Optimal. Leaf size=9 \[ 1+4 e^{-2 x} \]
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Rubi [A] time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2194} \begin {gather*} 4 e^{-2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (8 \int e^{-2 x} \, dx\right )\\ &=4 e^{-2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 0.78 \begin {gather*} 4 e^{-2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 6, normalized size = 0.67 \begin {gather*} 4 \, e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 6, normalized size = 0.67 \begin {gather*} 4 \, 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 = 0.78
method | result | size |
default | \(4 \,{\mathrm e}^{-2 x}\) | \(7\) |
norman | \(4 \,{\mathrm e}^{-2 x}\) | \(7\) |
risch | \(4 \,{\mathrm e}^{-2 x}\) | \(7\) |
meijerg | \(-4+4 \,{\mathrm e}^{-2 x}\) | \(9\) |
gosper | \(4 \left ({\mathrm e}^{-x}\right )^{2}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 6, normalized size = 0.67 \begin {gather*} 4 \, e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 6, normalized size = 0.67 \begin {gather*} 4\,{\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 = 0.56 \begin {gather*} 4 e^{- 2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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