Integrand size = 52, antiderivative size = 22 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{4 e^6 x \left (\frac {e^x}{2}+x-x^2\right )} \]
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Time = 0.14 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6838} \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{4 e^6 \left (x^2-x^3\right )+2 e^{x+6} x} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{2 e^{6+x} x+4 e^6 \left (x^2-x^3\right )} \\ \end{align*}
Time = 0.45 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{2 e^6 x \left (e^x-2 (-1+x) x\right )} \]
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Time = 0.18 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82
method | result | size |
parallelrisch | \({\mathrm e}^{2 \,{\mathrm e}^{6} x \left (-2 x^{2}+{\mathrm e}^{x}+2 x \right )}\) | \(18\) |
norman | \({\mathrm e}^{2 x \,{\mathrm e}^{6} {\mathrm e}^{x}+\left (-4 x^{3}+4 x^{2}\right ) {\mathrm e}^{6}}\) | \(24\) |
risch | \({\mathrm e}^{-2 x \left (2 x^{2} {\mathrm e}^{6}-2 x \,{\mathrm e}^{6}-{\mathrm e}^{6+x}\right )}\) | \(24\) |
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none
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{\left (-4 \, {\left (x^{3} - x^{2}\right )} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \]
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Time = 0.11 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{2 x e^{6} e^{x} + \left (- 4 x^{3} + 4 x^{2}\right ) e^{6}} \]
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none
Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{\left (-4 \, x^{3} e^{6} + 4 \, x^{2} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx=e^{\left (-4 \, x^{3} e^{6} + 4 \, x^{2} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \]
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Time = 7.68 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.14 \[ \int e^{2 e^{6+x} x+e^6 \left (4 x^2-4 x^3\right )} \left (e^{6+x} (2+2 x)+e^6 \left (8 x-12 x^2\right )\right ) \, dx={\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^6}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^6}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x} \]
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