Integrand size = 110, antiderivative size = 27 \[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=e^{(3-x-\log (3+x)) \left (5-\log \left (2+\frac {\log (x)}{4}\right )\right )} \]
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\[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=\int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{x (3+x)^6 (8+\log (x))} \, dx \\ & = \int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) \left (-9-160 x-39 x^2-5 x (4+x) \log (x)+(3+x) \log (3+x)+x (4+x) (8+\log (x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{x (3+x)^6 (8+\log (x))} \, dx \\ & = \int \left (-\frac {160 \exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^6 (8+\log (x))}-\frac {9 \exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{x (3+x)^6 (8+\log (x))}-\frac {39 \exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) x}{(3+x)^6 (8+\log (x))}-\frac {5 \exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) (4+x) \log (x)}{(3+x)^6 (8+\log (x))}+\frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) \log (3+x)}{x (3+x)^5 (8+\log (x))}+\frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) (4+x) \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^6}\right ) \, dx \\ & = -\left (5 \int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) (4+x) \log (x)}{(3+x)^6 (8+\log (x))} \, dx\right )-9 \int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{x (3+x)^6 (8+\log (x))} \, dx-39 \int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) x}{(3+x)^6 (8+\log (x))} \, dx-160 \int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^6 (8+\log (x))} \, dx+\int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) \log (3+x)}{x (3+x)^5 (8+\log (x))} \, dx+\int \frac {\exp \left (15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )\right ) (4+x) \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^6} \, dx \\ & = -\left (5 \int \left (\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} (4+x)}{(3+x)^6}-\frac {8 e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} (4+x)}{(3+x)^6 (8+\log (x))}\right ) \, dx\right )-9 \int \left (\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{729 x (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{3 (3+x)^6 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{9 (3+x)^5 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{27 (3+x)^4 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{81 (3+x)^3 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{243 (3+x)^2 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{729 (3+x) (8+\log (x))}\right ) \, dx-39 \int \left (-\frac {3 e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))}+\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))}\right ) \, dx-160 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx+\int \left (\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{243 x (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{3 (3+x)^5 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{9 (3+x)^4 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{27 (3+x)^3 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{81 (3+x)^2 (8+\log (x))}-\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{243 (3+x) (8+\log (x))}\right ) \, dx+\int \left (\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^6}+\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^5}\right ) \, dx \\ & = \frac {1}{243} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{x (8+\log (x))} \, dx-\frac {1}{243} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x) (8+\log (x))} \, dx-\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{x (8+\log (x))} \, dx+\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x) (8+\log (x))} \, dx-\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^2 (8+\log (x))} \, dx+\frac {1}{27} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^2 (8+\log (x))} \, dx-\frac {1}{27} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^3 (8+\log (x))} \, dx+\frac {1}{9} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^3 (8+\log (x))} \, dx-\frac {1}{9} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^4 (8+\log (x))} \, dx+\frac {1}{3} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^4 (8+\log (x))} \, dx-\frac {1}{3} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^5 (8+\log (x))} \, dx+3 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx-5 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} (4+x)}{(3+x)^6} \, dx-39 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+40 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} (4+x)}{(3+x)^6 (8+\log (x))} \, dx+117 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx-160 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^6} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^5} \, dx \\ & = \frac {1}{243} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{x (8+\log (x))} \, dx-\frac {1}{243} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x) (8+\log (x))} \, dx-\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{x (8+\log (x))} \, dx+\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x) (8+\log (x))} \, dx-\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^2 (8+\log (x))} \, dx+\frac {1}{27} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^2 (8+\log (x))} \, dx-\frac {1}{27} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^3 (8+\log (x))} \, dx+\frac {1}{9} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^3 (8+\log (x))} \, dx-\frac {1}{9} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^4 (8+\log (x))} \, dx+\frac {1}{3} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^4 (8+\log (x))} \, dx-\frac {1}{3} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^5 (8+\log (x))} \, dx+3 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx-5 \int \left (\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6}+\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5}\right ) \, dx-39 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+40 \int \left (\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))}+\frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))}\right ) \, dx+117 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx-160 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^6} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^5} \, dx \\ & = \frac {1}{243} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{x (8+\log (x))} \, dx-\frac {1}{243} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x) (8+\log (x))} \, dx-\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{x (8+\log (x))} \, dx+\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x) (8+\log (x))} \, dx-\frac {1}{81} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^2 (8+\log (x))} \, dx+\frac {1}{27} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^2 (8+\log (x))} \, dx-\frac {1}{27} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^3 (8+\log (x))} \, dx+\frac {1}{9} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^3 (8+\log (x))} \, dx-\frac {1}{9} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^4 (8+\log (x))} \, dx+\frac {1}{3} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^4 (8+\log (x))} \, dx-\frac {1}{3} \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log (3+x)}{(3+x)^5 (8+\log (x))} \, dx+3 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx-5 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6} \, dx-5 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5} \, dx-39 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+40 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx+40 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+117 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx-160 \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^6 (8+\log (x))} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )}}{(3+x)^5 (8+\log (x))} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^6} \, dx+\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \log \left (\frac {1}{4} (8+\log (x))\right )}{(3+x)^5} \, dx \\ \end{align*}
\[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=\int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx \]
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Time = 19.12 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00
method | result | size |
risch | \(\frac {\left (\frac {\ln \left (x \right )}{4}+2\right )^{\ln \left (3+x \right )+x -3} {\mathrm e}^{15-5 x}}{\left (3+x \right )^{5}}\) | \(27\) |
parallelrisch | \({\mathrm e}^{\left (\ln \left (3+x \right )+x -3\right ) \ln \left (\frac {\ln \left (x \right )}{4}+2\right )-5 \ln \left (3+x \right )+15-5 x}\) | \(28\) |
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Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=e^{\left ({\left (x + \log \left (x + 3\right ) - 3\right )} \log \left (\frac {1}{4} \, \log \left (x\right ) + 2\right ) - 5 \, x - 5 \, \log \left (x + 3\right ) + 15\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (19) = 38\).
Time = 1.05 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.70 \[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=\frac {e^{- 5 x + \left (x + \log {\left (x + 3 \right )} - 3\right ) \log {\left (\frac {\log {\left (x \right )}}{4} + 2 \right )} + 15}}{x^{5} + 15 x^{4} + 90 x^{3} + 270 x^{2} + 405 x + 243} \]
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Leaf count of result is larger than twice the leaf count of optimal. 149 vs. \(2 (18) = 36\).
Time = 0.46 (sec) , antiderivative size = 149, normalized size of antiderivative = 5.52 \[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=\frac {64 \, e^{\left (-2 \, x \log \left (2\right ) - 2 \, \log \left (2\right ) \log \left (x + 3\right ) + x \log \left (\log \left (x\right ) + 8\right ) + \log \left (x + 3\right ) \log \left (\log \left (x\right ) + 8\right ) - 5 \, x + 15\right )}}{512 \, x^{5} + 7680 \, x^{4} + {\left (x^{5} + 15 \, x^{4} + 90 \, x^{3} + 270 \, x^{2} + 405 \, x + 243\right )} \log \left (x\right )^{3} + 46080 \, x^{3} + 24 \, {\left (x^{5} + 15 \, x^{4} + 90 \, x^{3} + 270 \, x^{2} + 405 \, x + 243\right )} \log \left (x\right )^{2} + 138240 \, x^{2} + 192 \, {\left (x^{5} + 15 \, x^{4} + 90 \, x^{3} + 270 \, x^{2} + 405 \, x + 243\right )} \log \left (x\right ) + 207360 \, x + 124416} \]
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Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (18) = 36\).
Time = 1.26 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56 \[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=e^{\left (x \log \left (\frac {1}{4} \, \log \left (x\right ) + 2\right ) + \log \left (x + 3\right ) \log \left (\frac {1}{4} \, \log \left (x\right ) + 2\right ) - 5 \, x - 5 \, \log \left (x + 3\right ) - 3 \, \log \left (\frac {1}{4} \, \log \left (x\right ) + 2\right ) + 15\right )} \]
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Time = 8.69 (sec) , antiderivative size = 182, normalized size of antiderivative = 6.74 \[ \int \frac {e^{15-5 x+(-3+x+\log (3+x)) \log \left (\frac {1}{4} (8+\log (x))\right )} \left (-9-160 x-39 x^2+\left (-20 x-5 x^2\right ) \log (x)+(3+x) \log (3+x)+\left (32 x+8 x^2+\left (4 x+x^2\right ) \log (x)\right ) \log \left (\frac {1}{4} (8+\log (x))\right )\right )}{(3+x)^5 \left (24 x+8 x^2+\left (3 x+x^2\right ) \log (x)\right )} \, dx=\frac {64\,{\mathrm {e}}^{15-5\,x}\,{\left (\frac {\ln \left (x\right )}{4}+2\right )}^{x+\ln \left (x+3\right )}}{x^5\,{\ln \left (x\right )}^3+24\,x^5\,{\ln \left (x\right )}^2+192\,x^5\,\ln \left (x\right )+512\,x^5+15\,x^4\,{\ln \left (x\right )}^3+360\,x^4\,{\ln \left (x\right )}^2+2880\,x^4\,\ln \left (x\right )+7680\,x^4+90\,x^3\,{\ln \left (x\right )}^3+2160\,x^3\,{\ln \left (x\right )}^2+17280\,x^3\,\ln \left (x\right )+46080\,x^3+270\,x^2\,{\ln \left (x\right )}^3+6480\,x^2\,{\ln \left (x\right )}^2+51840\,x^2\,\ln \left (x\right )+138240\,x^2+405\,x\,{\ln \left (x\right )}^3+9720\,x\,{\ln \left (x\right )}^2+77760\,x\,\ln \left (x\right )+207360\,x+243\,{\ln \left (x\right )}^3+5832\,{\ln \left (x\right )}^2+46656\,\ln \left (x\right )+124416} \]
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