Optimal. Leaf size=10 \[ -\frac{1}{2} \log (3-2 x) \]
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Rubi [A] time = 0.0133504, 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} \[ -\frac{1}{2} \log (3-2 x) \]
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 = 0.0010264, size = 10, normalized size = 1. \[ -\frac{1}{2} \log (3-2 x) \]
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 = 0.920725, 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 = 1.35855, size = 26, normalized size = 2.6 \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 = 0.068114, size = 8, normalized size = 0.8 \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 = 1.05218, 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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