Optimal. Leaf size=8 \[ \frac {x}{2 e^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8}
\begin {gather*} \frac {x}{2 e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{2 e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {x}{2 e^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 8, normalized size = 1.00
method | result | size |
risch | \(\frac {{\mathrm e}^{-2} x}{2}\) | \(6\) |
default | \(\frac {{\mathrm e}^{-2} x}{2}\) | \(8\) |
norman | \(\frac {{\mathrm e}^{-2} x}{2}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 5, normalized size = 0.62 \begin {gather*} \frac {x}{2 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.00, size = 5, normalized size = 0.62 \begin {gather*} \frac {x\,{\mathrm {e}}^{-2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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