Integrand size = 26, antiderivative size = 17 \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=\frac {9}{4} e^{e^x} (6-e (2+x)) \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2326} \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=\frac {9}{4} e^{e^x} (6-e (x+2)) \]
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Rule 12
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \int e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx \\ & = \frac {9}{4} e^{e^x} (6-e (2+x)) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=-\frac {9}{4} e^{e^x} (-6+e (2+x)) \]
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Time = 0.06 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00
method | result | size |
risch | \(\frac {\left (-9 x \,{\mathrm e}-18 \,{\mathrm e}+54\right ) {\mathrm e}^{{\mathrm e}^{x}}}{4}\) | \(17\) |
norman | \(\left (-\frac {9 \,{\mathrm e}}{2}+\frac {27}{2}\right ) {\mathrm e}^{{\mathrm e}^{x}}-\frac {9 x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}}{4}\) | \(20\) |
parallelrisch | \(-\frac {9 x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}}{4}-\frac {9 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}}{2}+\frac {27 \,{\mathrm e}^{{\mathrm e}^{x}}}{2}\) | \(22\) |
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none
Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=-\frac {9}{4} \, {\left ({\left (x + 2\right )} e - 6\right )} e^{\left (e^{x}\right )} \]
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Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=\frac {\left (- 9 e x - 18 e + 54\right ) e^{e^{x}}}{4} \]
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\[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=\int { -\frac {9}{4} \, {\left ({\left ({\left (x + 2\right )} e - 6\right )} e^{x} + e\right )} e^{\left (e^{x}\right )} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 30 vs. \(2 (13) = 26\).
Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.76 \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=-\frac {9}{4} \, {\left (x e^{\left (x + e^{x} + 1\right )} + 2 \, e^{\left (x + e^{x} + 1\right )} - 6 \, e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {1}{4} e^{e^x} \left (-9 e+e^x (54+e (-18-9 x))\right ) \, dx=-\frac {9\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (2\,\mathrm {e}+x\,\mathrm {e}-6\right )}{4} \]
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