Optimal. Leaf size=26 \[ \frac {3}{\log \left (\frac {1}{\frac {3}{2}+\frac {36 (1-x) (2-x)}{x}}\right )} \]
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Rubi [A] time = 0.14, antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1594, 6686} \begin {gather*} \frac {3}{\log \left (\frac {2 x}{3 \left (24 x^2-71 x+48\right )}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 1594
Rule 6686
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-144+72 x^2}{x \left (48-71 x+24 x^2\right ) \log ^2\left (\frac {2 x}{144-213 x+72 x^2}\right )} \, dx\\ &=\frac {3}{\log \left (\frac {2 x}{3 \left (48-71 x+24 x^2\right )}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 0.77 \begin {gather*} \frac {3}{\log \left (\frac {2 x}{144-213 x+72 x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 20, normalized size = 0.77 \begin {gather*} \frac {3}{\log \left (\frac {2 \, x}{3 \, {\left (24 \, x^{2} - 71 \, x + 48\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 20, normalized size = 0.77 \begin {gather*} \frac {3}{\log \left (\frac {2 \, x}{3 \, {\left (24 \, x^{2} - 71 \, x + 48\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 21, normalized size = 0.81
method | result | size |
norman | \(\frac {3}{\ln \left (\frac {2 x}{72 x^{2}-213 x +144}\right )}\) | \(21\) |
risch | \(\frac {3}{\ln \left (\frac {2 x}{72 x^{2}-213 x +144}\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 26, normalized size = 1.00 \begin {gather*} -\frac {3}{\log \relax (3) - \log \relax (2) + \log \left (24 \, x^{2} - 71 \, x + 48\right ) - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.04, size = 20, normalized size = 0.77 \begin {gather*} \frac {3}{\ln \left (\frac {2\,x}{72\,x^2-213\,x+144}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 15, normalized size = 0.58 \begin {gather*} \frac {3}{\log {\left (\frac {2 x}{72 x^{2} - 213 x + 144} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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