Optimal. Leaf size=20 \[ \frac {2^x}{\log (2)}-\frac {2^{-x}}{\log (2)} \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194} \[ \frac {2^x}{\log (2)}-\frac {2^{-x}}{\log (2)} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {align*} \int \left (2^{-x}+2^x\right ) \, dx &=\int 2^{-x} \, dx+\int 2^x \, dx\\ &=-\frac {2^{-x}}{\log (2)}+\frac {2^x}{\log (2)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ \frac {2^x}{\log (2)}-\frac {2^{-x}}{\log (2)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 17, normalized size = 0.85 \[ \frac {2^{2 \, x} - 1}{2^{x} \log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 20, normalized size = 1.00 \[ \frac {2^{x}}{\log \relax (2)} - \frac {1}{2^{x} \log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 1.05 \[ \frac {2^{x}}{\ln \relax (2)}-\frac {2^{-x}}{\ln \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 20, normalized size = 1.00 \[ \frac {2^{x}}{\log \relax (2)} - \frac {1}{2^{x} \log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.45, size = 17, normalized size = 0.85 \[ \frac {2^{2\,x}-1}{2^x\,\ln \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 17, normalized size = 0.85 \[ \frac {2^{x} \log {\relax (2 )} - 2^{- x} \log {\relax (2 )}}{\log {\relax (2 )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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