Integrand size = 105, antiderivative size = 28 \[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=e^{e^{e^{\frac {e^{5 \left (-3-x+5 x^2\right )}}{x}+x}}}+x \]
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\[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=\int \frac {x^2+\exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}\right ) \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (1+\exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right )+\frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right ) (-1+5 x) (1+10 x)}{x^2}\right ) \, dx \\ & = x+\int \exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right ) \, dx+\int \frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right ) (-1+5 x) (1+10 x)}{x^2} \, dx \\ & = x+\int \exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right ) \, dx+\int \left (50 \exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )-\frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x^2}-\frac {5 \exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x}\right ) \, dx \\ & = x-5 \int \frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x} \, dx+50 \int \exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right ) \, dx+\int \exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right ) \, dx-\int \frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x^2} \, dx \\ \end{align*}
Time = 0.19 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=e^{e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}}+x \]
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Time = 1.89 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89
method | result | size |
risch | \(x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{25 x^{2}-5 x -15}+x^{2}}{x}}}}\) | \(25\) |
parallelrisch | \(x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{25 x^{2}-5 x -15}+x^{2}}{x}}}}\) | \(25\) |
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Leaf count of result is larger than twice the leaf count of optimal. 154 vs. \(2 (22) = 44\).
Time = 0.26 (sec) , antiderivative size = 154, normalized size of antiderivative = 5.50 \[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx={\left (x e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x} + e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} + e^{\left (\frac {x^{2} + x e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )} + x e^{\left (e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} e^{\left (-\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x} - e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} \]
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Time = 7.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=x + e^{e^{e^{\frac {x^{2} + e^{25 x^{2} - 5 x - 15}}{x}}}} \]
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Time = 0.50 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=x + e^{\left (e^{\left (e^{\left (x + \frac {e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )}\right )} \]
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\[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=\int { \frac {x^{2} + {\left (x^{2} + {\left (50 \, x^{2} - 5 \, x - 1\right )} e^{\left (25 \, x^{2} - 5 \, x - 15\right )}\right )} e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x} + e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )} + e^{\left (e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )}\right )}}{x^{2}} \,d x } \]
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Time = 9.45 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx=x+{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{-15}\,{\mathrm {e}}^{25\,x^2}}{x}}\,{\mathrm {e}}^x}} \]
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