Integrand size = 27, antiderivative size = 22 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=\frac {105}{16}+e^4+e^{2 e^{2 x}-2 x^2} \]
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Time = 0.04 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {6838} \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=e^{2 e^{2 x}-2 x^2} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{2 e^{2 x}-2 x^2} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=e^{2 e^{2 x}-2 x^2} \]
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Time = 0.08 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64
method | result | size |
norman | \({\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x^{2}}\) | \(14\) |
risch | \({\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x^{2}}\) | \(14\) |
parallelrisch | \({\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x^{2}}\) | \(14\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.59 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=e^{\left (-2 \, x^{2} + 2 \, e^{\left (2 \, x\right )}\right )} \]
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Time = 0.07 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.55 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=e^{- 2 x^{2} + 2 e^{2 x}} \]
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none
Time = 0.18 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.59 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=e^{\left (-2 \, x^{2} + 2 \, e^{\left (2 \, x\right )}\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.59 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx=e^{\left (-2 \, x^{2} + 2 \, e^{\left (2 \, x\right )}\right )} \]
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Time = 11.43 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.59 \[ \int e^{2 e^{2 x}-2 x^2} \left (4 e^{2 x}-4 x\right ) \, dx={\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}-2\,x^2} \]
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