Integrand size = 23, antiderivative size = 15 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 e^{e^x} x^2}{18+e} \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 2326} \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 e^{e^x} x^2}{18+e} \]
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Rule 12
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {\int e^{e^x} \left (28 x+14 e^x x^2\right ) \, dx}{18+e} \\ & = \frac {14 e^{e^x} x^2}{18+e} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 e^{e^x} x^2}{18+e} \]
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Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00
method | result | size |
norman | \(\frac {14 x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}+18}\) | \(15\) |
risch | \(\frac {14 x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}+18}\) | \(15\) |
parallelrisch | \(\frac {14 x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}+18}\) | \(15\) |
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Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 \, x^{2} e^{\left (e^{x}\right )}}{e + 18} \]
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Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 x^{2} e^{e^{x}}}{e + 18} \]
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Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 \, x^{2} e^{\left (e^{x}\right )}}{e + 18} \]
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14 \, x^{2} e^{\left (e^{x}\right )}}{e + 18} \]
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Time = 14.64 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{e^x} \left (28 x+14 e^x x^2\right )}{18+e} \, dx=\frac {14\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^x}}{\mathrm {e}+18} \]
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