Integrand size = 33, antiderivative size = 23 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=-x-e^{\frac {4 (3-\log (3))}{\log (2)}} x^4 \]
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Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {12} \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=x^4 \left (-e^{\frac {4 (3-\log (3))}{\log (2)}}\right )-x \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = e^{-\frac {4 (-3+\log (3))}{\log (2)}} \int \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx \\ & = -x-e^{\frac {4 (3-\log (3))}{\log (2)}} x^4 \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=-x-3^{-\frac {4}{\log (2)}} e^{\frac {12}{\log (2)}} x^4 \]
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Time = 0.08 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09
method | result | size |
risch | \(-3^{-\frac {4}{\ln \left (2\right )}} x^{4} {\mathrm e}^{\frac {12}{\ln \left (2\right )}}-x\) | \(25\) |
gosper | \(-x \left ({\mathrm e}^{\frac {4 \ln \left (3\right )-12}{\ln \left (2\right )}}+x^{3}\right ) {\mathrm e}^{-\frac {4 \left (\ln \left (3\right )-3\right )}{\ln \left (2\right )}}\) | \(32\) |
default | \({\mathrm e}^{-\frac {4 \left (\ln \left (3\right )-3\right )}{\ln \left (2\right )}} \left (-{\mathrm e}^{\frac {4 \ln \left (3\right )-12}{\ln \left (2\right )}} x -x^{4}\right )\) | \(35\) |
parallelrisch | \({\mathrm e}^{-\frac {4 \left (\ln \left (3\right )-3\right )}{\ln \left (2\right )}} \left (-{\mathrm e}^{\frac {4 \ln \left (3\right )-12}{\ln \left (2\right )}} x -x^{4}\right )\) | \(35\) |
norman | \(\left (-3^{-\frac {1}{\ln \left (2\right )}} {\mathrm e}^{\frac {3}{\ln \left (2\right )}} x^{4}-3^{\frac {3}{\ln \left (2\right )}} {\mathrm e}^{-\frac {9}{\ln \left (2\right )}} x \right ) {\mathrm e}^{-\frac {3 \left (\ln \left (3\right )-3\right )}{\ln \left (2\right )}}\) | \(53\) |
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none
Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=-{\left (x^{4} + x e^{\left (\frac {4 \, {\left (\log \left (3\right ) - 3\right )}}{\log \left (2\right )}\right )}\right )} e^{\left (-\frac {4 \, {\left (\log \left (3\right ) - 3\right )}}{\log \left (2\right )}\right )} \]
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Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=- \frac {x^{4} e^{\frac {12}{\log {\left (2 \right )}}}}{3^{\frac {4}{\log {\left (2 \right )}}}} - x \]
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none
Time = 0.18 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=-{\left (x^{4} + x e^{\left (\frac {4 \, {\left (\log \left (3\right ) - 3\right )}}{\log \left (2\right )}\right )}\right )} e^{\left (-\frac {4 \, {\left (\log \left (3\right ) - 3\right )}}{\log \left (2\right )}\right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=-{\left (x^{4} + x e^{\left (\frac {4 \, {\left (\log \left (3\right ) - 3\right )}}{\log \left (2\right )}\right )}\right )} e^{\left (-\frac {4 \, {\left (\log \left (3\right ) - 3\right )}}{\log \left (2\right )}\right )} \]
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Time = 0.05 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int e^{-\frac {4 (-3+\log (3))}{\log (2)}} \left (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3\right ) \, dx=-{\mathrm {e}}^{-\frac {\ln \left (81\right )-12}{\ln \left (2\right )}}\,x^4-x \]
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