Optimal. Leaf size=13 \[ 6+e^{-2 x} x+\log \left (\frac {5}{3}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.85, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2176, 2194} \begin {gather*} \frac {e^{-2 x}}{2}-\frac {1}{2} e^{-2 x} (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{2} e^{-2 x} (1-2 x)-\int e^{-2 x} \, dx\\ &=\frac {e^{-2 x}}{2}-\frac {1}{2} e^{-2 x} (1-2 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 0.54 \begin {gather*} e^{-2 x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.51, size = 6, normalized size = 0.46 \begin {gather*} x e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 6, normalized size = 0.46 \begin {gather*} x e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.54
method | result | size |
gosper | \({\mathrm e}^{-2 x} x\) | \(7\) |
default | \({\mathrm e}^{-2 x} x\) | \(7\) |
norman | \({\mathrm e}^{-2 x} x\) | \(7\) |
risch | \({\mathrm e}^{-2 x} x\) | \(7\) |
meijerg | \(-\frac {{\mathrm e}^{-2 x}}{2}+\frac {\left (4 x +2\right ) {\mathrm e}^{-2 x}}{4}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 18, normalized size = 1.38 \begin {gather*} \frac {1}{2} \, {\left (2 \, x + 1\right )} e^{\left (-2 \, x\right )} - \frac {1}{2} \, e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 6, normalized size = 0.46 \begin {gather*} x\,{\mathrm {e}}^{-2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.38 \begin {gather*} x e^{- 2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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