Integrand size = 18, antiderivative size = 21 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=-e^5+3 e^9+2 e^{-\frac {24}{x^2}} x \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.48, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2326} \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2 e^{-\frac {24}{x^2}} x \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = 2 e^{-\frac {24}{x^2}} x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.48 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2 e^{-\frac {24}{x^2}} x \]
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Time = 0.80 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.48
method | result | size |
derivativedivides | \(2 x \,{\mathrm e}^{-\frac {24}{x^{2}}}\) | \(10\) |
default | \(2 x \,{\mathrm e}^{-\frac {24}{x^{2}}}\) | \(10\) |
risch | \(2 x \,{\mathrm e}^{-\frac {24}{x^{2}}}\) | \(10\) |
gosper | \(2 x \,{\mathrm e}^{-\frac {24}{x^{2}}}\) | \(12\) |
norman | \(2 x \,{\mathrm e}^{-\frac {24}{x^{2}}}\) | \(12\) |
parallelrisch | \(2 x \,{\mathrm e}^{-\frac {24}{x^{2}}}\) | \(12\) |
meijerg | \(-2 \sqrt {6}\, \left (-\frac {x \sqrt {6}\, {\mathrm e}^{-\frac {24}{x^{2}}}}{6}-2 \sqrt {\pi }\, \operatorname {erf}\left (\frac {2 \sqrt {6}}{x}\right )\right )-4 \sqrt {6}\, \sqrt {\pi }\, \operatorname {erf}\left (\frac {2 \sqrt {6}}{x}\right )\) | \(51\) |
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none
Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2 \, x e^{\left (-\frac {24}{x^{2}}\right )} \]
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Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.38 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2 x e^{- \frac {24}{x^{2}}} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.29 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2 \, \sqrt {6} x \sqrt {\frac {1}{x^{2}}} \Gamma \left (-\frac {1}{2}, \frac {24}{x^{2}}\right ) - \frac {4 \, \sqrt {6} \sqrt {\pi } \sqrt {x^{2}} {\left (\operatorname {erf}\left (2 \, \sqrt {6} \sqrt {\frac {1}{x^{2}}}\right ) - 1\right )}}{x} \]
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none
Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2 \, x e^{\left (-\frac {24}{x^{2}}\right )} \]
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Time = 9.71 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.43 \[ \int \frac {e^{-\frac {24}{x^2}} \left (96+2 x^2\right )}{x^2} \, dx=2\,x\,{\mathrm {e}}^{-\frac {24}{x^2}} \]
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