Integrand size = 115, antiderivative size = 26 \[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\frac {\log \left (x \left (1-e^{-e^{e^{7+x^2}}} \log (x)\right )\right )}{x} \]
[Out]
\[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {2 e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)}-\frac {1-e^{e^{e^{7+x^2}}}+\log (x)+e^{e^{e^{7+x^2}}} \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )-\log (x) \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )}\right ) \, dx \\ & = 2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1-e^{e^{e^{7+x^2}}}+\log (x)+e^{e^{e^{7+x^2}}} \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )-\log (x) \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx \\ & = 2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \left (\frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )}+\frac {-1+\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2}\right ) \, dx \\ & = 2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx-\int \frac {-1+\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2} \, dx \\ & = 2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx-\int \left (-\frac {1}{x^2}+\frac {\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2}\right ) \, dx \\ & = -\frac {1}{x}+2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx-\int \frac {\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2} \, dx \\ \end{align*}
Time = 0.18 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96 \[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\frac {\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x} \]
[In]
[Out]
Time = 12.71 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23
method | result | size |
parallelrisch | \(\frac {\ln \left (-x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}{x}\) | \(32\) |
risch | \(-\frac {\ln \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}{x}+\frac {-2 i \pi {\operatorname {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}^{2}-i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right ) \operatorname {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )+i \pi \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}^{2}-i \pi \,\operatorname {csgn}\left (i \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right ) \operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right ) \operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right )+i \pi \,\operatorname {csgn}\left (i \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right ) \operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right )^{2}+i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right ) \operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right )^{2}-i \pi \operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right )^{3}+i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )\right ) {\operatorname {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}^{2}+i \pi {\operatorname {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}^{3}+2 i \pi +2 \ln \left (x \right )+2 \ln \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \left (x \right )\right )}{2 x}\) | \(470\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\frac {\log \left ({\left (x e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - x \log \left (x\right )\right )} e^{\left (-e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )}\right )}{x} \]
[In]
[Out]
Time = 29.11 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\frac {\log {\left (\left (x e^{e^{e^{x^{2} + 7}}} - x \log {\left (x \right )}\right ) e^{- e^{e^{x^{2} + 7}}} \right )}}{x} \]
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.27 \[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=-\frac {e^{\left (e^{\left (x^{2} + 7\right )}\right )} - \log \left (x\right ) - \log \left (e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - \log \left (x\right )\right )}{x} \]
[In]
[Out]
\[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\int { \frac {2 \, x^{2} e^{\left (x^{2} + e^{\left (x^{2} + 7\right )} + 7\right )} \log \left (x\right ) - {\left (e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - \log \left (x\right )\right )} \log \left ({\left (x e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - x \log \left (x\right )\right )} e^{\left (-e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )}\right ) + e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - \log \left (x\right ) - 1}{x^{2} e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - x^{2} \log \left (x\right )} \,d x } \]
[In]
[Out]
Time = 12.47 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88 \[ \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx=\frac {\ln \left (x-x\,{\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^7}}\,\ln \left (x\right )\right )}{x} \]
[In]
[Out]