Integrand size = 105, antiderivative size = 29 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=\frac {2 e^{e^8} x}{\left (5-e^x\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \]
[Out]
\[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=\int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (5-e^x\right )^2 \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx \\ & = \int \left (\frac {10 e^{e^8} x}{\left (-5+e^x\right )^2 \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}+\frac {2 e^{e^8} \left (-2+2 \log (x)-\log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )+x \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )\right )}{\left (-5+e^x\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}\right ) \, dx \\ & = \left (2 e^{e^8}\right ) \int \frac {-2+2 \log (x)-\log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )+x \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (-5+e^x\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx+\left (10 e^{e^8}\right ) \int \frac {x}{\left (-5+e^x\right )^2 \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx \\ & = \left (2 e^{e^8}\right ) \int \frac {2-\log (x) \left (2+(-1+x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )\right )}{\left (5-e^x\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx+\left (10 e^{e^8}\right ) \int \frac {x}{\left (-5+e^x\right )^2 \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx \\ & = \left (2 e^{e^8}\right ) \int \left (\frac {2}{\left (-5+e^x\right ) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}-\frac {2}{\left (-5+e^x\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}-\frac {1}{\left (-5+e^x\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}+\frac {x}{\left (-5+e^x\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}\right ) \, dx+\left (10 e^{e^8}\right ) \int \frac {x}{\left (-5+e^x\right )^2 \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx \\ & = -\left (\left (2 e^{e^8}\right ) \int \frac {1}{\left (-5+e^x\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx\right )+\left (2 e^{e^8}\right ) \int \frac {x}{\left (-5+e^x\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx+\left (4 e^{e^8}\right ) \int \frac {1}{\left (-5+e^x\right ) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx-\left (4 e^{e^8}\right ) \int \frac {1}{\left (-5+e^x\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx+\left (10 e^{e^8}\right ) \int \frac {x}{\left (-5+e^x\right )^2 \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx \\ \end{align*}
Time = 0.62 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 e^{e^8} x}{\left (-5+e^x\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \]
[In]
[Out]
Time = 157.73 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86
method | result | size |
parallelrisch | \(-\frac {2 \,{\mathrm e}^{{\mathrm e}^{8}} x}{\ln \left (\ln \left (\frac {x}{\ln \left (x \right )}\right )^{2}\right ) \left ({\mathrm e}^{x}-5\right )}\) | \(25\) |
risch | \(\text {Expression too large to display}\) | \(712\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 \, x e^{\left (e^{8}\right )}}{{\left (e^{x} - 5\right )} \log \left (\log \left (\frac {x}{\log \left (x\right )}\right )^{2}\right )} \]
[In]
[Out]
Time = 0.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.17 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=- \frac {2 x e^{e^{8}}}{e^{x} \log {\left (\log {\left (\frac {x}{\log {\left (x \right )}} \right )}^{2} \right )} - 5 \log {\left (\log {\left (\frac {x}{\log {\left (x \right )}} \right )}^{2} \right )}} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.79 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {x e^{\left (e^{8}\right )}}{{\left (e^{x} - 5\right )} \log \left (\log \left (x\right ) - \log \left (\log \left (x\right )\right )\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (24) = 48\).
Time = 49.18 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.72 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2 \, x e^{\left (e^{8}\right )}}{e^{x} \log \left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) \log \left (\log \left (x\right )\right ) + \log \left (\log \left (x\right )\right )^{2}\right ) - 5 \, \log \left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) \log \left (\log \left (x\right )\right ) + \log \left (\log \left (x\right )\right )^{2}\right )} \]
[In]
[Out]
Time = 14.29 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83 \[ \int \frac {e^{e^8} \left (20-4 e^x\right )+e^{e^8} \left (-20+4 e^x\right ) \log (x)+e^{e^8} \left (10+e^x (-2+2 x)\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log \left (\log ^2\left (\frac {x}{\log (x)}\right )\right )}{\left (25-10 e^x+e^{2 x}\right ) \log (x) \log \left (\frac {x}{\log (x)}\right ) \log ^2\left (\log ^2\left (\frac {x}{\log (x)}\right )\right )} \, dx=-\frac {2\,x\,{\mathrm {e}}^{{\mathrm {e}}^8}}{\ln \left ({\ln \left (\frac {x}{\ln \left (x\right )}\right )}^2\right )\,\left ({\mathrm {e}}^x-5\right )} \]
[In]
[Out]