Optimal. Leaf size=12 \[ \frac{1}{6} \log \left (3 e^x+2\right ) \]
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Rubi [A] time = 0.0168879, antiderivative size = 12, normalized size of antiderivative = 1., 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 2246
Rule 31
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*}
Mathematica [A] time = 0.0056498, size = 12, normalized size = 1. \[ \frac{1}{6} \log \left (3 e^x+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 10, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( 2+3\,{{\rm e}^{x}} \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13738, size = 12, normalized size = 1. \begin{align*} \frac{1}{6} \, \log \left (3 \, e^{x} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44771, size = 27, normalized size = 2.25 \begin{align*} \frac{1}{6} \, \log \left (3 \, e^{x} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12272, size = 8, normalized size = 0.67 \begin{align*} \frac{\log{\left (e^{x} + \frac{2}{3} \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28391, size = 12, normalized size = 1. \begin{align*} \frac{1}{6} \, \log \left (3 \, e^{x} + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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