \left (x \right )^{2} x^{2}-12 \,{\mathrm e}^{2 x} \ln \left (x \right )^{2} x +6 \,{\mathrm e}^{2 x} x^{4}+12 x \ln \left (x \right )^{4} {\mathrm e}^{x}+6 \,{\mathrm e}^{2 x} \ln \left (x \right )^{4}-4 \ln \left (x \right )^{2} {\mathrm e}^{3 x}-4 \ln \left (x \right )^{6} {\mathrm e}^{x}}\) | \(292\) |
int((5*x^4*ln(x)^2-8*x^4*ln(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(ln(x)^10+( -5*exp(x)+5*x^2-5*x)*ln(x)^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+10*x^4-20* x^3+10*x^2)*ln(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30*x^4+60*x^3-3 0*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*ln(x)^4+(5*exp(x)^4+(-20*x^2+20 *x)*exp(x)^3+(30*x^4-60*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-60*x^4+20*x^3 )*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*ln(x)^2-exp(x)^5+(5*x^2-5*x)*ex p(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp( x)^2+(-5*x^8+20*x^7-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5 *x^6-x^5),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 200 vs. \(2 (21) = 42\).
Time = 0.26 (sec) , antiderivative size = 200, normalized size of antiderivative = 9.09 \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\frac {x^{5}}{x^{8} + \log \left (x\right )^{8} - 4 \, x^{7} + 4 \, {\left (x^{2} - x - e^{x}\right )} \log \left (x\right )^{6} + 6 \, x^{6} - 4 \, x^{5} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2} - 2 \, {\left (x^{2} - x\right )} e^{x} + e^{\left (2 \, x\right )}\right )} \log \left (x\right )^{4} + x^{4} + 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3} + 3 \, {\left (x^{2} - x\right )} e^{\left (2 \, x\right )} - 3 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{x} - e^{\left (3 \, x\right )}\right )} \log \left (x\right )^{2} - 4 \, {\left (x^{2} - x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}} \]
integrate((5*x^4*log(x)^2-8*x^4*log(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(lo g(x)^10+(-5*exp(x)+5*x^2-5*x)*log(x)^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+ 10*x^4-20*x^3+10*x^2)*log(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30*x ^4+60*x^3-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*log(x)^4+(5*exp(x)^4 +(-20*x^2+20*x)*exp(x)^3+(30*x^4-60*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-6 0*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*log(x)^2-exp(x)^5+( 5*x^2-5*x)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4 -10*x^3)*exp(x)^2+(-5*x^8+20*x^7-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10 *x^8-10*x^7+5*x^6-x^5),x, algorithm=\
x^5/(x^8 + log(x)^8 - 4*x^7 + 4*(x^2 - x - e^x)*log(x)^6 + 6*x^6 - 4*x^5 + 6*(x^4 - 2*x^3 + x^2 - 2*(x^2 - x)*e^x + e^(2*x))*log(x)^4 + x^4 + 4*(x^6 - 3*x^5 + 3*x^4 - x^3 + 3*(x^2 - x)*e^(2*x) - 3*(x^4 - 2*x^3 + x^2)*e^x - e^(3*x))*log(x)^2 - 4*(x^2 - x)*e^(3*x) + 6*(x^4 - 2*x^3 + x^2)*e^(2*x) - 4*(x^6 - 3*x^5 + 3*x^4 - x^3)*e^x + e^(4*x))
Leaf count of result is larger than twice the leaf count of optimal. 270 vs. \(2 (26) = 52\).
Time = 0.39 (sec) , antiderivative size = 270, normalized size of antiderivative = 12.27 \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\frac {x^{5}}{x^{8} - 4 x^{7} + 4 x^{6} \log {\left (x \right )}^{2} + 6 x^{6} - 12 x^{5} \log {\left (x \right )}^{2} - 4 x^{5} + 6 x^{4} \log {\left (x \right )}^{4} + 12 x^{4} \log {\left (x \right )}^{2} + x^{4} - 12 x^{3} \log {\left (x \right )}^{4} - 4 x^{3} \log {\left (x \right )}^{2} + 4 x^{2} \log {\left (x \right )}^{6} + 6 x^{2} \log {\left (x \right )}^{4} - 4 x \log {\left (x \right )}^{6} + \left (- 4 x^{2} + 4 x - 4 \log {\left (x \right )}^{2}\right ) e^{3 x} + \left (6 x^{4} - 12 x^{3} + 12 x^{2} \log {\left (x \right )}^{2} + 6 x^{2} - 12 x \log {\left (x \right )}^{2} + 6 \log {\left (x \right )}^{4}\right ) e^{2 x} + \left (- 4 x^{6} + 12 x^{5} - 12 x^{4} \log {\left (x \right )}^{2} - 12 x^{4} + 24 x^{3} \log {\left (x \right )}^{2} + 4 x^{3} - 12 x^{2} \log {\left (x \right )}^{4} - 12 x^{2} \log {\left (x \right )}^{2} + 12 x \log {\left (x \right )}^{4} - 4 \log {\left (x \right )}^{6}\right ) e^{x} + e^{4 x} + \log {\left (x \right )}^{8}} \]
integrate((5*x**4*ln(x)**2-8*x**4*ln(x)+(4*x**5-5*x**4)*exp(x)-3*x**6-x**5 )/(ln(x)**10+(-5*exp(x)+5*x**2-5*x)*ln(x)**8+(10*exp(x)**2+(-20*x**2+20*x) *exp(x)+10*x**4-20*x**3+10*x**2)*ln(x)**6+(-10*exp(x)**3+(30*x**2-30*x)*ex p(x)**2+(-30*x**4+60*x**3-30*x**2)*exp(x)+10*x**6-30*x**5+30*x**4-10*x**3) *ln(x)**4+(5*exp(x)**4+(-20*x**2+20*x)*exp(x)**3+(30*x**4-60*x**3+30*x**2) *exp(x)**2+(-20*x**6+60*x**5-60*x**4+20*x**3)*exp(x)+5*x**8-20*x**7+30*x** 6-20*x**5+5*x**4)*ln(x)**2-exp(x)**5+(5*x**2-5*x)*exp(x)**4+(-10*x**4+20*x **3-10*x**2)*exp(x)**3+(10*x**6-30*x**5+30*x**4-10*x**3)*exp(x)**2+(-5*x** 8+20*x**7-30*x**6+20*x**5-5*x**4)*exp(x)+x**10-5*x**9+10*x**8-10*x**7+5*x* *6-x**5),x)
x**5/(x**8 - 4*x**7 + 4*x**6*log(x)**2 + 6*x**6 - 12*x**5*log(x)**2 - 4*x* *5 + 6*x**4*log(x)**4 + 12*x**4*log(x)**2 + x**4 - 12*x**3*log(x)**4 - 4*x **3*log(x)**2 + 4*x**2*log(x)**6 + 6*x**2*log(x)**4 - 4*x*log(x)**6 + (-4* x**2 + 4*x - 4*log(x)**2)*exp(3*x) + (6*x**4 - 12*x**3 + 12*x**2*log(x)**2 + 6*x**2 - 12*x*log(x)**2 + 6*log(x)**4)*exp(2*x) + (-4*x**6 + 12*x**5 - 12*x**4*log(x)**2 - 12*x**4 + 24*x**3*log(x)**2 + 4*x**3 - 12*x**2*log(x)* *4 - 12*x**2*log(x)**2 + 12*x*log(x)**4 - 4*log(x)**6)*exp(x) + exp(4*x) + log(x)**8)
Leaf count of result is larger than twice the leaf count of optimal. 202 vs. \(2 (21) = 42\).
Time = 1.23 (sec) , antiderivative size = 202, normalized size of antiderivative = 9.18 \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\frac {x^{5}}{x^{8} + \log \left (x\right )^{8} - 4 \, x^{7} + 4 \, {\left (x^{2} - x\right )} \log \left (x\right )^{6} + 6 \, x^{6} - 4 \, x^{5} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \left (x\right )^{4} + x^{4} + 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} \log \left (x\right )^{2} - 4 \, {\left (x^{2} + \log \left (x\right )^{2} - x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} + \log \left (x\right )^{4} - 2 \, x^{3} + 2 \, {\left (x^{2} - x\right )} \log \left (x\right )^{2} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} + \log \left (x\right )^{6} - 3 \, x^{5} + 3 \, {\left (x^{2} - x\right )} \log \left (x\right )^{4} + 3 \, x^{4} - x^{3} + 3 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \left (x\right )^{2}\right )} e^{x} + e^{\left (4 \, x\right )}} \]
integrate((5*x^4*log(x)^2-8*x^4*log(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(lo g(x)^10+(-5*exp(x)+5*x^2-5*x)*log(x)^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+ 10*x^4-20*x^3+10*x^2)*log(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30*x ^4+60*x^3-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*log(x)^4+(5*exp(x)^4 +(-20*x^2+20*x)*exp(x)^3+(30*x^4-60*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-6 0*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*log(x)^2-exp(x)^5+( 5*x^2-5*x)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4 -10*x^3)*exp(x)^2+(-5*x^8+20*x^7-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10 *x^8-10*x^7+5*x^6-x^5),x, algorithm=\
x^5/(x^8 + log(x)^8 - 4*x^7 + 4*(x^2 - x)*log(x)^6 + 6*x^6 - 4*x^5 + 6*(x^ 4 - 2*x^3 + x^2)*log(x)^4 + x^4 + 4*(x^6 - 3*x^5 + 3*x^4 - x^3)*log(x)^2 - 4*(x^2 + log(x)^2 - x)*e^(3*x) + 6*(x^4 + log(x)^4 - 2*x^3 + 2*(x^2 - x)* log(x)^2 + x^2)*e^(2*x) - 4*(x^6 + log(x)^6 - 3*x^5 + 3*(x^2 - x)*log(x)^4 + 3*x^4 - x^3 + 3*(x^4 - 2*x^3 + x^2)*log(x)^2)*e^x + e^(4*x))
Timed out. \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\text {Timed out} \]
integrate((5*x^4*log(x)^2-8*x^4*log(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(lo g(x)^10+(-5*exp(x)+5*x^2-5*x)*log(x)^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+ 10*x^4-20*x^3+10*x^2)*log(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30*x ^4+60*x^3-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*log(x)^4+(5*exp(x)^4 +(-20*x^2+20*x)*exp(x)^3+(30*x^4-60*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-6 0*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*log(x)^2-exp(x)^5+( 5*x^2-5*x)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4 -10*x^3)*exp(x)^2+(-5*x^8+20*x^7-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10 *x^8-10*x^7+5*x^6-x^5),x, algorithm=\
Timed out. \[ \int \frac {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx=\text {Hanged} \]
int((exp(x)*(5*x^4 - 4*x^5) + 8*x^4*log(x) - 5*x^4*log(x)^2 + x^5 + 3*x^6) /(exp(5*x) + exp(4*x)*(5*x - 5*x^2) - log(x)^10 + log(x)^8*(5*x + 5*exp(x) - 5*x^2) + exp(3*x)*(10*x^2 - 20*x^3 + 10*x^4) + exp(x)*(5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8) + log(x)^4*(10*exp(3*x) + exp(2*x)*(30*x - 30*x^ 2) + exp(x)*(30*x^2 - 60*x^3 + 30*x^4) + 10*x^3 - 30*x^4 + 30*x^5 - 10*x^6 ) - log(x)^2*(5*exp(4*x) + exp(3*x)*(20*x - 20*x^2) + exp(x)*(20*x^3 - 60* x^4 + 60*x^5 - 20*x^6) + exp(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + 5*x^4 - 20* x^5 + 30*x^6 - 20*x^7 + 5*x^8) + exp(2*x)*(10*x^3 - 30*x^4 + 30*x^5 - 10*x ^6) + x^5 - 5*x^6 + 10*x^7 - 10*x^8 + 5*x^9 - x^10 - log(x)^6*(10*exp(2*x) + exp(x)*(20*x - 20*x^2) + 10*x^2 - 20*x^3 + 10*x^4)),x)