Integrand size = 41, antiderivative size = 16 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=e^{2+4\ 3^{-1-e^4+x}} \]
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Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {12, 2320, 2225} \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=e^{4\ 3^{x-e^4-1}+2} \]
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Rule 12
Rule 2225
Rule 2320
Rubi steps \begin{align*} \text {integral}& = (4 \log (3)) \int 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \, dx \\ & = 4 \text {Subst}\left (\int e^{2+4 x} \, dx,x,3^{-1-e^4+x}\right ) \\ & = e^{2+4\ 3^{-1-e^4+x}} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=e^{2+4\ 3^{-1-e^4+x}} \]
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Time = 0.06 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.62
method | result | size |
risch | \({\mathrm e}^{\frac {2 \left (3^{{\mathrm e}^{4}-x +1}+2\right ) 3^{x -{\mathrm e}^{4}}}{3}}\) | \(26\) |
parallelrisch | \({\mathrm e}^{2 \left ({\mathrm e}^{\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}+2\right ) {\mathrm e}^{-\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}}\) | \(30\) |
derivativedivides | \({\mathrm e}^{\left (2 \,{\mathrm e}^{\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}+4\right ) {\mathrm e}^{-\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}}\) | \(31\) |
default | \({\mathrm e}^{\left (2 \,{\mathrm e}^{\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}+4\right ) {\mathrm e}^{-\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}}\) | \(31\) |
norman | \({\mathrm e}^{\left (2 \,{\mathrm e}^{\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}+4\right ) {\mathrm e}^{-\left ({\mathrm e}^{4}-x +1\right ) \ln \left (3\right )}}\) | \(31\) |
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Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.56 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=e^{\left (\frac {2 \, {\left (3^{-x + e^{4} + 1} + 2\right )}}{3^{-x + e^{4} + 1}}\right )} \]
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Time = 0.09 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.69 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=e^{\left (2 e^{\left (- x + 1 + e^{4}\right ) \log {\left (3 \right )}} + 4\right ) e^{- \left (- x + 1 + e^{4}\right ) \log {\left (3 \right )}}} \]
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Time = 0.17 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.50 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=3^{\frac {4 \cdot 3^{x - e^{4} - 1}}{\log \left (3\right )} + \frac {2}{\log \left (3\right )}} \]
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Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx=e^{\left (\frac {4 \cdot 3^{x}}{3 \cdot 3^{e^{4}}} + 2\right )} \]
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Time = 9.46 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int 4\ 3^{-1-e^4+x} e^{3^{-1-e^4+x} \left (4+2\ 3^{1+e^4-x}\right )} \log (3) \, dx={\mathrm {e}}^2\,{\mathrm {e}}^{4\,3^{x-{\mathrm {e}}^4-1}} \]
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