Integrand size = 11, antiderivative size = 11 \[ \int e^{4 x^3} x^2 \, dx=\frac {e^{4 x^3}}{12} \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2240} \[ \int e^{4 x^3} x^2 \, dx=\frac {e^{4 x^3}}{12} \]
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Rule 2240
Rubi steps \begin{align*} \text {integral}& = \frac {e^{4 x^3}}{12} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int e^{4 x^3} x^2 \, dx=\frac {e^{4 x^3}}{12} \]
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Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82
method | result | size |
gosper | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
derivativedivides | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
default | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
risch | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
parallelrisch | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
meijerg | \(-\frac {1}{12}+\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(11\) |
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none
Time = 0.29 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{4 x^3} x^2 \, dx=\frac {1}{12} \, e^{\left (4 \, x^{3}\right )} \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int e^{4 x^3} x^2 \, dx=\frac {e^{4 x^{3}}}{12} \]
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none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{4 x^3} x^2 \, dx=\frac {1}{12} \, e^{\left (4 \, x^{3}\right )} \]
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none
Time = 0.30 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{4 x^3} x^2 \, dx=\frac {1}{12} \, e^{\left (4 \, x^{3}\right )} \]
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Time = 0.11 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{4 x^3} x^2 \, dx=\frac {{\mathrm {e}}^{4\,x^3}}{12} \]
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