Integrand size = 93, antiderivative size = 25 \[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-x} \]
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\[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=\int \frac {\exp \left (\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}\right ) \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {1}{15} \int \frac {\exp \left (\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}\right ) \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{x^2} \, dx \\ & = \frac {1}{15} \int \left (15 \exp \left (\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )+x\right )-\frac {\exp \left (\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}\right ) \left (-8 e^5+15 e^{\frac {24 e^5}{5 x}} x^2\right )}{x^2}\right ) \, dx \\ & = -\left (\frac {1}{15} \int \frac {\exp \left (\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}\right ) \left (-8 e^5+15 e^{\frac {24 e^5}{5 x}} x^2\right )}{x^2} \, dx\right )+\int \exp \left (\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )+x\right ) \, dx \\ & = -\left (\frac {1}{15} \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-\frac {24 e^5}{5 x}-x} \left (-8 e^5+15 e^{\frac {24 e^5}{5 x}} x^2\right )}{x^2} \, dx\right )+\int e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x} \, dx \\ & = -\left (\frac {1}{15} \int \left (15 e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-x}-\frac {8 e^{5+\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-\frac {24 e^5}{5 x}-x}}{x^2}\right ) \, dx\right )+\int e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x} \, dx \\ & = \frac {8}{15} \int \frac {e^{5+\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-\frac {24 e^5}{5 x}-x}}{x^2} \, dx+\int e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x} \, dx-\int e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-x} \, dx \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}}+e^x-x} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(42\) vs. \(2(19)=38\).
Time = 0.18 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.72
\[{\mathrm e}^{-\frac {\left (9 \,{\mathrm e}^{\frac {24 \,{\mathrm e}^{5}}{5 x}} x -9 \,{\mathrm e}^{\frac {5 x^{2}+24 \,{\mathrm e}^{5}}{5 x}}-1\right ) {\mathrm e}^{-\frac {24 \,{\mathrm e}^{5}}{5 x}}}{9}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (17) = 34\).
Time = 0.25 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.04 \[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=e^{\left (-\frac {{\left (9 \, {\left (5 \, x^{2} - 5 \, x e^{x} + 24 \, e^{5}\right )} e^{\left (\frac {24 \, e^{5}}{5 \, x}\right )} - 5 \, x\right )} e^{\left (-\frac {24 \, e^{5}}{5 \, x}\right )}}{45 \, x} + \frac {24 \, e^{5}}{5 \, x}\right )} \]
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Time = 0.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.36 \[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=e^{\left (\frac {\left (- 9 x + 9 e^{x}\right ) e^{\frac {24 e^{5}}{5 x}}}{9} + \frac {1}{9}\right ) e^{- \frac {24 e^{5}}{5 x}}} \]
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\[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=\int { \frac {{\left (15 \, {\left (x^{2} e^{x} - x^{2}\right )} e^{\left (\frac {24 \, e^{5}}{5 \, x}\right )} + 8 \, e^{5}\right )} e^{\left (-\frac {1}{9} \, {\left (9 \, {\left (x - e^{x}\right )} e^{\left (\frac {24 \, e^{5}}{5 \, x}\right )} - 1\right )} e^{\left (-\frac {24 \, e^{5}}{5 \, x}\right )} - \frac {24 \, e^{5}}{5 \, x}\right )}}{15 \, x^{2}} \,d x } \]
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\[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx=\int { \frac {{\left (15 \, {\left (x^{2} e^{x} - x^{2}\right )} e^{\left (\frac {24 \, e^{5}}{5 \, x}\right )} + 8 \, e^{5}\right )} e^{\left (-\frac {1}{9} \, {\left (9 \, {\left (x - e^{x}\right )} e^{\left (\frac {24 \, e^{5}}{5 \, x}\right )} - 1\right )} e^{\left (-\frac {24 \, e^{5}}{5 \, x}\right )} - \frac {24 \, e^{5}}{5 \, x}\right )}}{15 \, x^{2}} \,d x } \]
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Time = 11.98 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.76 \[ \int \frac {e^{\frac {1}{9} e^{-\frac {24 e^5}{5 x}} \left (1+e^{\frac {24 e^5}{5 x}} \left (9 e^x-9 x\right )\right )-\frac {24 e^5}{5 x}} \left (8 e^5+e^{\frac {24 e^5}{5 x}} \left (-15 x^2+15 e^x x^2\right )\right )}{15 x^2} \, dx={\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{-\frac {24\,{\mathrm {e}}^5}{5\,x}}}{9}} \]
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