Integrand size = 151, antiderivative size = 29 \[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\frac {2 \left (-2+\log \left (\log \left (\frac {\log (x)}{\frac {37}{4}-e^{1-x}}\right )\right )\right )}{5 x} \]
[Out]
\[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {8 e-74 e^x+2 \log (x) \left (4 e x+\left (-4 e+37 e^x\right ) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right ) \left (-2+\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )\right )\right )}{5 \left (4 e-37 e^x\right ) x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = \frac {1}{5} \int \frac {8 e-74 e^x+2 \log (x) \left (4 e x+\left (-4 e+37 e^x\right ) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right ) \left (-2+\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )\right )\right )}{\left (4 e-37 e^x\right ) x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = \frac {1}{5} \int \left (-\frac {8 e}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}-\frac {2 \left (-1-2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )+\log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right ) \log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )\right )}{x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}\right ) \, dx \\ & = -\left (\frac {2}{5} \int \frac {-1-2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )+\log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right ) \log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx\right )-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = -\left (\frac {2}{5} \int \frac {-2-\frac {1}{\log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}+\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2} \, dx\right )-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = -\left (\frac {2}{5} \int \left (\frac {-1-2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}{x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}+\frac {\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2}\right ) \, dx\right )-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = -\left (\frac {2}{5} \int \frac {-1-2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}{x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx\right )-\frac {2}{5} \int \frac {\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2} \, dx-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = -\left (\frac {2}{5} \int \frac {-2-\frac {1}{\log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}}{x^2} \, dx\right )-\frac {2}{5} \int \frac {\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2} \, dx-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = -\left (\frac {2}{5} \int \left (-\frac {2}{x^2}-\frac {1}{x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )}\right ) \, dx\right )-\frac {2}{5} \int \frac {\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2} \, dx-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ & = -\frac {4}{5 x}+\frac {2}{5} \int \frac {1}{x^2 \log (x) \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx-\frac {2}{5} \int \frac {\log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x^2} \, dx-\frac {1}{5} (8 e) \int \frac {1}{\left (-4 e+37 e^x\right ) x \log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )} \, dx \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.21 \[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\frac {1}{5} \left (-\frac {4}{x}+\frac {2 \log \left (\log \left (\frac {4 e^x \log (x)}{-4 e+37 e^x}\right )\right )}{x}\right ) \]
[In]
[Out]
Time = 15.24 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97
method | result | size |
parallelrisch | \(\frac {-1184+592 \ln \left (\ln \left (-\frac {4 \ln \left (x \right )}{4 \,{\mathrm e}^{1-x}-37}\right )\right )}{1480 x}\) | \(28\) |
risch | \(\frac {2 \ln \left (i \pi +\ln \left (\ln \left (x \right )\right )-\ln \left ({\mathrm e}^{1-x}-\frac {37}{4}\right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \ln \left (x \right )}{{\mathrm e}^{1-x}-\frac {37}{4}}\right ) \left (-\operatorname {csgn}\left (\frac {i \ln \left (x \right )}{{\mathrm e}^{1-x}-\frac {37}{4}}\right )+\operatorname {csgn}\left (i \ln \left (x \right )\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \ln \left (x \right )}{{\mathrm e}^{1-x}-\frac {37}{4}}\right )+\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{1-x}-\frac {37}{4}}\right )\right )}{2}+i \pi \operatorname {csgn}\left (\frac {i \ln \left (x \right )}{{\mathrm e}^{1-x}-\frac {37}{4}}\right )^{2} \left (\operatorname {csgn}\left (\frac {i \ln \left (x \right )}{{\mathrm e}^{1-x}-\frac {37}{4}}\right )-1\right )\right )}{5 x}-\frac {4}{5 x}\) | \(150\) |
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86 \[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\frac {2 \, {\left (\log \left (\log \left (-\frac {4 \, \log \left (x\right )}{4 \, e^{\left (-x + 1\right )} - 37}\right )\right ) - 2\right )}}{5 \, x} \]
[In]
[Out]
Time = 18.73 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\frac {2 \log {\left (\log {\left (- \frac {4 \log {\left (x \right )}}{4 e^{1 - x} - 37} \right )} \right )}}{5 x} - \frac {4}{5 x} \]
[In]
[Out]
none
Time = 0.34 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\frac {2 \, {\left (\log \left (x + 2 \, \log \left (2\right ) - \log \left (-4 \, e + 37 \, e^{x}\right ) + \log \left (\log \left (x\right )\right )\right ) - 2\right )}}{5 \, x} \]
[In]
[Out]
\[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\int { -\frac {2 \, {\left ({\left (4 \, e^{\left (-x + 1\right )} - 37\right )} \log \left (x\right ) \log \left (-\frac {4 \, \log \left (x\right )}{4 \, e^{\left (-x + 1\right )} - 37}\right ) \log \left (\log \left (-\frac {4 \, \log \left (x\right )}{4 \, e^{\left (-x + 1\right )} - 37}\right )\right ) - 4 \, x e^{\left (-x + 1\right )} \log \left (x\right ) - 2 \, {\left (4 \, e^{\left (-x + 1\right )} - 37\right )} \log \left (x\right ) \log \left (-\frac {4 \, \log \left (x\right )}{4 \, e^{\left (-x + 1\right )} - 37}\right ) - 4 \, e^{\left (-x + 1\right )} + 37\right )}}{5 \, {\left (4 \, x^{2} e^{\left (-x + 1\right )} - 37 \, x^{2}\right )} \log \left (x\right ) \log \left (-\frac {4 \, \log \left (x\right )}{4 \, e^{\left (-x + 1\right )} - 37}\right )} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {-74+8 e^{1-x}+8 e^{1-x} x \log (x)+\left (-148+16 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )+\left (74-8 e^{1-x}\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right ) \log \left (\log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )\right )}{\left (-185 x^2+20 e^{1-x} x^2\right ) \log (x) \log \left (-\frac {4 \log (x)}{-37+4 e^{1-x}}\right )} \, dx=\int \frac {8\,{\mathrm {e}}^{1-x}+\ln \left (-\frac {4\,\ln \left (x\right )}{4\,{\mathrm {e}}^{1-x}-37}\right )\,\ln \left (x\right )\,\left (16\,{\mathrm {e}}^{1-x}-148\right )+8\,x\,{\mathrm {e}}^{1-x}\,\ln \left (x\right )-\ln \left (-\frac {4\,\ln \left (x\right )}{4\,{\mathrm {e}}^{1-x}-37}\right )\,\ln \left (\ln \left (-\frac {4\,\ln \left (x\right )}{4\,{\mathrm {e}}^{1-x}-37}\right )\right )\,\ln \left (x\right )\,\left (8\,{\mathrm {e}}^{1-x}-74\right )-74}{\ln \left (-\frac {4\,\ln \left (x\right )}{4\,{\mathrm {e}}^{1-x}-37}\right )\,\ln \left (x\right )\,\left (20\,x^2\,{\mathrm {e}}^{1-x}-185\,x^2\right )} \,d x \]
[In]
[Out]