Optimal. Leaf size=27 \[ e^{\frac {2 x+x^2+\frac {1}{3} \left (-3+x-\frac {x^2}{4}\right )}{x}} \]
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Rubi [A] time = 0.17, antiderivative size = 19, normalized size of antiderivative = 0.70, number of steps used = 2, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {12, 6706} \begin {gather*} e^{-\frac {-11 x^2-28 x+12}{12 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{12} \int \frac {e^{\frac {-12+28 x+11 x^2}{12 x}} \left (12+11 x^2\right )}{x^2} \, dx\\ &=e^{-\frac {12-28 x-11 x^2}{12 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 16, normalized size = 0.59 \begin {gather*} e^{\frac {7}{3}-\frac {1}{x}+\frac {11 x}{12}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 16, normalized size = 0.59 \begin {gather*} e^{\left (\frac {11 \, x^{2} + 28 \, x - 12}{12 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 11, normalized size = 0.41 \begin {gather*} e^{\left (\frac {11}{12} \, x - \frac {1}{x} + \frac {7}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 17, normalized size = 0.63
method | result | size |
gosper | \({\mathrm e}^{\frac {11 x^{2}+28 x -12}{12 x}}\) | \(17\) |
norman | \({\mathrm e}^{\frac {11 x^{2}+28 x -12}{12 x}}\) | \(17\) |
risch | \({\mathrm e}^{\frac {11 x^{2}+28 x -12}{12 x}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 11, normalized size = 0.41 \begin {gather*} e^{\left (\frac {11}{12} \, x - \frac {1}{x} + \frac {7}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.00, size = 13, normalized size = 0.48 \begin {gather*} {\mathrm {e}}^{\frac {11\,x}{12}}\,{\mathrm {e}}^{7/3}\,{\mathrm {e}}^{-\frac {1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.56 \begin {gather*} e^{\frac {\frac {11 x^{2}}{12} + \frac {7 x}{3} - 1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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