Integrand size = 118, antiderivative size = 27 \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=\frac {\log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{3 \left (e^x-x\right )} \]
[Out]
\[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=\int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{3 \left (e^x-x\right )^2 x^2 \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx \\ & = \frac {1}{3} \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2 x^2 \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx \\ & = \frac {1}{3} \int \left (-\frac {(-1+x) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2}-\frac {-x+3 \log (x)-x \log (x)+x^2 \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right ) x^2 \log (x) \log \left (-10 e^{3/x} x \log (x)\right )}\right ) \, dx \\ & = -\left (\frac {1}{3} \int \frac {(-1+x) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2} \, dx\right )-\frac {1}{3} \int \frac {-x+3 \log (x)-x \log (x)+x^2 \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right ) x^2 \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx \\ & = -\left (\frac {1}{3} \int \left (\frac {3}{\left (e^x-x\right ) x^2 \log \left (-10 e^{3/x} x \log (x)\right )}-\frac {1}{\left (e^x-x\right ) x \log \left (-10 e^{3/x} x \log (x)\right )}-\frac {1}{\left (e^x-x\right ) x \log (x) \log \left (-10 e^{3/x} x \log (x)\right )}+\frac {\log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{e^x-x}\right ) \, dx\right )-\frac {1}{3} \int \left (-\frac {\log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2}+\frac {x \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2}\right ) \, dx \\ & = \frac {1}{3} \int \frac {1}{\left (e^x-x\right ) x \log \left (-10 e^{3/x} x \log (x)\right )} \, dx+\frac {1}{3} \int \frac {1}{\left (e^x-x\right ) x \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx+\frac {1}{3} \int \frac {\log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2} \, dx-\frac {1}{3} \int \frac {\log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{e^x-x} \, dx-\frac {1}{3} \int \frac {x \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (e^x-x\right )^2} \, dx-\int \frac {1}{\left (e^x-x\right ) x^2 \log \left (-10 e^{3/x} x \log (x)\right )} \, dx \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=\frac {\log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{3 \left (e^x-x\right )} \]
[In]
[Out]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.44 (sec) , antiderivative size = 195, normalized size of antiderivative = 7.22
\[-\frac {\ln \left (\ln \left (2\right )+\ln \left (5\right )+i \pi +\ln \left (x \right )+\ln \left ({\mathrm e}^{\frac {3}{x}}\right )+\ln \left (\ln \left (x \right )\right )-\frac {i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right ) \left (-\operatorname {csgn}\left (i {\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )+\operatorname {csgn}\left (i {\mathrm e}^{\frac {3}{x}}\right )\right ) \left (-\operatorname {csgn}\left (i {\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )+\operatorname {csgn}\left (i \ln \left (x \right )\right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x \,{\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right ) \left (-\operatorname {csgn}\left (i x \,{\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )+\operatorname {csgn}\left (i x \right )\right ) \left (-\operatorname {csgn}\left (i x \,{\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )+\operatorname {csgn}\left (i {\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )\right )}{2}+i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )^{2} \left (\operatorname {csgn}\left (i x \,{\mathrm e}^{\frac {3}{x}} \ln \left (x \right )\right )-1\right )\right )}{3 \left (x -{\mathrm e}^{x}\right )}\]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=-\frac {\log \left (\log \left (-10 \, x e^{\frac {3}{x}} \log \left (x\right )\right )\right )}{3 \, {\left (x - e^{x}\right )}} \]
[In]
[Out]
Time = 1.45 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=- \frac {\log {\left (\log {\left (- 10 x e^{\frac {3}{x}} \log {\left (x \right )} \right )} \right )}}{3 x - 3 e^{x}} \]
[In]
[Out]
none
Time = 0.34 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=-\frac {\log \left (x {\left (\log \left (5\right ) + \log \left (2\right )\right )} + x \log \left (x\right ) + x \log \left (-\log \left (x\right )\right ) + 3\right ) - \log \left (x\right )}{3 \, {\left (x - e^{x}\right )}} \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=-\frac {\log \left (x \log \left (x\right ) + x \log \left (-10 \, \log \left (x\right )\right ) + 3\right ) - \log \left (x\right )}{3 \, {\left (x - e^{x}\right )}} \]
[In]
[Out]
Timed out. \[ \int \frac {e^x x-x^2+\left (e^x (-3+x)+3 x-x^2\right ) \log (x)+\left (x^2-e^x x^2\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right ) \log \left (\log \left (-10 e^{3/x} x \log (x)\right )\right )}{\left (3 e^{2 x} x^2-6 e^x x^3+3 x^4\right ) \log (x) \log \left (-10 e^{3/x} x \log (x)\right )} \, dx=\int \frac {x\,{\mathrm {e}}^x+\ln \left (x\right )\,\left (3\,x+{\mathrm {e}}^x\,\left (x-3\right )-x^2\right )-x^2-\ln \left (\ln \left (-10\,x\,{\mathrm {e}}^{3/x}\,\ln \left (x\right )\right )\right )\,\ln \left (-10\,x\,{\mathrm {e}}^{3/x}\,\ln \left (x\right )\right )\,\ln \left (x\right )\,\left (x^2\,{\mathrm {e}}^x-x^2\right )}{\ln \left (-10\,x\,{\mathrm {e}}^{3/x}\,\ln \left (x\right )\right )\,\ln \left (x\right )\,\left (3\,x^2\,{\mathrm {e}}^{2\,x}-6\,x^3\,{\mathrm {e}}^x+3\,x^4\right )} \,d x \]
[In]
[Out]