Optimal. Leaf size=19 \[ \frac {\log \left (\frac {625}{331776 e^2}\right )}{1-\log \left (x^2\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {12, 32} \begin {gather*} -\frac {2+\log \left (\frac {331776}{625}\right )}{1-\log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (2 \left (2+\log \left (\frac {331776}{625}\right )\right )\right ) \int \frac {1}{x-2 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx\right )\\ &=-\left (\left (2+\log \left (\frac {331776}{625}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{(-1+x)^2} \, dx,x,\log \left (x^2\right )\right )\right )\\ &=-\frac {2+\log \left (\frac {331776}{625}\right )}{1-\log \left (x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.79 \begin {gather*} \frac {2+\log \left (\frac {331776}{625}\right )}{-1+\log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 14, normalized size = 0.74 \begin {gather*} -\frac {\log \left (\frac {625}{331776}\right ) - 2}{\log \left (x^{2}\right ) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 15, normalized size = 0.79 \begin {gather*} -\frac {\log \left (\frac {625}{331776} \, e^{\left (-2\right )}\right )}{\log \left (x^{2}\right ) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.95
method | result | size |
default | \(-\frac {\ln \left (\frac {625 \,{\mathrm e}^{-2}}{331776}\right )}{\ln \left (x^{2}\right )-1}\) | \(18\) |
norman | \(\frac {2-4 \ln \relax (5)+4 \ln \left (24\right )}{\ln \left (x^{2}\right )-1}\) | \(20\) |
risch | \(-\frac {4 \ln \relax (5)}{\ln \left (x^{2}\right )-1}+\frac {12 \ln \relax (2)}{\ln \left (x^{2}\right )-1}+\frac {4 \ln \relax (3)}{\ln \left (x^{2}\right )-1}+\frac {2}{\ln \left (x^{2}\right )-1}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 15, normalized size = 0.79 \begin {gather*} -\frac {\log \left (\frac {625}{331776} \, e^{\left (-2\right )}\right )}{2 \, \log \relax (x) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 14, normalized size = 0.74 \begin {gather*} \frac {\ln \left (\frac {331776\,{\mathrm {e}}^2}{625}\right )}{\ln \left (x^2\right )-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.89 \begin {gather*} \frac {- 4 \log {\relax (5 )} + 2 + 4 \log {\left (24 \right )}}{\log {\left (x^{2} \right )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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