Integrand size = 55, antiderivative size = 20 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{22-2 e^{e^{-\frac {2}{3} (3+x)}}+x^2} \]
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Time = 0.12 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 6838} \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{x^2-2 e^{e^{-\frac {2}{3} (x+3)}}+22} \]
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Rule 12
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \int e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx \\ & = e^{22-2 e^{e^{-\frac {2}{3} (3+x)}}+x^2} \\ \end{align*}
Time = 0.54 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{22-2 e^{e^{-2-\frac {2 x}{3}}}+x^2} \]
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Time = 0.07 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80
method | result | size |
norman | \({\mathrm e}^{-2 \,{\mathrm e}^{{\mathrm e}^{-\frac {2 x}{3}-2}}+x^{2}+22}\) | \(16\) |
risch | \({\mathrm e}^{-2 \,{\mathrm e}^{{\mathrm e}^{-\frac {2 x}{3}-2}}+x^{2}+22}\) | \(16\) |
parallelrisch | \({\mathrm e}^{-2 \,{\mathrm e}^{{\mathrm e}^{-\frac {2 x}{3}-2}}+x^{2}+22}\) | \(16\) |
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Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{\left (x^{2} - 2 \, e^{\left (e^{\left (-\frac {2}{3} \, x - 2\right )}\right )} + 22\right )} \]
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Time = 0.13 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{x^{2} - 2 e^{e^{- \frac {2 x}{3} - 2}} + 22} \]
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none
Time = 0.17 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{\left (x^{2} - 2 \, e^{\left (e^{\left (-\frac {2}{3} \, x - 2\right )}\right )} + 22\right )} \]
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none
Time = 0.29 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx=e^{\left (x^{2} - 2 \, e^{\left (e^{\left (-\frac {2}{3} \, x - 2\right )}\right )} + 22\right )} \]
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Time = 0.12 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {1}{3} e^{22-2 e^{e^{\frac {1}{3} (-6-2 x)}}+x^2} \left (4 e^{e^{\frac {1}{3} (-6-2 x)}+\frac {1}{3} (-6-2 x)}+6 x\right ) \, dx={\mathrm {e}}^{-2\,{\mathrm {e}}^{{\mathrm {e}}^{-\frac {2\,x}{3}}\,{\mathrm {e}}^{-2}}}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{22} \]
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