Integrand size = 32, antiderivative size = 20 \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=-4-2 e^{\frac {1}{2} \left (-e^x+x\right )} x^3 \]
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Time = 0.04 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.80, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2326} \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=-\frac {2 e^{\frac {1}{2} \left (x-e^x\right )} \left (x^3-e^x x^3\right )}{1-e^x} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = -\frac {2 e^{\frac {1}{2} \left (-e^x+x\right )} \left (x^3-e^x x^3\right )}{1-e^x} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=-2 e^{\frac {1}{2} \left (-e^x+x\right )} x^3 \]
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Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75
method | result | size |
norman | \(-2 x^{3} {\mathrm e}^{\frac {x}{2}-\frac {{\mathrm e}^{x}}{2}}\) | \(15\) |
risch | \(-2 x^{3} {\mathrm e}^{\frac {x}{2}-\frac {{\mathrm e}^{x}}{2}}\) | \(15\) |
parallelrisch | \(-2 x^{3} {\mathrm e}^{\frac {x}{2}-\frac {{\mathrm e}^{x}}{2}}\) | \(15\) |
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none
Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=-2 \, x^{3} e^{\left (\frac {1}{2} \, x - \frac {1}{2} \, e^{x}\right )} \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=- 2 x^{3} e^{\frac {x}{2} - \frac {e^{x}}{2}} \]
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\[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=\int { {\left (x^{3} e^{x} - x^{3} - 6 \, x^{2}\right )} e^{\left (\frac {1}{2} \, x - \frac {1}{2} \, e^{x}\right )} \,d x } \]
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none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=-2 \, x^{3} e^{\left (\frac {1}{2} \, x - \frac {1}{2} \, e^{x}\right )} \]
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Time = 10.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int e^{\frac {1}{2} \left (-e^x+x\right )} \left (-6 x^2-x^3+e^x x^3\right ) \, dx=-2\,x^3\,{\mathrm {e}}^{x/2}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^x}{2}} \]
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