Optimal. Leaf size=25 \[ \frac {1}{4} e^{\frac {\frac {265}{3}-\frac {1}{256} (1-x)^2}{x}} \]
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Rubi [A]
time = 0.11, antiderivative size = 23, normalized size of antiderivative = 0.92, 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, 6838}
\begin {gather*} \frac {1}{4} e^{\frac {-3 x^2+6 x+67837}{768 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{\frac {67837+6 x-3 x^2}{768 x}} \left (-67837-3 x^2\right )}{x^2} \, dx}{3072}\\ &=\frac {1}{4} e^{\frac {67837+6 x-3 x^2}{768 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{4} e^{\frac {1}{128}+\frac {67837}{768 x}-\frac {x}{256}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 19, normalized size = 0.76
method | result | size |
gosper | \(\frac {{\mathrm e}^{-\frac {3 x^{2}-6 x -67837}{768 x}}}{4}\) | \(19\) |
norman | \(\frac {{\mathrm e}^{\frac {-3 x^{2}+6 x +67837}{768 x}}}{4}\) | \(19\) |
risch | \(\frac {{\mathrm e}^{-\frac {3 x^{2}-6 x -67837}{768 x}}}{4}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.96, size = 13, normalized size = 0.52 \begin {gather*} \frac {1}{4} \, e^{\left (-\frac {1}{256} \, x + \frac {67837}{768 \, x} + \frac {1}{128}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 18, normalized size = 0.72 \begin {gather*} \frac {1}{4} \, e^{\left (-\frac {3 \, x^{2} - 6 \, x - 67837}{768 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.60 \begin {gather*} \frac {e^{\frac {- \frac {x^{2}}{256} + \frac {x}{128} + \frac {67837}{768}}{x}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.14, size = 13, normalized size = 0.52 \begin {gather*} \frac {{\mathrm {e}}^{\frac {67837}{768\,x}-\frac {x}{256}+\frac {1}{128}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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