Integrand size = 172, antiderivative size = 26 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{3+\frac {5}{-\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}+x}} \]
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\[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=\int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left (-1280 x+5 x^2-\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{(256-x) \left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x} \, dx \\ & = \int \left (-\frac {5 \exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}+\frac {20 \exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-512 \log \left ((-256+x)^2\right )+2 x \log \left ((-256+x)^2\right )+x \log \left (x^2\right )\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x) x}\right ) \, dx \\ & = -\left (5 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx\right )+20 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-512 \log \left ((-256+x)^2\right )+2 x \log \left ((-256+x)^2\right )+x \log \left (x^2\right )\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x) x} \, dx \\ & = -\left (5 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx\right )+20 \int \left (\frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-512 \log \left ((-256+x)^2\right )+2 x \log \left ((-256+x)^2\right )+x \log \left (x^2\right )\right )}{256 \left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)}-\frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-512 \log \left ((-256+x)^2\right )+2 x \log \left ((-256+x)^2\right )+x \log \left (x^2\right )\right )}{256 \left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x}\right ) \, dx \\ & = \frac {5}{64} \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-512 \log \left ((-256+x)^2\right )+2 x \log \left ((-256+x)^2\right )+x \log \left (x^2\right )\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)} \, dx-\frac {5}{64} \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left (x^2\right ) \left (-512 \log \left ((-256+x)^2\right )+2 x \log \left ((-256+x)^2\right )+x \log \left (x^2\right )\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x} \, dx-5 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx \\ & = -\left (\frac {5}{64} \int \left (\frac {2 \exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}-\frac {512 \exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x}+\frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}\right ) \, dx\right )+\frac {5}{64} \int \left (-\frac {512 \exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)}+\frac {2 \exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} x \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)}+\frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} x \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)}\right ) \, dx-5 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx \\ & = -\left (\frac {5}{64} \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx\right )+\frac {5}{64} \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} x \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)} \, dx-\frac {5}{32} \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx+\frac {5}{32} \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} x \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)} \, dx-5 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx-40 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)} \, dx+40 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x} \, dx \\ & = -\left (\frac {5}{64} \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx\right )+\frac {5}{64} \int \left (\frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}+\frac {256 e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)}\right ) \, dx-\frac {5}{32} \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx+\frac {5}{32} \int \left (\frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2}+\frac {256 e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)}\right ) \, dx-5 \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}}}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx-40 \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)} \, dx+40 \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x} \, dx \\ & = -\left (5 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2} \, dx\right )+20 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log ^2\left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 (-256+x)} \, dx+40 \int \frac {\exp \left (\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}\right ) \left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )} \log \left ((-256+x)^2\right ) \log \left (x^2\right )}{\left (\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x\right )^2 x} \, dx \\ \end{align*}
Time = 0.28 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{3-\frac {5}{\left ((-256+x)^2\right )^{2 \log ^2\left (x^2\right )}-x}} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.56 (sec) , antiderivative size = 266, normalized size of antiderivative = 10.23
\[{\mathrm e}^{\frac {-3 \,{\mathrm e}^{\frac {\left (-i \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{3} \pi +2 i \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{2} \operatorname {csgn}\left (i \left (x -256\right )\right ) \pi -i \operatorname {csgn}\left (i \left (x -256\right )^{2}\right ) \operatorname {csgn}\left (i \left (x -256\right )\right )^{2} \pi +4 \ln \left (x -256\right )\right ) {\left (4 \ln \left (x \right )-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )}^{2}}{4}}+3 x +5}{-{\mathrm e}^{\frac {\left (-i \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{3} \pi +2 i \operatorname {csgn}\left (i \left (x -256\right )^{2}\right )^{2} \operatorname {csgn}\left (i \left (x -256\right )\right ) \pi -i \operatorname {csgn}\left (i \left (x -256\right )^{2}\right ) \operatorname {csgn}\left (i \left (x -256\right )\right )^{2} \pi +4 \ln \left (x -256\right )\right ) {\left (4 \ln \left (x \right )-i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )^{2}+2 i \pi \operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}\right )}^{2}}{4}}+x}}\]
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Time = 0.28 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.88 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{\left (\frac {3 \, {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - 3 \, x - 5}{{\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - x}\right )} \]
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Timed out. \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=\text {Timed out} \]
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Time = 0.41 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=e^{\left (-\frac {5}{{\left (x - 256\right )}^{16 \, \log \left (x\right )^{2}} - x} + 3\right )} \]
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\[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx=\int { \frac {5 \, {\left (4 \, {\left (2 \, {\left (x - 256\right )} \log \left (x^{2} - 512 \, x + 65536\right ) \log \left (x^{2}\right ) + x \log \left (x^{2}\right )^{2}\right )} {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - x^{2} + 256 \, x\right )} e^{\left (\frac {3 \, {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - 3 \, x - 5}{{\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}} - x}\right )}}{x^{4} - 256 \, x^{3} + {\left (x^{2} - 256 \, x\right )} {\left (x^{2} - 512 \, x + 65536\right )}^{4 \, \log \left (x^{2}\right )^{2}} - 2 \, {\left (x^{3} - 256 \, x^{2}\right )} {\left (x^{2} - 512 \, x + 65536\right )}^{2 \, \log \left (x^{2}\right )^{2}}} \,d x } \]
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Time = 13.28 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.73 \[ \int \frac {e^{\frac {-5-3 x+3 \left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}{-x+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )}}} \left (1280 x-5 x^2+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (20 x \log ^2\left (x^2\right )+(-10240+40 x) \log \left (x^2\right ) \log \left (65536-512 x+x^2\right )\right )\right )}{-256 x^3+x^4+\left (65536-512 x+x^2\right )^{4 \log ^2\left (x^2\right )} \left (-256 x+x^2\right )+\left (65536-512 x+x^2\right )^{2 \log ^2\left (x^2\right )} \left (512 x^2-2 x^3\right )} \, dx={\mathrm {e}}^{-\frac {3\,{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}{x-{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}}\,{\mathrm {e}}^{\frac {3\,x}{x-{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}}\,{\mathrm {e}}^{\frac {5}{x-{\left (x^2-512\,x+65536\right )}^{2\,{\ln \left (x^2\right )}^2}}} \]
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