Optimal. Leaf size=10 \[ -\frac {1}{2} \log (3-2 x) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, 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 31
Rule 1586
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*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ -\frac {1}{2} \log (3-2 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 8, normalized size = 0.80 \[ -\frac {1}{2} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 9, normalized size = 0.90 \[ -\frac {1}{2} \, \log \left ({\left | 2 \, x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 9, normalized size = 0.90 \[ -\frac {\ln \left (2 x -3\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.39, size = 8, normalized size = 0.80 \[ -\frac {1}{2} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.99, size = 6, normalized size = 0.60 \[ -\frac {\ln \left (x-\frac {3}{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.80 \[ - \frac {\log {\left (2 x - 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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