Integrand size = 5, antiderivative size = 11 \[ \int e^x x \, dx=-e^x+e^x x \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2207, 2225} \[ \int e^x x \, dx=e^x x-e^x \]
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Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = e^x x-\int e^x \, dx \\ & = -e^x+e^x x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int e^x x \, dx=e^x (-1+x) \]
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Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64
method | result | size |
gosper | \(\left (-1+x \right ) {\mathrm e}^{x}\) | \(7\) |
risch | \(\left (-1+x \right ) {\mathrm e}^{x}\) | \(7\) |
default | \(-{\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(10\) |
norman | \(-{\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(10\) |
parallelrisch | \(-{\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(10\) |
parts | \(-{\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(10\) |
meijerg | \(1-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}\) | \(12\) |
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none
Time = 0.23 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int e^x x \, dx={\left (x - 1\right )} e^{x} \]
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Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.45 \[ \int e^x x \, dx=\left (x - 1\right ) e^{x} \]
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none
Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int e^x x \, dx={\left (x - 1\right )} e^{x} \]
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int e^x x \, dx={\left (x - 1\right )} e^{x} \]
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Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int e^x x \, dx={\mathrm {e}}^x\,\left (x-1\right ) \]
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