Optimal. Leaf size=14 \[ \frac {1}{e^3}-e^{-5 x/4}+x \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 2194} \begin {gather*} x-e^{-5 x/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (4+5 e^{-5 x/4}\right ) \, dx\\ &=x+\frac {5}{4} \int e^{-5 x/4} \, dx\\ &=-e^{-5 x/4}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 0.79 \begin {gather*} -e^{-5 x/4}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 8, normalized size = 0.57 \begin {gather*} x - e^{\left (-\frac {5}{4} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 8, normalized size = 0.57 \begin {gather*} x - e^{\left (-\frac {5}{4} \, x\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 |
default | \(x -{\mathrm e}^{-\frac {5 x}{4}}\) | \(9\) |
norman | \(x -{\mathrm e}^{-\frac {5 x}{4}}\) | \(9\) |
risch | \(x -{\mathrm e}^{-\frac {5 x}{4}}\) | \(9\) |
derivativedivides | \(-{\mathrm e}^{-\frac {5 x}{4}}-\frac {4 \ln \left ({\mathrm e}^{-\frac {5 x}{4}}\right )}{5}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 8, normalized size = 0.57 \begin {gather*} x - e^{\left (-\frac {5}{4} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 8, normalized size = 0.57 \begin {gather*} x-{\mathrm {e}}^{-\frac {5\,x}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 8, normalized size = 0.57 \begin {gather*} x - e^{- \frac {5 x}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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