Integrand size = 251, antiderivative size = 31 \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=x+\frac {3 (16+x)^2}{x \log (3) \left (-2 x+(3-x+\log (x))^2\right )} \]
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\[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=\int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-11520+13248 x-16 x^5 \log (3)+x^6 \log (3)-6 x^3 (31+24 \log (3))+3 x^2 (-445+27 \log (3))+x^4 (-3+82 \log (3))-4 \left (1536-720 x+33 x^3 \log (3)-11 x^4 \log (3)+x^5 \log (3)-3 x^2 (17+9 \log (3))\right ) \log (x)+\left (-768-40 x^3 \log (3)+6 x^4 \log (3)+x^2 (3+54 \log (3))\right ) \log ^2(x)-4 (-3+x) x^2 \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{x^2 \log (3) \left (9-8 x+x^2-2 (-3+x) \log (x)+\log ^2(x)\right )^2} \, dx \\ & = \frac {\int \frac {-11520+13248 x-16 x^5 \log (3)+x^6 \log (3)-6 x^3 (31+24 \log (3))+3 x^2 (-445+27 \log (3))+x^4 (-3+82 \log (3))-4 \left (1536-720 x+33 x^3 \log (3)-11 x^4 \log (3)+x^5 \log (3)-3 x^2 (17+9 \log (3))\right ) \log (x)+\left (-768-40 x^3 \log (3)+6 x^4 \log (3)+x^2 (3+54 \log (3))\right ) \log ^2(x)-4 (-3+x) x^2 \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{x^2 \left (9-8 x+x^2-2 (-3+x) \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)} \\ & = \frac {\int \left (\log (3)-\frac {6 (16+x)^2 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {3 \left (-256+x^2\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}\right ) \, dx}{\log (3)} \\ & = x+\frac {3 \int \frac {-256+x^2}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {6 \int \frac {(16+x)^2 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)} \\ & = x+\frac {3 \int \left (\frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)}-\frac {256}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}\right ) \, dx}{\log (3)}-\frac {6 \int \left (\frac {3-5 x+x^2+\log (x)-x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {256 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {32 \left (3-5 x+x^2+\log (x)-x \log (x)\right )}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}\right ) \, dx}{\log (3)} \\ & = x+\frac {3 \int \frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)} \, dx}{\log (3)}-\frac {6 \int \frac {3-5 x+x^2+\log (x)-x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {192 \int \frac {3-5 x+x^2+\log (x)-x \log (x)}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {768 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {1536 \int \frac {3-5 x+x^2+\log (x)-x \log (x)}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)} \\ & = x+\frac {96}{\log (3) \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}+\frac {3 \int \frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)} \, dx}{\log (3)}-\frac {6 \int \left (\frac {3}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {5 x}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {x^2}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}\right ) \, dx}{\log (3)}-\frac {768 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {1536 \int \left (\frac {1}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {3}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {5}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}+\frac {\log (x)}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}-\frac {\log (x)}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2}\right ) \, dx}{\log (3)} \\ & = x+\frac {96}{\log (3) \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )}+\frac {3 \int \frac {1}{9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)} \, dx}{\log (3)}-\frac {6 \int \frac {x^2}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {6 \int \frac {\log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {6 \int \frac {x \log (x)}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {18 \int \frac {1}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {30 \int \frac {x}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {768 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )} \, dx}{\log (3)}-\frac {1536 \int \frac {1}{\left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {1536 \int \frac {\log (x)}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {1536 \int \frac {\log (x)}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}-\frac {4608 \int \frac {1}{x^2 \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)}+\frac {7680 \int \frac {1}{x \left (9-8 x+x^2+6 \log (x)-2 x \log (x)+\log ^2(x)\right )^2} \, dx}{\log (3)} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.32 \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=\frac {x \log (3)+\frac {3 (16+x)^2}{x \left (9-8 x+x^2-2 (-3+x) \log (x)+\log ^2(x)\right )}}{\log (3)} \]
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Time = 1.53 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39
method | result | size |
default | \(x +\frac {3 x^{2}+96 x +768}{\ln \left (3\right ) x \left (\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}+6 \ln \left (x \right )-8 x +9\right )}\) | \(43\) |
risch | \(x +\frac {3 x^{2}+96 x +768}{\ln \left (3\right ) x \left (\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}+6 \ln \left (x \right )-8 x +9\right )}\) | \(43\) |
parallelrisch | \(\frac {768+96 x +6 x^{2} \ln \left (3\right ) \ln \left (x \right )-8 x^{3} \ln \left (3\right )+x^{4} \ln \left (3\right )+9 x^{2} \ln \left (3\right )+3 x^{2}-2 \ln \left (x \right ) \ln \left (3\right ) x^{3}+x^{2} \ln \left (3\right ) \ln \left (x \right )^{2}}{x \ln \left (3\right ) \left (\ln \left (x \right )^{2}-2 x \ln \left (x \right )+x^{2}+6 \ln \left (x \right )-8 x +9\right )}\) | \(90\) |
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Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (31) = 62\).
Time = 0.26 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.97 \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=\frac {x^{2} \log \left (3\right ) \log \left (x\right )^{2} - 2 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (3\right ) \log \left (x\right ) + 3 \, x^{2} + {\left (x^{4} - 8 \, x^{3} + 9 \, x^{2}\right )} \log \left (3\right ) + 96 \, x + 768}{x \log \left (3\right ) \log \left (x\right )^{2} - 2 \, {\left (x^{2} - 3 \, x\right )} \log \left (3\right ) \log \left (x\right ) + {\left (x^{3} - 8 \, x^{2} + 9 \, x\right )} \log \left (3\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (24) = 48\).
Time = 0.12 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.97 \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=x + \frac {3 x^{2} + 96 x + 768}{x^{3} \log {\left (3 \right )} - 8 x^{2} \log {\left (3 \right )} + x \log {\left (3 \right )} \log {\left (x \right )}^{2} + 9 x \log {\left (3 \right )} + \left (- 2 x^{2} \log {\left (3 \right )} + 6 x \log {\left (3 \right )}\right ) \log {\left (x \right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 103 vs. \(2 (31) = 62\).
Time = 0.31 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=\frac {x^{4} \log \left (3\right ) + x^{2} \log \left (3\right ) \log \left (x\right )^{2} - 8 \, x^{3} \log \left (3\right ) + 3 \, x^{2} {\left (3 \, \log \left (3\right ) + 1\right )} - 2 \, {\left (x^{3} \log \left (3\right ) - 3 \, x^{2} \log \left (3\right )\right )} \log \left (x\right ) + 96 \, x + 768}{x^{3} \log \left (3\right ) + x \log \left (3\right ) \log \left (x\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 9 \, x \log \left (3\right ) - 2 \, {\left (x^{2} \log \left (3\right ) - 3 \, x \log \left (3\right )\right )} \log \left (x\right )} \]
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Time = 0.31 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.84 \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=x + \frac {3 \, {\left (x^{2} + 32 \, x + 256\right )}}{x^{3} \log \left (3\right ) - 2 \, x^{2} \log \left (3\right ) \log \left (x\right ) + x \log \left (3\right ) \log \left (x\right )^{2} - 8 \, x^{2} \log \left (3\right ) + 6 \, x \log \left (3\right ) \log \left (x\right ) + 9 \, x \log \left (3\right )} \]
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Timed out. \[ \int \frac {-11520+13248 x-1335 x^2-186 x^3-3 x^4+\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (-6144+2880 x+204 x^2+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3)\right ) \log (x)+\left (-768+3 x^2+\left (54 x^2-40 x^3+6 x^4\right ) \log (3)\right ) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)}{\left (81 x^2-144 x^3+82 x^4-16 x^5+x^6\right ) \log (3)+\left (108 x^2-132 x^3+44 x^4-4 x^5\right ) \log (3) \log (x)+\left (54 x^2-40 x^3+6 x^4\right ) \log (3) \log ^2(x)+\left (12 x^2-4 x^3\right ) \log (3) \log ^3(x)+x^2 \log (3) \log ^4(x)} \, dx=\int \frac {13248\,x+{\ln \left (x\right )}^2\,\left (\ln \left (3\right )\,\left (6\,x^4-40\,x^3+54\,x^2\right )+3\,x^2-768\right )+\ln \left (x\right )\,\left (2880\,x+\ln \left (3\right )\,\left (-4\,x^5+44\,x^4-132\,x^3+108\,x^2\right )+204\,x^2-6144\right )-1335\,x^2-186\,x^3-3\,x^4+\ln \left (3\right )\,\left (x^6-16\,x^5+82\,x^4-144\,x^3+81\,x^2\right )+\ln \left (3\right )\,{\ln \left (x\right )}^3\,\left (12\,x^2-4\,x^3\right )+x^2\,\ln \left (3\right )\,{\ln \left (x\right )}^4-11520}{\ln \left (3\right )\,\left (x^6-16\,x^5+82\,x^4-144\,x^3+81\,x^2\right )+\ln \left (3\right )\,{\ln \left (x\right )}^2\,\left (6\,x^4-40\,x^3+54\,x^2\right )+\ln \left (3\right )\,{\ln \left (x\right )}^3\,\left (12\,x^2-4\,x^3\right )+x^2\,\ln \left (3\right )\,{\ln \left (x\right )}^4+\ln \left (3\right )\,\ln \left (x\right )\,\left (-4\,x^5+44\,x^4-132\,x^3+108\,x^2\right )} \,d x \]
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