Integrand size = 95, antiderivative size = 25 \[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=e^{e^{11-x \left (x-\left (-x+\frac {\log (x)}{x}\right )^2\right )}} \]
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\[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (-2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right )-2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x+3 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2-\frac {2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-1+x^2\right ) \log (x)}{x^2}-\frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2}\right ) \, dx \\ & = -\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-1+x^2\right ) \log (x)}{x^2} \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx \\ & = -\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \left (\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)-\frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)}{x^2}\right ) \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx \\ & = -\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x) \, dx+2 \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)}{x^2} \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx \\ \end{align*}
\[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=\int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx \]
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Time = 0.38 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16
method | result | size |
risch | \({\mathrm e}^{x^{-2 x} {\mathrm e}^{\frac {x^{4}-x^{3}+\ln \left (x \right )^{2}+11 x}{x}}}\) | \(29\) |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{\frac {\ln \left (x \right )^{2}-2 x^{2} \ln \left (x \right )+x^{4}-x^{3}+11 x}{x}}}\) | \(30\) |
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Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (21) = 42\).
Time = 0.25 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.48 \[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + x e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2} + 11 \, x}{x}\right )} + \log \left (x\right )^{2} + 11 \, x}{x} - \frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2} + 11 \, x}{x}\right )} \]
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Time = 0.52 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=e^{e^{\frac {x^{4} - x^{3} - 2 x^{2} \log {\left (x \right )} + 11 x + \log {\left (x \right )}^{2}}{x}}} \]
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Time = 0.47 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=e^{\left (e^{\left (x^{3} - x^{2} - 2 \, x \log \left (x\right ) + \frac {\log \left (x\right )^{2}}{x} + 11\right )}\right )} \]
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\[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx=\int { \frac {{\left (3 \, x^{4} - 2 \, x^{3} - 2 \, x^{2} - 2 \, {\left (x^{2} - 1\right )} \log \left (x\right ) - \log \left (x\right )^{2}\right )} e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2} + 11 \, x}{x} + e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2} + 11 \, x}{x}\right )}\right )}}{x^{2}} \,d x } \]
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Time = 9.34 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx={\mathrm {e}}^{\frac {{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{11}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{\frac {{\ln \left (x\right )}^2}{x}}}{x^{2\,x}}} \]
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