Optimal. Leaf size=9 \[ e^{-x}+e^x \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2225}
\begin {gather*} e^{-x}+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {align*} \int \left (-e^{-x}+e^x\right ) \, dx &=-\int e^{-x} \, dx+\int e^x \, dx\\ &=e^{-x}+e^x\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 1.00 \begin {gather*} e^{-x}+e^x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 8, normalized size = 0.89
method | result | size |
derivativedivides | \({\mathrm e}^{-x}+{\mathrm e}^{x}\) | \(8\) |
default | \({\mathrm e}^{-x}+{\mathrm e}^{x}\) | \(8\) |
risch | \({\mathrm e}^{-x}+{\mathrm e}^{x}\) | \(8\) |
meijerg | \(-2+{\mathrm e}^{-x}+{\mathrm e}^{x}\) | \(9\) |
norman | \(\left (1+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-x}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.09, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (-x\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.35, size = 11, normalized size = 1.22 \begin {gather*} {\left (e^{\left (2 \, x\right )} + 1\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.78 \begin {gather*} e^{x} + e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.46, size = 7, normalized size = 0.78 \begin {gather*} e^{\left (-x\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 4, normalized size = 0.44 \begin {gather*} 2\,\mathrm {cosh}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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