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 = {2194} \[ e^{-x}+e^x \]
Antiderivative was successfully verified.
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Rule 2194
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 = 0.00, size = 9, normalized size = 1.00 \[ e^{-x}+e^x \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (-e^{-x}+e^x\right ) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.11, size = 11, normalized size = 1.22 \[ {\left (e^{\left (2 \, x\right )} + 1\right )} e^{\left (-x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.60, size = 7, normalized size = 0.78 \[ e^{\left (-x\right )} + e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, 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 = 0.55, size = 7, normalized size = 0.78 \[ e^{\left (-x\right )} + e^{x} \]
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 \[ 2\,\mathrm {cosh}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.78 \[ e^{x} + e^{- x} \]
Verification of antiderivative is not currently implemented for this CAS.
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