Integrand size = 76, antiderivative size = 21 \[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)} \]
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\[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=\int \frac {\exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) \left (-e^{32}-25 \left (1+\frac {e^{32}}{25}\right ) x+10 x \log (x)-x \log ^2(x)\right )}{x (5-\log (x))^2} \, dx \\ & = 2 \int \frac {\exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) \left (-e^{32}-25 \left (1+\frac {e^{32}}{25}\right ) x+10 x \log (x)-x \log ^2(x)\right )}{x (5-\log (x))^2} \, dx \\ & = 2 \int \left (-\exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right )-\frac {\exp \left (32+e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) (1+x)}{x (-5+\log (x))^2}\right ) \, dx \\ & = -\left (2 \int \exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) \, dx\right )-2 \int \frac {\exp \left (32+e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) (1+x)}{x (-5+\log (x))^2} \, dx \\ & = -\left (2 \int \exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) \, dx\right )-2 \int \left (\frac {\exp \left (32+e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right )}{(-5+\log (x))^2}+\frac {\exp \left (32+e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right )}{x (-5+\log (x))^2}\right ) \, dx \\ & = -\left (2 \int \exp \left (e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right ) \, dx\right )-2 \int \frac {\exp \left (32+e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right )}{(-5+\log (x))^2} \, dx-2 \int \frac {\exp \left (32+e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}\right )}{x (-5+\log (x))^2} \, dx \\ \end{align*}
Time = 3.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=e^{-2 e^{-\frac {e^{32}}{-5+\log (x)}} (1+x)} \]
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Time = 12.39 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86
method | result | size |
risch | \({\mathrm e}^{-2 \left (1+x \right ) {\mathrm e}^{-\frac {{\mathrm e}^{32}}{\ln \left (x \right )-5}}}\) | \(18\) |
parallelrisch | \({\mathrm e}^{\left (-2-2 x \right ) {\mathrm e}^{-\frac {{\mathrm e}^{32}}{\ln \left (x \right )-5}}}\) | \(21\) |
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Timed out. \[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=\text {Timed out} \]
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Time = 1.72 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=e^{\left (- 2 x - 2\right ) e^{- \frac {e^{32}}{\log {\left (x \right )} - 5}}} \]
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Time = 0.53 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.38 \[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=e^{\left (-2 \, x e^{\left (-\frac {e^{32}}{\log \left (x\right ) - 5}\right )} - 2 \, e^{\left (-\frac {e^{32}}{\log \left (x\right ) - 5}\right )}\right )} \]
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\[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx=\int { -\frac {2 \, {\left (x \log \left (x\right )^{2} + {\left (x + 1\right )} e^{32} - 10 \, x \log \left (x\right ) + 25 \, x\right )} e^{\left (-2 \, {\left (x + 1\right )} e^{\left (-\frac {e^{32}}{\log \left (x\right ) - 5}\right )} - \frac {e^{32}}{\log \left (x\right ) - 5}\right )}}{x \log \left (x\right )^{2} - 10 \, x \log \left (x\right ) + 25 \, x} \,d x } \]
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Time = 13.86 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.43 \[ \int \frac {e^{e^{-\frac {e^{32}}{-5+\log (x)}} (-2-2 x)-\frac {e^{32}}{-5+\log (x)}} \left (e^{32} (-2-2 x)-50 x+20 x \log (x)-2 x \log ^2(x)\right )}{25 x-10 x \log (x)+x \log ^2(x)} \, dx={\mathrm {e}}^{-2\,x\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{32}}{\ln \left (x\right )-5}}}\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{32}}{\ln \left (x\right )-5}}} \]
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