Optimal. Leaf size=29 \[ \frac {e^{10-e^4-2 (4-x)^2+2 x} \log ^2(5)}{x^2} \]
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Rubi [A]
time = 0.05, antiderivative size = 41, normalized size of antiderivative = 1.41, number of steps
used = 2, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {12, 2326}
\begin {gather*} \frac {e^{-2 x^2+18 x-e^4-22} \left (9 x-2 x^2\right ) \log ^2(5)}{(9-2 x) x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^2(5) \int \frac {e^{-22-e^4+18 x-2 x^2} \left (-2+18 x-4 x^2\right )}{x^3} \, dx\\ &=\frac {e^{-22-e^4+18 x-2 x^2} \left (9 x-2 x^2\right ) \log ^2(5)}{(9-2 x) x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.19, size = 25, normalized size = 0.86 \begin {gather*} \frac {e^{-22-e^4+18 x-2 x^2} \log ^2(5)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 24, normalized size = 0.83
method | result | size |
risch | \(\frac {\ln \left (5\right )^{2} {\mathrm e}^{-22-2 x^{2}+18 x -{\mathrm e}^{4}}}{x^{2}}\) | \(24\) |
gosper | \(\frac {{\mathrm e}^{10} \ln \left (5\right )^{2} {\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{-2 x^{2}+18 x -32}}{x^{2}}\) | \(31\) |
norman | \(\frac {{\mathrm e}^{10} \ln \left (5\right )^{2} {\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{-2 x^{2}+18 x -32}}{x^{2}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 23, normalized size = 0.79 \begin {gather*} \frac {e^{\left (-2 \, x^{2} + 18 \, x - e^{4} - 22\right )} \log \left (5\right )^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 23, normalized size = 0.79 \begin {gather*} \frac {e^{\left (-2 \, x^{2} + 18 \, x - e^{4} - 22\right )} \log \left (5\right )^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 27, normalized size = 0.93 \begin {gather*} \frac {e^{10} e^{- 2 x^{2} + 18 x - 32} \log {\left (5 \right )}^{2}}{x^{2} e^{e^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 23, normalized size = 0.79 \begin {gather*} \frac {e^{\left (-2 \, x^{2} + 18 \, x - e^{4} - 22\right )} \log \left (5\right )^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 25, normalized size = 0.86 \begin {gather*} \frac {{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{18\,x}\,{\mathrm {e}}^{-22}\,{\mathrm {e}}^{-2\,x^2}\,{\ln \left (5\right )}^2}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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