Integrand size = 279, antiderivative size = 33 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5}{\frac {5}{1+e^{3 e^{-e^5}}}+x^2+(1+x \log (x))^2} \]
Leaf count is larger than twice the leaf count of optimal. \(97\) vs. \(2(33)=66\).
Time = 0.12 (sec) , antiderivative size = 97, normalized size of antiderivative = 2.94 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {10 \left (1+e^{3 e^{-e^5}}\right )^2}{\left (2+2 e^{3 e^{-e^5}}\right ) \left (6+x^2+e^{3 e^{-e^5}} \left (1+x^2\right )+2 \left (1+e^{3 e^{-e^5}}\right ) x \log (x)+\left (1+e^{3 e^{-e^5}}\right ) x^2 \log ^2(x)\right )} \]
Integrate[(-10 - 10*x + (-10 - 10*x)*Log[x] - 10*x*Log[x]^2 + E^(3/E^E^5)* (-20 - 20*x + (-20 - 20*x)*Log[x] - 20*x*Log[x]^2) + E^(6/E^E^5)*(-10 - 10 *x + (-10 - 10*x)*Log[x] - 10*x*Log[x]^2))/(36 + 12*x^2 + x^4 + (24*x + 4* x^3)*Log[x] + (16*x^2 + 2*x^4)*Log[x]^2 + 4*x^3*Log[x]^3 + x^4*Log[x]^4 + E^(6/E^E^5)*(1 + 2*x^2 + x^4 + (4*x + 4*x^3)*Log[x] + (6*x^2 + 2*x^4)*Log[ x]^2 + 4*x^3*Log[x]^3 + x^4*Log[x]^4) + E^(3/E^E^5)*(12 + 14*x^2 + 2*x^4 + (28*x + 8*x^3)*Log[x] + (22*x^2 + 4*x^4)*Log[x]^2 + 8*x^3*Log[x]^3 + 2*x^ 4*Log[x]^4)),x]
(10*(1 + E^(3/E^E^5))^2)/((2 + 2*E^(3/E^E^5))*(6 + x^2 + E^(3/E^E^5)*(1 + x^2) + 2*(1 + E^(3/E^E^5))*x*Log[x] + (1 + E^(3/E^E^5))*x^2*Log[x]^2))
Leaf count is larger than twice the leaf count of optimal. \(78\) vs. \(2(33)=66\).
Time = 0.98 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.36, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {7239, 27, 25, 7237}
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.
| \(\displaystyle \int \frac {-10 x-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20 x-20 x \log ^2(x)+(-20 x-20) \log (x)-20\right )+e^{6 e^{-e^5}} \left (-10 x-10 x \log ^2(x)+(-10 x-10) \log (x)-10\right )+(-10 x-10) \log (x)-10}{x^4+x^4 \log ^4(x)+4 x^3 \log ^3(x)+\left (4 x^3+24 x\right ) \log (x)+12 x^2+\left (2 x^4+16 x^2\right ) \log ^2(x)+e^{6 e^{-e^5}} \left (x^4+x^4 \log ^4(x)+4 x^3 \log ^3(x)+\left (4 x^3+4 x\right ) \log (x)+2 x^2+\left (2 x^4+6 x^2\right ) \log ^2(x)+1\right )+e^{3 e^{-e^5}} \left (2 x^4+2 x^4 \log ^4(x)+8 x^3 \log ^3(x)+\left (8 x^3+28 x\right ) \log (x)+14 x^2+\left (4 x^4+22 x^2\right ) \log ^2(x)+12\right )+36} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {10 \left (1+e^{3 e^{-e^5}}\right )^2 \left (-x-x \log ^2(x)-(x+1) \log (x)-1\right )}{\left (x^2+e^{3 e^{-e^5}} \left (x^2+1\right )+\left (1+e^{3 e^{-e^5}}\right ) x^2 \log ^2(x)+2 \left (1+e^{3 e^{-e^5}}\right ) x \log (x)+6\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 10 \left (1+e^{3 e^{-e^5}}\right )^2 \int -\frac {x \log ^2(x)+(x+1) \log (x)+x+1}{\left (\left (1+e^{3 e^{-e^5}}\right ) \log ^2(x) x^2+x^2+2 \left (1+e^{3 e^{-e^5}}\right ) \log (x) x+e^{3 e^{-e^5}} \left (x^2+1\right )+6\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -10 \left (1+e^{3 e^{-e^5}}\right )^2 \int \frac {x \log ^2(x)+(x+1) \log (x)+x+1}{\left (\left (1+e^{3 e^{-e^5}}\right ) \log ^2(x) x^2+x^2+2 \left (1+e^{3 e^{-e^5}}\right ) \log (x) x+e^{3 e^{-e^5}} \left (x^2+1\right )+6\right )^2}dx\) |
| \(\Big \downarrow \) 7237 |
| \(\displaystyle \frac {5 \left (1+e^{3 e^{-e^5}}\right )}{x^2+e^{3 e^{-e^5}} \left (x^2+1\right )+\left (1+e^{3 e^{-e^5}}\right ) x^2 \log ^2(x)+2 \left (1+e^{3 e^{-e^5}}\right ) x \log (x)+6}\) |
Int[(-10 - 10*x + (-10 - 10*x)*Log[x] - 10*x*Log[x]^2 + E^(3/E^E^5)*(-20 - 20*x + (-20 - 20*x)*Log[x] - 20*x*Log[x]^2) + E^(6/E^E^5)*(-10 - 10*x + ( -10 - 10*x)*Log[x] - 10*x*Log[x]^2))/(36 + 12*x^2 + x^4 + (24*x + 4*x^3)*L og[x] + (16*x^2 + 2*x^4)*Log[x]^2 + 4*x^3*Log[x]^3 + x^4*Log[x]^4 + E^(6/E ^E^5)*(1 + 2*x^2 + x^4 + (4*x + 4*x^3)*Log[x] + (6*x^2 + 2*x^4)*Log[x]^2 + 4*x^3*Log[x]^3 + x^4*Log[x]^4) + E^(3/E^E^5)*(12 + 14*x^2 + 2*x^4 + (28*x + 8*x^3)*Log[x] + (22*x^2 + 4*x^4)*Log[x]^2 + 8*x^3*Log[x]^3 + 2*x^4*Log[ x]^4)),x]
(5*(1 + E^(3/E^E^5)))/(6 + x^2 + E^(3/E^E^5)*(1 + x^2) + 2*(1 + E^(3/E^E^5 ))*x*Log[x] + (1 + E^(3/E^E^5))*x^2*Log[x]^2)
3.3.74.3.1 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_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Si mp[q*(y^(m + 1)/(m + 1)), x] /; !FalseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(82\) vs. \(2(30)=60\).
Time = 13.77 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.52
| method | result | size |
| norman | \(\frac {5 \,{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+5}{\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6}\) | \(83\) |
| default | \(-\frac {10 \left (-\frac {{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}}{2}-\frac {1}{2}\right )}{\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6}\) | \(84\) |
| parallelrisch | \(\frac {5 \,{\mathrm e}^{6 \,{\mathrm e}^{-{\mathrm e}^{5}}}+10 \,{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+5}{\left ({\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+1\right ) \left (\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6\right )}\) | \(107\) |
| risch | \(\frac {5 \,{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}}{\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6}+\frac {5}{\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6}\) | \(152\) |
int(((-10*x*ln(x)^2+(-10*x-10)*ln(x)-10*x-10)*exp(3/exp(exp(5)))^2+(-20*x* ln(x)^2+(-20*x-20)*ln(x)-20*x-20)*exp(3/exp(exp(5)))-10*x*ln(x)^2+(-10*x-1 0)*ln(x)-10*x-10)/((x^4*ln(x)^4+4*x^3*ln(x)^3+(2*x^4+6*x^2)*ln(x)^2+(4*x^3 +4*x)*ln(x)+x^4+2*x^2+1)*exp(3/exp(exp(5)))^2+(2*x^4*ln(x)^4+8*x^3*ln(x)^3 +(4*x^4+22*x^2)*ln(x)^2+(8*x^3+28*x)*ln(x)+2*x^4+14*x^2+12)*exp(3/exp(exp( 5)))+x^4*ln(x)^4+4*x^3*ln(x)^3+(2*x^4+16*x^2)*ln(x)^2+(4*x^3+24*x)*ln(x)+x ^4+12*x^2+36),x,method=_RETURNVERBOSE)
(5*exp(1/exp(exp(5)))^3+5)/(ln(x)^2*exp(3/exp(exp(5)))*x^2+x^2*ln(x)^2+2*l n(x)*exp(3/exp(exp(5)))*x+exp(3/exp(exp(5)))*x^2+2*x*ln(x)+x^2+exp(3/exp(e xp(5)))+6)
Time = 0.25 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.79 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \, {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )}}{x^{2} \log \left (x\right )^{2} + x^{2} + {\left (x^{2} \log \left (x\right )^{2} + x^{2} + 2 \, x \log \left (x\right ) + 1\right )} e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 2 \, x \log \left (x\right ) + 6} \]
integrate(((-10*x*log(x)^2+(-10*x-10)*log(x)-10*x-10)*exp(3/exp(exp(5)))^2 +(-20*x*log(x)^2+(-20*x-20)*log(x)-20*x-20)*exp(3/exp(exp(5)))-10*x*log(x) ^2+(-10*x-10)*log(x)-10*x-10)/((x^4*log(x)^4+4*x^3*log(x)^3+(2*x^4+6*x^2)* log(x)^2+(4*x^3+4*x)*log(x)+x^4+2*x^2+1)*exp(3/exp(exp(5)))^2+(2*x^4*log(x )^4+8*x^3*log(x)^3+(4*x^4+22*x^2)*log(x)^2+(8*x^3+28*x)*log(x)+2*x^4+14*x^ 2+12)*exp(3/exp(exp(5)))+x^4*log(x)^4+4*x^3*log(x)^3+(2*x^4+16*x^2)*log(x) ^2+(4*x^3+24*x)*log(x)+x^4+12*x^2+36),x, algorithm=\
5*(e^(3*e^(-e^5)) + 1)/(x^2*log(x)^2 + x^2 + (x^2*log(x)^2 + x^2 + 2*x*log (x) + 1)*e^(3*e^(-e^5)) + 2*x*log(x) + 6)
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).
Time = 0.33 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.27 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 + 5 e^{\frac {3}{e^{e^{5}}}}}{x^{2} + x^{2} e^{\frac {3}{e^{e^{5}}}} + \left (2 x + 2 x e^{\frac {3}{e^{e^{5}}}}\right ) \log {\left (x \right )} + \left (x^{2} + x^{2} e^{\frac {3}{e^{e^{5}}}}\right ) \log {\left (x \right )}^{2} + e^{\frac {3}{e^{e^{5}}}} + 6} \]
integrate(((-10*x*ln(x)**2+(-10*x-10)*ln(x)-10*x-10)*exp(3/exp(exp(5)))**2 +(-20*x*ln(x)**2+(-20*x-20)*ln(x)-20*x-20)*exp(3/exp(exp(5)))-10*x*ln(x)** 2+(-10*x-10)*ln(x)-10*x-10)/((x**4*ln(x)**4+4*x**3*ln(x)**3+(2*x**4+6*x**2 )*ln(x)**2+(4*x**3+4*x)*ln(x)+x**4+2*x**2+1)*exp(3/exp(exp(5)))**2+(2*x**4 *ln(x)**4+8*x**3*ln(x)**3+(4*x**4+22*x**2)*ln(x)**2+(8*x**3+28*x)*ln(x)+2* x**4+14*x**2+12)*exp(3/exp(exp(5)))+x**4*ln(x)**4+4*x**3*ln(x)**3+(2*x**4+ 16*x**2)*ln(x)**2+(4*x**3+24*x)*ln(x)+x**4+12*x**2+36),x)
(5 + 5*exp(3*exp(-exp(5))))/(x**2 + x**2*exp(3*exp(-exp(5))) + (2*x + 2*x* exp(3*exp(-exp(5))))*log(x) + (x**2 + x**2*exp(3*exp(-exp(5))))*log(x)**2 + exp(3*exp(-exp(5))) + 6)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (30) = 60\).
Time = 0.28 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.15 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \, {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )}}{x^{2} {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )} \log \left (x\right )^{2} + x^{2} {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )} + 2 \, x {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )} \log \left (x\right ) + e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 6} \]
integrate(((-10*x*log(x)^2+(-10*x-10)*log(x)-10*x-10)*exp(3/exp(exp(5)))^2 +(-20*x*log(x)^2+(-20*x-20)*log(x)-20*x-20)*exp(3/exp(exp(5)))-10*x*log(x) ^2+(-10*x-10)*log(x)-10*x-10)/((x^4*log(x)^4+4*x^3*log(x)^3+(2*x^4+6*x^2)* log(x)^2+(4*x^3+4*x)*log(x)+x^4+2*x^2+1)*exp(3/exp(exp(5)))^2+(2*x^4*log(x )^4+8*x^3*log(x)^3+(4*x^4+22*x^2)*log(x)^2+(8*x^3+28*x)*log(x)+2*x^4+14*x^ 2+12)*exp(3/exp(exp(5)))+x^4*log(x)^4+4*x^3*log(x)^3+(2*x^4+16*x^2)*log(x) ^2+(4*x^3+24*x)*log(x)+x^4+12*x^2+36),x, algorithm=\
5*(e^(3*e^(-e^5)) + 1)/(x^2*(e^(3*e^(-e^5)) + 1)*log(x)^2 + x^2*(e^(3*e^(- e^5)) + 1) + 2*x*(e^(3*e^(-e^5)) + 1)*log(x) + e^(3*e^(-e^5)) + 6)
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (30) = 60\).
Time = 0.75 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.45 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \, {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )}}{x^{2} e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} \log \left (x\right )^{2} + x^{2} \log \left (x\right )^{2} + x^{2} e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 2 \, x e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} \log \left (x\right ) + x^{2} + 2 \, x \log \left (x\right ) + e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 6} \]
integrate(((-10*x*log(x)^2+(-10*x-10)*log(x)-10*x-10)*exp(3/exp(exp(5)))^2 +(-20*x*log(x)^2+(-20*x-20)*log(x)-20*x-20)*exp(3/exp(exp(5)))-10*x*log(x) ^2+(-10*x-10)*log(x)-10*x-10)/((x^4*log(x)^4+4*x^3*log(x)^3+(2*x^4+6*x^2)* log(x)^2+(4*x^3+4*x)*log(x)+x^4+2*x^2+1)*exp(3/exp(exp(5)))^2+(2*x^4*log(x )^4+8*x^3*log(x)^3+(4*x^4+22*x^2)*log(x)^2+(8*x^3+28*x)*log(x)+2*x^4+14*x^ 2+12)*exp(3/exp(exp(5)))+x^4*log(x)^4+4*x^3*log(x)^3+(2*x^4+16*x^2)*log(x) ^2+(4*x^3+24*x)*log(x)+x^4+12*x^2+36),x, algorithm=\
5*(e^(3*e^(-e^5)) + 1)/(x^2*e^(3*e^(-e^5))*log(x)^2 + x^2*log(x)^2 + x^2*e ^(3*e^(-e^5)) + 2*x*e^(3*e^(-e^5))*log(x) + x^2 + 2*x*log(x) + e^(3*e^(-e^ 5)) + 6)
Timed out. \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\int -\frac {10\,x+10\,x\,{\ln \left (x\right )}^2+{\mathrm {e}}^{6\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left (10\,x\,{\ln \left (x\right )}^2+\left (10\,x+10\right )\,\ln \left (x\right )+10\,x+10\right )+{\mathrm {e}}^{3\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left (20\,x\,{\ln \left (x\right )}^2+\left (20\,x+20\right )\,\ln \left (x\right )+20\,x+20\right )+\ln \left (x\right )\,\left (10\,x+10\right )+10}{{\mathrm {e}}^{3\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left ({\ln \left (x\right )}^2\,\left (4\,x^4+22\,x^2\right )+8\,x^3\,{\ln \left (x\right )}^3+2\,x^4\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (8\,x^3+28\,x\right )+14\,x^2+2\,x^4+12\right )+{\ln \left (x\right )}^2\,\left (2\,x^4+16\,x^2\right )+4\,x^3\,{\ln \left (x\right )}^3+x^4\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (4\,x^3+24\,x\right )+{\mathrm {e}}^{6\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left ({\ln \left (x\right )}^2\,\left (2\,x^4+6\,x^2\right )+4\,x^3\,{\ln \left (x\right )}^3+x^4\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (4\,x^3+4\,x\right )+2\,x^2+x^4+1\right )+12\,x^2+x^4+36} \,d x \]
int(-(10*x + 10*x*log(x)^2 + exp(6*exp(-exp(5)))*(10*x + 10*x*log(x)^2 + l og(x)*(10*x + 10) + 10) + exp(3*exp(-exp(5)))*(20*x + 20*x*log(x)^2 + log( x)*(20*x + 20) + 20) + log(x)*(10*x + 10) + 10)/(exp(3*exp(-exp(5)))*(log( x)^2*(22*x^2 + 4*x^4) + 8*x^3*log(x)^3 + 2*x^4*log(x)^4 + log(x)*(28*x + 8 *x^3) + 14*x^2 + 2*x^4 + 12) + log(x)^2*(16*x^2 + 2*x^4) + 4*x^3*log(x)^3 + x^4*log(x)^4 + log(x)*(24*x + 4*x^3) + exp(6*exp(-exp(5)))*(log(x)^2*(6* x^2 + 2*x^4) + 4*x^3*log(x)^3 + x^4*log(x)^4 + log(x)*(4*x + 4*x^3) + 2*x^ 2 + x^4 + 1) + 12*x^2 + x^4 + 36),x)
int(-(10*x + 10*x*log(x)^2 + exp(6*exp(-exp(5)))*(10*x + 10*x*log(x)^2 + l og(x)*(10*x + 10) + 10) + exp(3*exp(-exp(5)))*(20*x + 20*x*log(x)^2 + log( x)*(20*x + 20) + 20) + log(x)*(10*x + 10) + 10)/(exp(3*exp(-exp(5)))*(log( x)^2*(22*x^2 + 4*x^4) + 8*x^3*log(x)^3 + 2*x^4*log(x)^4 + log(x)*(28*x + 8 *x^3) + 14*x^2 + 2*x^4 + 12) + log(x)^2*(16*x^2 + 2*x^4) + 4*x^3*log(x)^3 + x^4*log(x)^4 + log(x)*(24*x + 4*x^3) + exp(6*exp(-exp(5)))*(log(x)^2*(6* x^2 + 2*x^4) + 4*x^3*log(x)^3 + x^4*log(x)^4 + log(x)*(4*x + 4*x^3) + 2*x^ 2 + x^4 + 1) + 12*x^2 + x^4 + 36), x)