Optimal. Leaf size=20 \[ -5+\log \left (-3+32 e^{2+4 x-x^2} x\right ) \]
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Rubi [A] time = 0.20, antiderivative size = 27, normalized size of antiderivative = 1.35, number of steps used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6684} \begin {gather*} \log \left (e^{-x^2} \left (3 e^{x^2}-32 e^{4 x+2} x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (e^{-x^2} \left (3 e^{x^2}-32 e^{2+4 x} x\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 33, normalized size = 1.65 \begin {gather*} 32 \left (-\frac {x^2}{32}+\frac {1}{32} \log \left (3 e^{x^2}-32 e^{2+4 x} x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 24, normalized size = 1.20 \begin {gather*} \log \relax (x) + \log \left (\frac {32 \, x e^{\left (-x^{2} + 4 \, x + 2\right )} - 3}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 17, normalized size = 0.85 \begin {gather*} \log \left (32 \, x e^{\left (-x^{2} + 4 \, x + 2\right )} - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.90
method | result | size |
norman | \(\ln \left (32 x \,{\mathrm e}^{-x^{2}+4 x +2}-3\right )\) | \(18\) |
risch | \(\ln \relax (x )-2+\ln \left ({\mathrm e}^{-x^{2}+4 x +2}-\frac {3}{32 x}\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 21, normalized size = 1.05 \begin {gather*} -x^{2} + \log \left (-\frac {32}{3} \, x e^{\left (4 \, x + 2\right )} + e^{\left (x^{2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 18, normalized size = 0.90 \begin {gather*} \ln \left (32\,x\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{-x^2}-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 19, normalized size = 0.95 \begin {gather*} \log {\relax (x )} + \log {\left (e^{- x^{2} + 4 x + 2} - \frac {3}{32 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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