Integrand size = 41, antiderivative size = 19 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{e^{2 \left (-x+e^{16} x\right )}+8 x} \]
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Time = 0.09 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6838} \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{8 x+e^{-2 \left (1-e^{16}\right ) x}} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{e^{-2 \left (1-e^{16}\right ) x}+8 x} \\ \end{align*}
Time = 0.52 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{e^{2 \left (-1+e^{16}\right ) x}+8 x} \]
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Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{2 x \left (-1+{\mathrm e}^{16}\right )}+8 x}\) | \(14\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\) | \(18\) |
default | \({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\) | \(18\) |
norman | \({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\) | \(18\) |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\) | \(18\) |
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Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{\left (8 \, x + e^{\left (2 \, x e^{16} - 2 \, x\right )}\right )} \]
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Time = 0.10 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{8 x + e^{- 2 x + 2 x e^{16}}} \]
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none
Time = 0.28 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{\left (8 \, x + e^{\left (2 \, x e^{16} - 2 \, x\right )}\right )} \]
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none
Time = 0.28 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx=e^{\left (8 \, x + e^{\left (2 \, x e^{16} - 2 \, x\right )}\right )} \]
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Time = 0.13 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^{-2 x+2 e^{16} x}+8 x} \left (8+e^{-2 x+2 e^{16} x} \left (-2+2 e^{16}\right )\right ) \, dx={\mathrm {e}}^{8\,x+{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{16}-2\,x}} \]
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