Optimal. Leaf size=12 \[ \frac {1}{6} \log \left (3 e^x+2\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2246, 31} \[ \frac {1}{6} \log \left (3 e^x+2\right ) \]
Antiderivative was successfully verified.
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Rule 31
Rule 2246
Rubi steps
\begin {align*} \int \frac {e^x}{4+6 e^x} \, dx &=\operatorname {Subst}\left (\int \frac {1}{4+6 x} \, dx,x,e^x\right )\\ &=\frac {1}{6} \log \left (2+3 e^x\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ \frac {1}{6} \log \left (3 e^x+2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 9, normalized size = 0.75 \[ \frac {1}{6} \, \log \left (3 \, e^{x} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 9, normalized size = 0.75 \[ \frac {1}{6} \, \log \left (3 \, e^{x} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.83 \[ \frac {\ln \left (3 \,{\mathrm e}^{x}+2\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 9, normalized size = 0.75 \[ \frac {1}{6} \, \log \left (3 \, e^{x} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 9, normalized size = 0.75 \[ \frac {\ln \left (3\,{\mathrm {e}}^x+2\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.67 \[ \frac {\log {\left (e^{x} + \frac {2}{3} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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