Integrand size = 279, antiderivative size = 33 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5}{\frac {5}{1+e^{3 e^{-e^5}}}+x^2+(1+x \log (x))^2} \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(78\) vs. \(2(33)=66\).
Time = 0.42 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.36, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6820, 12, 6818} \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \left (1+e^{3 e^{-e^5}}\right )}{x^2+e^{3 e^{-e^5}} \left (x^2+1\right )+\left (1+e^{3 e^{-e^5}}\right ) x^2 \log ^2(x)+2 \left (1+e^{3 e^{-e^5}}\right ) x \log (x)+6} \]
[In]
[Out]
Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {10 \left (1+e^{3 e^{-e^5}}\right )^2 \left (-1-x-(1+x) \log (x)-x \log ^2(x)\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 )^2} \, dx \\ & = \left (10 \left (1+e^{3 e^{-e^5}}\right )^2\right ) \int \frac {-1-x-(1+x) \log (x)-x \log ^2(x)}{\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 )^2} \, dx \\ & = \frac {5 \left (1+e^{3 e^{-e^5}}\right )}{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)} \\ \end{align*}
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 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {10 \left (1+e^{3 e^{-e^5}}\right )^2}{\left (2+2 e^{3 e^{-e^5}}\right ) \left (6+x^2+e^{3 e^{-e^5}} \left (1+x^2\right )+2 \left (1+e^{3 e^{-e^5}}\right ) x \log (x)+\left (1+e^{3 e^{-e^5}}\right ) x^2 \log ^2(x)\right )} \]
[In]
[Out]
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 | \(\frac {5 \,{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}}{\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6}+\frac {5}{\ln \left (x \right )^{2} {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x^{2}+2 \ln \left (x \right ) {\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}} x +x^{2} \ln \left (x \right )^{2}+{\mathrm e}^{3 \,{\mathrm e}^{-{\mathrm e}^{5}}}+x^{2}+2 x \ln \left (x \right )+6}\) | \(152\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.79 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \, {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )}}{x^{2} \log \left (x\right )^{2} + x^{2} + {\left (x^{2} \log \left (x\right )^{2} + x^{2} + 2 \, x \log \left (x\right ) + 1\right )} e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 2 \, x \log \left (x\right ) + 6} \]
[In]
[Out]
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 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 + 5 e^{\frac {3}{e^{e^{5}}}}}{x^{2} + x^{2} e^{\frac {3}{e^{e^{5}}}} + \left (2 x + 2 x e^{\frac {3}{e^{e^{5}}}}\right ) \log {\left (x \right )} + \left (x^{2} + x^{2} e^{\frac {3}{e^{e^{5}}}}\right ) \log {\left (x \right )}^{2} + e^{\frac {3}{e^{e^{5}}}} + 6} \]
[In]
[Out]
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 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \, {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )}}{x^{2} {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )} \log \left (x\right )^{2} + x^{2} {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )} + 2 \, x {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )} \log \left (x\right ) + e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 6} \]
[In]
[Out]
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 \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\frac {5 \, {\left (e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 1\right )}}{x^{2} e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} \log \left (x\right )^{2} + x^{2} \log \left (x\right )^{2} + x^{2} e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 2 \, x e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} \log \left (x\right ) + x^{2} + 2 \, x \log \left (x\right ) + e^{\left (3 \, e^{\left (-e^{5}\right )}\right )} + 6} \]
[In]
[Out]
Timed out. \[ \int \frac {-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)+e^{3 e^{-e^5}} \left (-20-20 x+(-20-20 x) \log (x)-20 x \log ^2(x)\right )+e^{6 e^{-e^5}} \left (-10-10 x+(-10-10 x) \log (x)-10 x \log ^2(x)\right )}{36+12 x^2+x^4+\left (24 x+4 x^3\right ) \log (x)+\left (16 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)+e^{6 e^{-e^5}} \left (1+2 x^2+x^4+\left (4 x+4 x^3\right ) \log (x)+\left (6 x^2+2 x^4\right ) \log ^2(x)+4 x^3 \log ^3(x)+x^4 \log ^4(x)\right )+e^{3 e^{-e^5}} \left (12+14 x^2+2 x^4+\left (28 x+8 x^3\right ) \log (x)+\left (22 x^2+4 x^4\right ) \log ^2(x)+8 x^3 \log ^3(x)+2 x^4 \log ^4(x)\right )} \, dx=\int -\frac {10\,x+10\,x\,{\ln \left (x\right )}^2+{\mathrm {e}}^{6\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left (10\,x\,{\ln \left (x\right )}^2+\left (10\,x+10\right )\,\ln \left (x\right )+10\,x+10\right )+{\mathrm {e}}^{3\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left (20\,x\,{\ln \left (x\right )}^2+\left (20\,x+20\right )\,\ln \left (x\right )+20\,x+20\right )+\ln \left (x\right )\,\left (10\,x+10\right )+10}{{\mathrm {e}}^{3\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left ({\ln \left (x\right )}^2\,\left (4\,x^4+22\,x^2\right )+8\,x^3\,{\ln \left (x\right )}^3+2\,x^4\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (8\,x^3+28\,x\right )+14\,x^2+2\,x^4+12\right )+{\ln \left (x\right )}^2\,\left (2\,x^4+16\,x^2\right )+4\,x^3\,{\ln \left (x\right )}^3+x^4\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (4\,x^3+24\,x\right )+{\mathrm {e}}^{6\,{\mathrm {e}}^{-{\mathrm {e}}^5}}\,\left ({\ln \left (x\right )}^2\,\left (2\,x^4+6\,x^2\right )+4\,x^3\,{\ln \left (x\right )}^3+x^4\,{\ln \left (x\right )}^4+\ln \left (x\right )\,\left (4\,x^3+4\,x\right )+2\,x^2+x^4+1\right )+12\,x^2+x^4+36} \,d x \]
[In]
[Out]