Optimal. Leaf size=13 \[ -\frac {1}{\left (3^x+1\right ) \log (3)} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2282, 32} \[ -\frac {1}{\left (3^x+1\right ) \log (3)} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2282
Rubi steps
\begin {align*} \int \frac {1}{2+3^{-x}+3^x} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{(1+x)^2} \, dx,x,3^x\right )}{\log (3)}\\ &=-\frac {1}{\left (1+3^x\right ) \log (3)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \[ -\frac {1}{\left (3^x+1\right ) \log (3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 13, normalized size = 1.00 \[ -\frac {1}{3^{x} \log \relax (3) + \log \relax (3)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 13, normalized size = 1.00 \[ -\frac {1}{{\left (3^{x} + 1\right )} \log \relax (3)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 1.08 \[ -\frac {1}{\left (3^{x}+1\right ) \ln \relax (3)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 14, normalized size = 1.08 \[ \frac {1}{{\left (\frac {1}{3^{x}} + 1\right )} \log \relax (3)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 13, normalized size = 1.00 \[ -\frac {1}{\ln \relax (3)\,\left (3^x+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.92 \[ - \frac {1}{3^{x} \log {\relax (3 )} + \log {\relax (3 )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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