Integrand size = 15, antiderivative size = 20 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=\frac {1}{2} \left (5-e^7-x-3 e^x x\right ) \]
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Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2207, 2225} \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=-\frac {x}{2}+\frac {3 e^x}{2}-\frac {3}{2} e^x (x+1) \]
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Rule 12
Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \left (-1+e^x (-3-3 x)\right ) \, dx \\ & = -\frac {x}{2}+\frac {1}{2} \int e^x (-3-3 x) \, dx \\ & = -\frac {x}{2}-\frac {3}{2} e^x (1+x)+\frac {3 \int e^x \, dx}{2} \\ & = \frac {3 e^x}{2}-\frac {x}{2}-\frac {3}{2} e^x (1+x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.70 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=\frac {1}{2} \left (-x-3 e^x x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50
method | result | size |
default | \(-\frac {x}{2}-\frac {3 \,{\mathrm e}^{x} x}{2}\) | \(10\) |
norman | \(-\frac {x}{2}-\frac {3 \,{\mathrm e}^{x} x}{2}\) | \(10\) |
risch | \(-\frac {x}{2}-\frac {3 \,{\mathrm e}^{x} x}{2}\) | \(10\) |
parallelrisch | \(-\frac {x}{2}-\frac {3 \,{\mathrm e}^{x} x}{2}\) | \(10\) |
parts | \(-\frac {x}{2}-\frac {3 \,{\mathrm e}^{x} x}{2}\) | \(10\) |
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Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=-\frac {3}{2} \, x e^{x} - \frac {1}{2} \, x \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=- \frac {3 x e^{x}}{2} - \frac {x}{2} \]
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Time = 0.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=-\frac {3}{2} \, {\left (x - 1\right )} e^{x} - \frac {1}{2} \, x - \frac {3}{2} \, e^{x} \]
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Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=-\frac {3}{2} \, x e^{x} - \frac {1}{2} \, x \]
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Time = 13.39 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {1}{2} \left (-1+e^x (-3-3 x)\right ) \, dx=-\frac {x\,\left (3\,{\mathrm {e}}^x+1\right )}{2} \]
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