Optimal. Leaf size=17 \[ 4 \log \left (3+\frac {\log \left (3-4 x^2\right )}{x}\right ) \]
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Rubi [A]
time = 0.38, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6873, 6844, 31}
\begin {gather*} 4 \log \left (\frac {\log \left (3-4 x^2\right )}{x}+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 6844
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-32 x^2-\left (12-16 x^2\right ) \log \left (3-4 x^2\right )}{x \left (3-4 x^2\right ) \left (3 x+\log \left (3-4 x^2\right )\right )} \, dx\\ &=4 \text {Subst}\left (\int \frac {1}{3+x} \, dx,x,\frac {\log \left (3-4 x^2\right )}{x}\right )\\ &=4 \log \left (3+\frac {\log \left (3-4 x^2\right )}{x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 20, normalized size = 1.18 \begin {gather*} 4 \left (-\log (x)+\log \left (3 x+\log \left (3-4 x^2\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.36, size = 21, normalized size = 1.24
method | result | size |
norman | \(-4 \ln \left (x \right )+4 \ln \left (\ln \left (-4 x^{2}+3\right )+3 x \right )\) | \(21\) |
risch | \(-4 \ln \left (x \right )+4 \ln \left (\ln \left (-4 x^{2}+3\right )+3 x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 20, normalized size = 1.18 \begin {gather*} 4 \, \log \left (3 \, x + \log \left (-4 \, x^{2} + 3\right )\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 20, normalized size = 1.18 \begin {gather*} 4 \, \log \left (3 \, x + \log \left (-4 \, x^{2} + 3\right )\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 19, normalized size = 1.12 \begin {gather*} - 4 \log {\left (x \right )} + 4 \log {\left (3 x + \log {\left (3 - 4 x^{2} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 1.18 \begin {gather*} 4 \, \log \left (3 \, x + \log \left (-4 \, x^{2} + 3\right )\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.20, size = 20, normalized size = 1.18 \begin {gather*} 4\,\ln \left (3\,x+\ln \left (3-4\,x^2\right )\right )-4\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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