Integrand size = 30, antiderivative size = 15 \[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=e^{12+4 e^{-2 x^3}} x \]
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Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2326} \[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=e^{4 e^{-2 x^3}+12} x \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = e^{12+4 e^{-2 x^3}} x \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=e^{4 \left (3+e^{-2 x^3}\right )} x \]
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Time = 1.43 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93
method | result | size |
risch | \(x \,{\mathrm e}^{4 \,{\mathrm e}^{-2 x^{3}}+12}\) | \(14\) |
parallelrisch | \(x \,{\mathrm e}^{4 \,{\mathrm e}^{-2 x^{3}}} {\mathrm e}^{12}\) | \(18\) |
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none
Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=x e^{\left (4 \, e^{\left (-2 \, x^{3}\right )} + 12\right )} \]
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Time = 0.53 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=x e^{12} e^{4 e^{- 2 x^{3}}} \]
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\[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=\int { -{\left (24 \, x^{3} e^{\left (-2 \, x^{3} + 12\right )} - e^{12}\right )} e^{\left (4 \, e^{\left (-2 \, x^{3}\right )}\right )} \,d x } \]
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\[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=\int { -{\left (24 \, x^{3} e^{\left (-2 \, x^{3} + 12\right )} - e^{12}\right )} e^{\left (4 \, e^{\left (-2 \, x^{3}\right )}\right )} \,d x } \]
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Time = 15.41 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{4 e^{-2 x^3}} \left (e^{12}-24 e^{12-2 x^3} x^3\right ) \, dx=x\,{\mathrm {e}}^{4\,{\mathrm {e}}^{-2\,x^3}}\,{\mathrm {e}}^{12} \]
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