Optimal. Leaf size=17 \[ \frac {-e^{4-x}+3 x}{e^2} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2194} \begin {gather*} \frac {3 x}{e^2}-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} &=\frac {\int \left (3+e^{4-x}\right ) \, dx}{e^2}\\ &=\frac {3 x}{e^2}+\frac {\int e^{4-x} \, dx}{e^2}\\ &=-e^{2-x}+\frac {3 x}{e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} \frac {-e^{4-x}+3 x}{e^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 15, normalized size = 0.88 \begin {gather*} {\left (3 \, x - e^{\left (-x + 4\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 15, normalized size = 0.88 \begin {gather*} {\left (3 \, x - e^{\left (-x + 4\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 15, normalized size = 0.88
method | result | size |
risch | \(3 \,{\mathrm e}^{-2} x -{\mathrm e}^{2-x}\) | \(15\) |
default | \(\left (3 x -{\mathrm e}^{-x +4}\right ) {\mathrm e}^{-2}\) | \(18\) |
norman | \(3 \,{\mathrm e}^{-2} x -{\mathrm e}^{-x +4} {\mathrm e}^{-2}\) | \(21\) |
derivativedivides | \(-{\mathrm e}^{-2} \left ({\mathrm e}^{-x +4}+3 \ln \left ({\mathrm e}^{-x +4}\right )\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 15, normalized size = 0.88 \begin {gather*} {\left (3 \, x - e^{\left (-x + 4\right )}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 14, normalized size = 0.82 \begin {gather*} 3\,x\,{\mathrm {e}}^{-2}-{\mathrm {e}}^{2-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 14, normalized size = 0.82 \begin {gather*} \frac {3 x}{e^{2}} - \frac {e^{4 - x}}{e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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