Optimal. Leaf size=30 \[ 4-\log ^2\left (\frac {\log (3+x)}{\left (x-\frac {9}{64} x \left (-x+x^2\right )^2\right )^2}\right ) \]
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Rubi [F]
time = 162.61, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A]
time = 0.04, size = 33, normalized size = 1.10 \begin {gather*} -\log ^2\left (\frac {4096 \log (3+x)}{x^2 \left (64-9 x^2+18 x^3-9 x^4\right )^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (180 x^{5}+252 x^{4}-756 x^{3}+324 x^{2}-256 x -768\right ) \ln \left (3+x \right )-18 x^{5}+36 x^{4}-18 x^{3}+128 x \right ) \ln \left (\frac {4096 \ln \left (3+x \right )}{81 x^{10}-324 x^{9}+486 x^{8}-324 x^{7}-1071 x^{6}+2304 x^{5}-1152 x^{4}+4096 x^{2}}\right )}{\left (9 x^{6}+9 x^{5}-45 x^{4}+27 x^{3}-64 x^{2}-192 x \right ) \ln \left (3+x \right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 206 vs.
\(2 (31) = 62\).
time = 0.66, size = 206, normalized size = 6.87 \begin {gather*} 4 \, {\left (2 \, \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (3 \, x^{2} - 3 \, x + 8\right ) + 4 \, \log \left (3 \, x^{2} - 3 \, x + 8\right )^{2} + 4 \, {\left (2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 4 \, \log \left (3 \, x^{2} - 3 \, x - 8\right )^{2} + 4 \, \log \left (x\right )^{2} + 2 \, {\left (2 \, \log \left (3 \, x^{2} - 3 \, x + 8\right ) + 2 \, \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (\frac {4096 \, \log \left (x + 3\right )}{81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}}\right ) - 4 \, \log \left (x\right ) \log \left (\log \left (x + 3\right )\right ) + \log \left (\log \left (x + 3\right )\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 54, normalized size = 1.80 \begin {gather*} -\log \left (\frac {4096 \, \log \left (x + 3\right )}{81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.29, size = 51, normalized size = 1.70 \begin {gather*} - \log {\left (\frac {4096 \log {\left (x + 3 \right )}}{81 x^{10} - 324 x^{9} + 486 x^{8} - 324 x^{7} - 1071 x^{6} + 2304 x^{5} - 1152 x^{4} + 4096 x^{2}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 207 vs.
\(2 (31) = 62\).
time = 0.54, size = 207, normalized size = 6.90 \begin {gather*} -2 \, {\left (2 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}\right ) + 4 \, {\left (2 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + 2 \, \log \left (x\right ) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) - 4 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right )^{2} + 4 \, \log \left (x\right )^{2} + 4 \, {\left (\log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + \log \left (x\right )\right )} \log \left (4096 \, \log \left (x + 3\right )\right ) - \log \left (4096 \, \log \left (x + 3\right )\right )^{2} - 4 \, \log \left (x\right ) \log \left (\log \left (x + 3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.69, size = 54, normalized size = 1.80 \begin {gather*} -{\ln \left (\frac {4096\,\ln \left (x+3\right )}{81\,x^{10}-324\,x^9+486\,x^8-324\,x^7-1071\,x^6+2304\,x^5-1152\,x^4+4096\,x^2}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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