Integrand size = 13, antiderivative size = 17 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {11+e^x-x+e^3 x}{x} \]
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Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {14, 2228} \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {e^x}{x}+\frac {11}{x} \]
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Rule 14
Rule 2228
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {11}{x^2}+\frac {e^x (-1+x)}{x^2}\right ) \, dx \\ & = \frac {11}{x}+\int \frac {e^x (-1+x)}{x^2} \, dx \\ & = \frac {11}{x}+\frac {e^x}{x} \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.53 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {11+e^x}{x} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.53
method | result | size |
norman | \(\frac {11+{\mathrm e}^{x}}{x}\) | \(9\) |
parallelrisch | \(\frac {11+{\mathrm e}^{x}}{x}\) | \(9\) |
default | \(\frac {11}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(13\) |
risch | \(\frac {11}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(13\) |
parts | \(\frac {11}{x}+\frac {{\mathrm e}^{x}}{x}\) | \(13\) |
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none
Time = 0.22 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {e^{x} + 11}{x} \]
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Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {e^{x}}{x} + \frac {11}{x} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {11}{x} + {\rm Ei}\left (x\right ) - \Gamma \left (-1, -x\right ) \]
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none
Time = 0.30 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {e^{x} + 11}{x} \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {-11+e^x (-1+x)}{x^2} \, dx=\frac {{\mathrm {e}}^x+11}{x} \]
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