Integrand size = 16, antiderivative size = 19 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=\frac {3-e^2+e^x-\frac {2 x}{3}}{x} \]
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Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {14, 2228} \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=\frac {e^x}{x}+\frac {3-e^2}{x} \]
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Rule 14
Rule 2228
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {-3+e^2}{x^2}+\frac {e^x (-1+x)}{x^2}\right ) \, dx \\ & = \frac {3-e^2}{x}+\int \frac {e^x (-1+x)}{x^2} \, dx \\ & = \frac {e^x}{x}+\frac {3-e^2}{x} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=\frac {3-e^2+e^x}{x} \]
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Time = 0.33 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68
method | result | size |
norman | \(\frac {-{\mathrm e}^{2}+3+{\mathrm e}^{x}}{x}\) | \(13\) |
parallelrisch | \(-\frac {{\mathrm e}^{2}-3-{\mathrm e}^{x}}{x}\) | \(14\) |
parts | \(-\frac {{\mathrm e}^{2}-3}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(17\) |
default | \(-\frac {{\mathrm e}^{2}}{x}+\frac {3}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(20\) |
risch | \(-\frac {{\mathrm e}^{2}}{x}+\frac {3}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(20\) |
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=-\frac {e^{2} - e^{x} - 3}{x} \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=\frac {e^{x}}{x} - \frac {-3 + e^{2}}{x} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.21 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.16 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=-\frac {e^{2}}{x} + \frac {3}{x} + {\rm Ei}\left (x\right ) - \Gamma \left (-1, -x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=-\frac {e^{2} - e^{x} - 3}{x} \]
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Time = 0.07 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {-3+e^2+e^x (-1+x)}{x^2} \, dx=\frac {{\mathrm {e}}^x-{\mathrm {e}}^2+3}{x} \]
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