Integrand size = 175, antiderivative size = 30 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{e^{e^x}+x+\frac {\left (4+\frac {5}{\log \left (-3+x^2\right )}\right )^2}{e^4 x}} \]
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\[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=\int \frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{x^2 \left (-3+x^2\right ) \log ^3\left (-3+x^2\right )} \, dx \\ & = \int \left (\exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right )+\frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (100 x^2-75 \log \left (-3+x^2\right )+105 x^2 \log \left (-3+x^2\right )-120 \log ^2\left (-3+x^2\right )+40 x^2 \log ^2\left (-3+x^2\right )-48 \log ^3\left (-3+x^2\right )+16 \left (1+\frac {3 e^4}{16}\right ) x^2 \log ^3\left (-3+x^2\right )-e^4 x^4 \log ^3\left (-3+x^2\right )\right )}{x^2 \left (3-x^2\right ) \log ^3\left (-3+x^2\right )}\right ) \, dx \\ & = \int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \frac {\exp \left (-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \left (100 x^2-75 \log \left (-3+x^2\right )+105 x^2 \log \left (-3+x^2\right )-120 \log ^2\left (-3+x^2\right )+40 x^2 \log ^2\left (-3+x^2\right )-48 \log ^3\left (-3+x^2\right )+16 \left (1+\frac {3 e^4}{16}\right ) x^2 \log ^3\left (-3+x^2\right )-e^4 x^4 \log ^3\left (-3+x^2\right )\right )}{x^2 \left (3-x^2\right ) \log ^3\left (-3+x^2\right )} \, dx \\ & = \int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (100 x^2+15 \left (-5+7 x^2\right ) \log \left (-3+x^2\right )+40 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )-\left (-3+x^2\right ) \left (-16+e^4 x^2\right ) \log ^3\left (-3+x^2\right )\right )}{x^2 \left (3-x^2\right ) \log ^3\left (-3+x^2\right )} \, dx \\ & = \int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \left (\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-16+e^4 x^2\right )}{x^2}-\frac {100 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (-3+x^2\right ) \log ^3\left (-3+x^2\right )}-\frac {15 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-5+7 x^2\right )}{x^2 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )}-\frac {40 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )}\right ) \, dx \\ & = -\left (15 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-5+7 x^2\right )}{x^2 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )} \, dx\right )-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-100 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (-3+x^2\right ) \log ^3\left (-3+x^2\right )} \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \left (-16+e^4 x^2\right )}{x^2} \, dx \\ & = -\left (15 \int \left (\frac {5 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{3 x^2 \log ^2\left (-3+x^2\right )}+\frac {16 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{3 \left (-3+x^2\right ) \log ^2\left (-3+x^2\right )}\right ) \, dx\right )-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-100 \int \left (-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )}-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx+\int \left (\exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )-\frac {16 \exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2}\right ) \, dx \\ & = -\left (16 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2} \, dx\right )-25 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log ^2\left (-3+x^2\right )} \, dx-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-80 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (-3+x^2\right ) \log ^2\left (-3+x^2\right )} \, dx+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\int \exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx \\ & = -\left (16 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2} \, dx\right )-25 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log ^2\left (-3+x^2\right )} \, dx-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx-80 \int \left (-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}-x\right ) \log ^2\left (-3+x^2\right )}-\frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{2 \sqrt {3} \left (\sqrt {3}+x\right ) \log ^2\left (-3+x^2\right )}\right ) \, dx+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\int \exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx \\ & = -\left (16 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2} \, dx\right )-25 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log ^2\left (-3+x^2\right )} \, dx-40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{x^2 \log \left (-3+x^2\right )} \, dx+\frac {40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^2\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {40 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^2\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}-x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\frac {50 \int \frac {\exp \left (-4+e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right )}{\left (\sqrt {3}+x\right ) \log ^3\left (-3+x^2\right )} \, dx}{\sqrt {3}}+\int \exp \left (e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}\right ) \, dx+\int \exp \left (e^x+x+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}\right ) \, dx \\ \end{align*}
Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{e^{e^x}+\frac {16}{e^4 x}+x+\frac {25}{e^4 x \log ^2\left (-3+x^2\right )}+\frac {40}{e^4 x \log \left (-3+x^2\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(64\) vs. \(2(28)=56\).
Time = 0.19 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17
\[{\mathrm e}^{\frac {\left ({\mathrm e}^{4} \ln \left (x^{2}-3\right )^{2} x^{2}+x \ln \left (x^{2}-3\right )^{2} {\mathrm e}^{{\mathrm e}^{x}+4}+16 \ln \left (x^{2}-3\right )^{2}+40 \ln \left (x^{2}-3\right )+25\right ) {\mathrm e}^{-4}}{x \ln \left (x^{2}-3\right )^{2}}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.50 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{\left (\frac {{\left (x e^{\left (x + e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{2} + {\left ({\left (x^{2} - 4 \, x\right )} e^{4} + 16\right )} e^{x} \log \left (x^{2} - 3\right )^{2} + 40 \, e^{x} \log \left (x^{2} - 3\right ) + 25 \, e^{x}\right )} e^{\left (-x - 4\right )}}{x \log \left (x^{2} - 3\right )^{2}} + 4\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (24) = 48\).
Time = 1.84 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.00 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{\frac {x e^{4} e^{e^{x}} \log {\left (x^{2} - 3 \right )}^{2} + \left (x^{2} e^{4} + 16\right ) \log {\left (x^{2} - 3 \right )}^{2} + 40 \log {\left (x^{2} - 3 \right )} + 25}{x e^{4} \log {\left (x^{2} - 3 \right )}^{2}}} \]
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Time = 0.43 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.43 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=e^{\left (x + \frac {16 \, e^{\left (-4\right )}}{x} + \frac {40 \, e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )} + \frac {25 \, e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )^{2}} + e^{\left (e^{x}\right )}\right )} \]
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\[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx=\int { \frac {{\left ({\left (x^{4} - 3 \, x^{2}\right )} e^{\left (x + e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{3} - {\left (16 \, x^{2} - {\left (x^{4} - 3 \, x^{2}\right )} e^{4} - 48\right )} \log \left (x^{2} - 3\right )^{3} - 40 \, {\left (x^{2} - 3\right )} \log \left (x^{2} - 3\right )^{2} - 100 \, x^{2} - 15 \, {\left (7 \, x^{2} - 5\right )} \log \left (x^{2} - 3\right )\right )} e^{\left (\frac {{\left (x e^{\left (e^{x} + 4\right )} \log \left (x^{2} - 3\right )^{2} + {\left (x^{2} e^{4} + 16\right )} \log \left (x^{2} - 3\right )^{2} + 40 \, \log \left (x^{2} - 3\right ) + 25\right )} e^{\left (-4\right )}}{x \log \left (x^{2} - 3\right )^{2}} - 4\right )}}{{\left (x^{4} - 3 \, x^{2}\right )} \log \left (x^{2} - 3\right )^{3}} \,d x } \]
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Time = 12.82 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {e^{-4+\frac {25+40 \log \left (-3+x^2\right )+e^{4+e^x} x \log ^2\left (-3+x^2\right )+\left (16+e^4 x^2\right ) \log ^2\left (-3+x^2\right )}{e^4 x \log ^2\left (-3+x^2\right )}} \left (-100 x^2+\left (75-105 x^2\right ) \log \left (-3+x^2\right )+\left (120-40 x^2\right ) \log ^2\left (-3+x^2\right )+e^{4+e^x+x} \left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )+\left (48-16 x^2+e^4 \left (-3 x^2+x^4\right )\right ) \log ^3\left (-3+x^2\right )\right )}{\left (-3 x^2+x^4\right ) \log ^3\left (-3+x^2\right )} \, dx={\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{-4}}{x}}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{-4}}{x\,{\ln \left (x^2-3\right )}^2}}\,{\mathrm {e}}^{\frac {40\,{\mathrm {e}}^{-4}}{x\,\ln \left (x^2-3\right )}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^x \]
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