Optimal. Leaf size=22 \[ \left (x+\log \left (-5+\frac {16}{x^4}-\log (-2+x)+\log \left (x^2\right )\right )\right )^2 \]
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Rubi [A]
time = 0.63, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 200, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6820, 12,
6818} \begin {gather*} \left (\log \left (\frac {16}{x^4}+\log \left (x^2\right )-\log (x-2)-5\right )+x\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (128-96 x+16 x^2-4 x^4+11 x^5-5 x^6-(-2+x) x^5 \log (-2+x)+(-2+x) x^5 \log \left (x^2\right )\right ) \left (-x-\log \left (-5+\frac {16}{x^4}-\log (-2+x)+\log \left (x^2\right )\right )\right )}{(2-x) x \left (16-5 x^4-x^4 \log (-2+x)+x^4 \log \left (x^2\right )\right )} \, dx\\ &=2 \int \frac {\left (128-96 x+16 x^2-4 x^4+11 x^5-5 x^6-(-2+x) x^5 \log (-2+x)+(-2+x) x^5 \log \left (x^2\right )\right ) \left (-x-\log \left (-5+\frac {16}{x^4}-\log (-2+x)+\log \left (x^2\right )\right )\right )}{(2-x) x \left (16-5 x^4-x^4 \log (-2+x)+x^4 \log \left (x^2\right )\right )} \, dx\\ &=\left (x+\log \left (-5+\frac {16}{x^4}-\log (-2+x)+\log \left (x^2\right )\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(22)=44\).
time = 0.08, size = 54, normalized size = 2.45 \begin {gather*} 2 \left (\frac {x^2}{2}+x \log \left (-5+\frac {16}{x^4}-\log (-2+x)+\log \left (x^2\right )\right )+\frac {1}{2} \log ^2\left (-5+\frac {16}{x^4}-\log (-2+x)+\log \left (x^2\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 x^{6}-4 x^{5}\right ) \ln \left (x^{2}\right )+\left (-2 x^{6}+4 x^{5}\right ) \ln \left (x -2\right )-10 x^{6}+22 x^{5}-8 x^{4}+32 x^{2}-192 x +256\right ) \ln \left (\frac {x^{4} \ln \left (x^{2}\right )-x^{4} \ln \left (x -2\right )-5 x^{4}+16}{x^{4}}\right )+\left (2 x^{7}-4 x^{6}\right ) \ln \left (x^{2}\right )+\left (-2 x^{7}+4 x^{6}\right ) \ln \left (x -2\right )-10 x^{7}+22 x^{6}-8 x^{5}+32 x^{3}-192 x^{2}+256 x}{\left (x^{6}-2 x^{5}\right ) \ln \left (x^{2}\right )+\left (-x^{6}+2 x^{5}\right ) \ln \left (x -2\right )-5 x^{6}+10 x^{5}+16 x^{2}-32 x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 67 vs.
\(2 (22) = 44\).
time = 0.40, size = 67, normalized size = 3.05 \begin {gather*} x^{2} + 2 \, x \log \left (\frac {x^{4} \log \left (x^{2}\right ) - x^{4} \log \left (x - 2\right ) - 5 \, x^{4} + 16}{x^{4}}\right ) + \log \left (\frac {x^{4} \log \left (x^{2}\right ) - x^{4} \log \left (x - 2\right ) - 5 \, x^{4} + 16}{x^{4}}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (20) = 40\).
time = 1.40, size = 65, normalized size = 2.95 \begin {gather*} x^{2} + 2 x \log {\left (\frac {x^{4} \log {\left (x^{2} \right )} - x^{4} \log {\left (x - 2 \right )} - 5 x^{4} + 16}{x^{4}} \right )} + \log {\left (\frac {x^{4} \log {\left (x^{2} \right )} - x^{4} \log {\left (x - 2 \right )} - 5 x^{4} + 16}{x^{4}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.45, size = 34, normalized size = 1.55 \begin {gather*} {\left (x+\ln \left (-\frac {x^4\,\ln \left (x-2\right )-x^4\,\ln \left (x^2\right )+5\,x^4-16}{x^4}\right )\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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