Integrand size = 278, antiderivative size = 34 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4 (1+x)))\right )}{x}} x \]
[Out]
\[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\int \frac {\exp \left (-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}\right ) \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}\right ) \left (\left (6+e^3\right ) x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx \\ & = \int \frac {e \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-\left (\left (6+e^3\right ) x^2\right )+x^3-x (1+x) \left (-7-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x))-(1+x) \left (-6-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{x (1+x) (x-\log (4+4 x))} \, dx \\ & = e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-\left (\left (6+e^3\right ) x^2\right )+x^3-x (1+x) \left (-7-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x))-(1+x) \left (-6-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{x (1+x) (x-\log (4+4 x))} \, dx \\ & = e \int \left (\frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-6 \left (1+\frac {e^3}{6}\right ) x+x^2+7 \left (1+\frac {e^3}{7}\right ) x \log (x-\log (4+4 x))+6 \left (1+\frac {e^3}{6}\right ) x^2 \log (x-\log (4+4 x))-x^3 \log (x-\log (4+4 x))-7 \left (1+\frac {e^3}{7}\right ) \log (4+4 x) \log (x-\log (4+4 x))-6 \left (1+\frac {e^3}{6}\right ) x \log (4+4 x) \log (x-\log (4+4 x))+x^2 \log (4+4 x) \log (x-\log (4+4 x))\right )}{(1+x) (x-\log (4+4 x))}+\frac {\left (6+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}\right ) \, dx \\ & = e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (-6 \left (1+\frac {e^3}{6}\right ) x+x^2+7 \left (1+\frac {e^3}{7}\right ) x \log (x-\log (4+4 x))+6 \left (1+\frac {e^3}{6}\right ) x^2 \log (x-\log (4+4 x))-x^3 \log (x-\log (4+4 x))-7 \left (1+\frac {e^3}{7}\right ) \log (4+4 x) \log (x-\log (4+4 x))-6 \left (1+\frac {e^3}{6}\right ) x \log (4+4 x) \log (x-\log (4+4 x))+x^2 \log (4+4 x) \log (x-\log (4+4 x))\right )}{(1+x) (x-\log (4+4 x))} \, dx+e \int \frac {\left (6+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx \\ & = e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \left (x \left (-6-e^3+x\right )-(1+x) \left (-7-e^3+x\right ) (x-\log (4+4 x)) \log (x-\log (4+4 x))\right )}{(1+x) (x-\log (4+4 x))} \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx \\ & = e \int \left (\frac {x \left (-6-e^3+x\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))}+\left (7+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}\right ) \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx \\ & = e \int \frac {x \left (-6-e^3+x\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))} \, dx+e \int \left (7+e^3-x\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx \\ & = e \int \left (-\frac {7 \left (1+\frac {e^3}{7}\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)}+\frac {x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)}+\frac {\left (7+e^3\right ) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))}\right ) \, dx+e \int \left (7 \left (1+\frac {e^3}{7}\right ) \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}-x \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}\right ) \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx \\ & = e \int \frac {x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)} \, dx-e \int x \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \, dx+e \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x} \, dx-\left (e \left (7+e^3\right )\right ) \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{x-\log (4+4 x)} \, dx+\left (e \left (7+e^3\right )\right ) \int \frac {\left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}}}{(1+x) (x-\log (4+4 x))} \, dx+\left (e \left (7+e^3\right )\right ) \int \log (x-\log (4+4 x)) \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1-\frac {1}{x}} \, dx \\ \end{align*}
Time = 0.30 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=e x \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )^{-1/x} \]
[In]
[Out]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.27 (sec) , antiderivative size = 205, normalized size of antiderivative = 6.03
\[x \left ({\mathrm e}^{3}-x +6\right )^{-\frac {1}{x}} \ln \left (-\ln \left (4+4 x \right )+x \right )^{-\frac {1}{x}} {\mathrm e}^{\frac {i \pi {\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )}^{3}-i \pi {\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )}^{2} \operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right )\right )-i \pi {\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right )}^{2} \operatorname {csgn}\left (i \left ({\mathrm e}^{3}-x +6\right )\right )+i \pi \,\operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right ) \left ({\mathrm e}^{3}-x +6\right )\right ) \operatorname {csgn}\left (i \ln \left (-\ln \left (4+4 x \right )+x \right )\right ) \operatorname {csgn}\left (i \left ({\mathrm e}^{3}-x +6\right )\right )+2 x}{2 x}}\]
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=x e^{\left (\frac {x - \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )}{x}\right )} \]
[In]
[Out]
Timed out. \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\text {Timed out} \]
[In]
[Out]
none
Time = 0.46 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.09 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=x e^{\left (-\frac {\log \left (-x + e^{3} + 6\right )}{x} - \frac {\log \left (\log \left (x - 2 \, \log \left (2\right ) - \log \left (x + 1\right )\right )\right )}{x} + 1\right )} \]
[In]
[Out]
\[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\int { -\frac {{\left (x^{3} - x^{2} e^{3} - {\left (x^{3} - 5 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - {\left (x^{2} - {\left (x + 1\right )} e^{3} - 5 \, x - 6\right )} \log \left (4 \, x + 4\right ) - 6 \, x\right )} \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right ) \log \left (x - \log \left (4 \, x + 4\right )\right ) - 6 \, x^{2} - {\left (x^{4} - 6 \, x^{3} - 7 \, x^{2} - {\left (x^{3} + x^{2}\right )} e^{3} - {\left (x^{3} - 6 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - 7 \, x\right )} \log \left (4 \, x + 4\right )\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )} e^{\left (\frac {x - \log \left (-{\left (x - e^{3} - 6\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )\right )}{x}\right )}}{{\left (x^{4} - 5 \, x^{3} - 6 \, x^{2} - {\left (x^{3} + x^{2}\right )} e^{3} - {\left (x^{3} - 5 \, x^{2} - {\left (x^{2} + x\right )} e^{3} - 6 \, x\right )} \log \left (4 \, x + 4\right )\right )} \log \left (x - \log \left (4 \, x + 4\right )\right )} \,d x } \]
[In]
[Out]
Time = 19.38 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.53 \[ \int \frac {e^{-\frac {-x+\log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )}{x}} \left (6 x^2+e^3 x^2-x^3+\left (-7 x^2-6 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (7 x+6 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))+\left (-6 x-5 x^2+x^3+e^3 \left (-x-x^2\right )+\left (6+5 x-x^2+e^3 (1+x)\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x)) \log \left (\left (6+e^3-x\right ) \log (x-\log (4+4 x))\right )\right )}{\left (-6 x^2-5 x^3+x^4+e^3 \left (-x^2-x^3\right )+\left (6 x+5 x^2-x^3+e^3 \left (x+x^2\right )\right ) \log (4+4 x)\right ) \log (x-\log (4+4 x))} \, dx=\frac {x\,\mathrm {e}}{{\left (6\,\ln \left (x-\ln \left (4\,x+4\right )\right )+\ln \left (x-\ln \left (4\,x+4\right )\right )\,{\mathrm {e}}^3-x\,\ln \left (x-\ln \left (4\,x+4\right )\right )\right )}^{1/x}} \]
[In]
[Out]