Integrand size = 63, antiderivative size = 25 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=x \left (1+\frac {\left (-5+\left (9-\frac {x}{16}-\log (5)\right )^2\right )^2}{x^2}\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(25)=50\).
Time = 0.03 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.08, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {12, 14} \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=\frac {x^3}{65536}-\frac {x^2 (9-\log (5))}{1024}+\frac {3}{128} x \left (122+\log ^2(5)-18 \log (5)\right )+\frac {\left (76+\log ^2(5)-18 \log (5)\right )^2}{x} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{x^2} \, dx}{65536} \\ & = \frac {\int \left (3 x^2+128 x (-9+\log (5))-\frac {65536 \left (76-18 \log (5)+\log ^2(5)\right )^2}{x^2}+1536 \left (122-18 \log (5)+\log ^2(5)\right )\right ) \, dx}{65536} \\ & = \frac {x^3}{65536}-\frac {x^2 (9-\log (5))}{1024}+\frac {\left (76-18 \log (5)+\log ^2(5)\right )^2}{x}+\frac {3}{128} x \left (122-18 \log (5)+\log ^2(5)\right ) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.00 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=\frac {x^3}{65536}+\frac {x^2 (-9+\log (5))}{1024}+\frac {\left (76-18 \log (5)+\log ^2(5)\right )^2}{x}+\frac {3}{128} x \left (122-18 \log (5)+\log ^2(5)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(23)=46\).
Time = 0.07 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32
method | result | size |
norman | \(\frac {\left (\frac {\ln \left (5\right )}{1024}-\frac {9}{1024}\right ) x^{3}+\left (\frac {3 \ln \left (5\right )^{2}}{128}-\frac {27 \ln \left (5\right )}{64}+\frac {183}{64}\right ) x^{2}+\frac {x^{4}}{65536}+\ln \left (5\right )^{4}-36 \ln \left (5\right )^{3}+476 \ln \left (5\right )^{2}-2736 \ln \left (5\right )+5776}{x}\) | \(58\) |
default | \(\frac {3 x \ln \left (5\right )^{2}}{128}+\frac {x^{2} \ln \left (5\right )}{1024}+\frac {x^{3}}{65536}-\frac {27 x \ln \left (5\right )}{64}-\frac {9 x^{2}}{1024}+\frac {183 x}{64}-\frac {-65536 \ln \left (5\right )^{4}+2359296 \ln \left (5\right )^{3}-31195136 \ln \left (5\right )^{2}+179306496 \ln \left (5\right )-378535936}{65536 x}\) | \(63\) |
gosper | \(\frac {65536 \ln \left (5\right )^{4}+1536 x^{2} \ln \left (5\right )^{2}+64 x^{3} \ln \left (5\right )+x^{4}-2359296 \ln \left (5\right )^{3}-27648 x^{2} \ln \left (5\right )-576 x^{3}+31195136 \ln \left (5\right )^{2}+187392 x^{2}-179306496 \ln \left (5\right )+378535936}{65536 x}\) | \(66\) |
parallelrisch | \(\frac {65536 \ln \left (5\right )^{4}+1536 x^{2} \ln \left (5\right )^{2}+64 x^{3} \ln \left (5\right )+x^{4}-2359296 \ln \left (5\right )^{3}-27648 x^{2} \ln \left (5\right )-576 x^{3}+31195136 \ln \left (5\right )^{2}+187392 x^{2}-179306496 \ln \left (5\right )+378535936}{65536 x}\) | \(66\) |
risch | \(\frac {3 x \ln \left (5\right )^{2}}{128}+\frac {x^{2} \ln \left (5\right )}{1024}+\frac {x^{3}}{65536}-\frac {27 x \ln \left (5\right )}{64}-\frac {9 x^{2}}{1024}+\frac {183 x}{64}+\frac {\ln \left (5\right )^{4}}{x}-\frac {36 \ln \left (5\right )^{3}}{x}+\frac {476 \ln \left (5\right )^{2}}{x}-\frac {2736 \ln \left (5\right )}{x}+\frac {5776}{x}\) | \(72\) |
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Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (22) = 44\).
Time = 0.23 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.36 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=\frac {x^{4} + 65536 \, \log \left (5\right )^{4} - 576 \, x^{3} + 512 \, {\left (3 \, x^{2} + 60928\right )} \log \left (5\right )^{2} - 2359296 \, \log \left (5\right )^{3} + 187392 \, x^{2} + 64 \, {\left (x^{3} - 432 \, x^{2} - 2801664\right )} \log \left (5\right ) + 378535936}{65536 \, x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (19) = 38\).
Time = 0.09 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.52 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=\frac {x^{3}}{65536} + \frac {x^{2} \left (-576 + 64 \log {\left (5 \right )}\right )}{65536} + \frac {x \left (- 27648 \log {\left (5 \right )} + 1536 \log {\left (5 \right )}^{2} + 187392\right )}{65536} + \frac {- 179306496 \log {\left (5 \right )} - 2359296 \log {\left (5 \right )}^{3} + 65536 \log {\left (5 \right )}^{4} + 31195136 \log {\left (5 \right )}^{2} + 378535936}{65536 x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (22) = 44\).
Time = 0.19 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.16 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=\frac {1}{65536} \, x^{3} + \frac {1}{1024} \, x^{2} {\left (\log \left (5\right ) - 9\right )} + \frac {3}{128} \, {\left (\log \left (5\right )^{2} - 18 \, \log \left (5\right ) + 122\right )} x + \frac {\log \left (5\right )^{4} - 36 \, \log \left (5\right )^{3} + 476 \, \log \left (5\right )^{2} - 2736 \, \log \left (5\right ) + 5776}{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (22) = 44\).
Time = 0.26 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.36 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=\frac {1}{65536} \, x^{3} + \frac {1}{1024} \, x^{2} \log \left (5\right ) + \frac {3}{128} \, x \log \left (5\right )^{2} - \frac {9}{1024} \, x^{2} - \frac {27}{64} \, x \log \left (5\right ) + \frac {183}{64} \, x + \frac {\log \left (5\right )^{4} - 36 \, \log \left (5\right )^{3} + 476 \, \log \left (5\right )^{2} - 2736 \, \log \left (5\right ) + 5776}{x} \]
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Time = 8.14 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.24 \[ \int \frac {-378535936+187392 x^2-1152 x^3+3 x^4+\left (179306496-27648 x^2+128 x^3\right ) \log (5)+\left (-31195136+1536 x^2\right ) \log ^2(5)+2359296 \log ^3(5)-65536 \log ^4(5)}{65536 x^2} \, dx=x\,\left (\frac {3\,{\ln \left (5\right )}^2}{128}-\frac {27\,\ln \left (5\right )}{64}+\frac {183}{64}\right )+x^2\,\left (\frac {\ln \left (5\right )}{1024}-\frac {9}{1024}\right )+\frac {476\,{\ln \left (5\right )}^2-2736\,\ln \left (5\right )-36\,{\ln \left (5\right )}^3+{\ln \left (5\right )}^4+5776}{x}+\frac {x^3}{65536} \]
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