Optimal. Leaf size=19 \[ 2+e^{-5-x+\frac {\log (5)}{x^2}} x^2 \]
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Rubi [A]
time = 0.23, antiderivative size = 25, normalized size of antiderivative = 1.32, number of steps
used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6820, 2326}
\begin {gather*} \frac {5^{\frac {1}{x^2}} e^{-x-5} x^2 \log (25)}{2 \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5^{\frac {1}{x^2}} e^{-5-x} \left (2 x^2-x^3-\log (25)\right )}{x} \, dx\\ &=\frac {5^{\frac {1}{x^2}} e^{-5-x} x^2 \log (25)}{2 \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 16, normalized size = 0.84 \begin {gather*} 5^{\frac {1}{x^2}} e^{-5-x} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.36, size = 18, normalized size = 0.95
method | result | size |
risch | \(x^{2} 5^{\frac {1}{x^{2}}} {\mathrm e}^{-x -5}\) | \(18\) |
gosper | \(x \,{\mathrm e}^{\frac {x^{2} \ln \left (x \right )-x^{3}-5 x^{2}+\ln \left (5\right )}{x^{2}}}\) | \(30\) |
norman | \(x \,{\mathrm e}^{-\frac {-x^{2} \ln \left (x \right )-\ln \left (5\right )+x^{3}+5 x^{2}}{x^{2}}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 16, normalized size = 0.84 \begin {gather*} x^{2} e^{\left (-x + \frac {\log \left (5\right )}{x^{2}} - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 28, normalized size = 1.47 \begin {gather*} x e^{\left (-\frac {x^{3} - x^{2} \log \left (x\right ) + 5 \, x^{2} - \log \left (5\right )}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 24, normalized size = 1.26 \begin {gather*} x e^{- \frac {x^{3} - x^{2} \log {\left (x \right )} + 5 x^{2} - \log {\left (5 \right )}}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 23, normalized size = 1.21 \begin {gather*} x^{2} e^{\left (-\frac {x^{3} + 5 \, x^{2} - \log \left (5\right )}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.59, size = 15, normalized size = 0.79 \begin {gather*} 5^{\frac {1}{x^2}}\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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