Optimal. Leaf size=14 \[ \frac {4 \left (-2+3 e^{-x}\right )}{e^{10}} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} 12 e^{-x-10} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (12 \int e^{-10-x} \, dx\right )\\ &=12 e^{-10-x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} 12 e^{-10-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 8, normalized size = 0.57 \begin {gather*} 12 \, e^{\left (-x - 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.73, size = 8, normalized size = 0.57 \begin {gather*} 12 \, e^{\left (-x - 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 9, normalized size = 0.64
method | result | size |
risch | \(12 \,{\mathrm e}^{-10-x}\) | \(9\) |
meijerg | \(-12 \,{\mathrm e}^{-10} \left (1-{\mathrm e}^{-x}\right )\) | \(13\) |
gosper | \(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\) | \(15\) |
derivativedivides | \(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\) | \(15\) |
default | \(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\) | \(15\) |
norman | \(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 8, normalized size = 0.57 \begin {gather*} 12 \, e^{\left (-x - 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 8, normalized size = 0.57 \begin {gather*} 12\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.50 \begin {gather*} \frac {12 e^{- x}}{e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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