Optimal. Leaf size=10 \[ \frac{1}{2} \log (2 x+3) \]
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Rubi [A] time = 0.0146238, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.057, Rules used = {1586, 31} \[ \frac{1}{2} \log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 1586
Rule 31
Rubi steps
\begin{align*} \int \frac{243-162 x+108 x^2-72 x^3+48 x^4-32 x^5}{729-64 x^6} \, dx &=\int \frac{1}{3+2 x} \, dx\\ &=\frac{1}{2} \log (3+2 x)\\ \end{align*}
Mathematica [A] time = 0.0010186, size = 10, normalized size = 1. \[ \frac{1}{2} \log (2 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 9, normalized size = 0.9 \begin{align*}{\frac{\ln \left ( 3+2\,x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.928414, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \log \left (2 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.34647, size = 24, normalized size = 2.4 \begin{align*} \frac{1}{2} \, \log \left (2 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070157, size = 7, normalized size = 0.7 \begin{align*} \frac{\log{\left (2 x + 3 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05907, size = 12, normalized size = 1.2 \begin{align*} \frac{1}{2} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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