Optimal. Leaf size=10 \[ \frac{1}{6} \tanh ^{-1}\left (\frac{2 x}{3}\right ) \]
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Rubi [A] time = 0.009933, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {1586, 206} \[ \frac{1}{6} \tanh ^{-1}\left (\frac{2 x}{3}\right ) \]
Antiderivative was successfully verified.
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Rule 1586
Rule 206
Rubi steps
\begin{align*} \int \frac{81+36 x^2+16 x^4}{729-64 x^6} \, dx &=\int \frac{1}{9-4 x^2} \, dx\\ &=\frac{1}{6} \tanh ^{-1}\left (\frac{2 x}{3}\right )\\ \end{align*}
Mathematica [B] time = 0.0026819, size = 21, normalized size = 2.1 \[ \frac{1}{12} \log (2 x+3)-\frac{1}{12} \log (3-2 x) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 18, normalized size = 1.8 \begin{align*}{\frac{\ln \left ( 3+2\,x \right ) }{12}}-{\frac{\ln \left ( -3+2\,x \right ) }{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.895089, size = 23, normalized size = 2.3 \begin{align*} \frac{1}{12} \, \log \left (2 \, x + 3\right ) - \frac{1}{12} \, \log \left (2 \, x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.35319, size = 53, normalized size = 5.3 \begin{align*} \frac{1}{12} \, \log \left (2 \, x + 3\right ) - \frac{1}{12} \, \log \left (2 \, x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.0933, size = 15, normalized size = 1.5 \begin{align*} - \frac{\log{\left (x - \frac{3}{2} \right )}}{12} + \frac{\log{\left (x + \frac{3}{2} \right )}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.04777, size = 20, normalized size = 2. \begin{align*} \frac{1}{12} \, \log \left ({\left | x + \frac{3}{2} \right |}\right ) - \frac{1}{12} \, \log \left ({\left | x - \frac{3}{2} \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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