Integrand size = 56, antiderivative size = 21 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=\frac {\left (4+x+\frac {5}{3} \log ^2\left (\frac {14 x}{3}\right )\right )^2}{x} \]
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Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(21)=42\).
Time = 0.11 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.71, number of steps used = 18, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14, 45, 2372, 2338, 2342, 2341} \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=x+\frac {16}{x}+\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{9 x}+\frac {40 \log ^2\left (\frac {14 x}{3}\right )}{3 x}-\frac {10 \log ^2(x)}{3}+\frac {20}{3} \log (x) \log \left (\frac {14 x}{3}\right ) \]
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Rule 12
Rule 14
Rule 45
Rule 2338
Rule 2341
Rule 2342
Rule 2372
Rubi steps \begin{align*} \text {integral}& = \frac {1}{9} \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{x^2} \, dx \\ & = \frac {1}{9} \int \left (\frac {9 \left (-16+x^2\right )}{x^2}+\frac {60 (4+x) \log \left (\frac {14 x}{3}\right )}{x^2}-\frac {120 \log ^2\left (\frac {14 x}{3}\right )}{x^2}+\frac {100 \log ^3\left (\frac {14 x}{3}\right )}{x^2}-\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{x^2}\right ) \, dx \\ & = -\left (\frac {25}{9} \int \frac {\log ^4\left (\frac {14 x}{3}\right )}{x^2} \, dx\right )+\frac {20}{3} \int \frac {(4+x) \log \left (\frac {14 x}{3}\right )}{x^2} \, dx+\frac {100}{9} \int \frac {\log ^3\left (\frac {14 x}{3}\right )}{x^2} \, dx-\frac {40}{3} \int \frac {\log ^2\left (\frac {14 x}{3}\right )}{x^2} \, dx+\int \frac {-16+x^2}{x^2} \, dx \\ & = -\frac {80 \log \left (\frac {14 x}{3}\right )}{3 x}+\frac {20}{3} \log (x) \log \left (\frac {14 x}{3}\right )+\frac {40 \log ^2\left (\frac {14 x}{3}\right )}{3 x}-\frac {100 \log ^3\left (\frac {14 x}{3}\right )}{9 x}+\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{9 x}-\frac {20}{3} \int \frac {-4+x \log (x)}{x^2} \, dx-\frac {100}{9} \int \frac {\log ^3\left (\frac {14 x}{3}\right )}{x^2} \, dx-\frac {80}{3} \int \frac {\log \left (\frac {14 x}{3}\right )}{x^2} \, dx+\frac {100}{3} \int \frac {\log ^2\left (\frac {14 x}{3}\right )}{x^2} \, dx+\int \left (1-\frac {16}{x^2}\right ) \, dx \\ & = \frac {128}{3 x}+x+\frac {20}{3} \log (x) \log \left (\frac {14 x}{3}\right )-\frac {20 \log ^2\left (\frac {14 x}{3}\right )}{x}+\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{9 x}-\frac {20}{3} \int \left (-\frac {4}{x^2}+\frac {\log (x)}{x}\right ) \, dx-\frac {100}{3} \int \frac {\log ^2\left (\frac {14 x}{3}\right )}{x^2} \, dx+\frac {200}{3} \int \frac {\log \left (\frac {14 x}{3}\right )}{x^2} \, dx \\ & = -\frac {152}{3 x}+x-\frac {200 \log \left (\frac {14 x}{3}\right )}{3 x}+\frac {20}{3} \log (x) \log \left (\frac {14 x}{3}\right )+\frac {40 \log ^2\left (\frac {14 x}{3}\right )}{3 x}+\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{9 x}-\frac {20}{3} \int \frac {\log (x)}{x} \, dx-\frac {200}{3} \int \frac {\log \left (\frac {14 x}{3}\right )}{x^2} \, dx \\ & = \frac {16}{x}+x-\frac {10 \log ^2(x)}{3}+\frac {20}{3} \log (x) \log \left (\frac {14 x}{3}\right )+\frac {40 \log ^2\left (\frac {14 x}{3}\right )}{3 x}+\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{9 x} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(49\) vs. \(2(21)=42\).
Time = 0.02 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.33 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=\frac {16}{x}+x+\frac {10}{3} \log ^2\left (\frac {14 x}{3}\right )+\frac {40 \log ^2\left (\frac {14 x}{3}\right )}{3 x}+\frac {25 \log ^4\left (\frac {14 x}{3}\right )}{9 x} \]
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Time = 0.09 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.67
method | result | size |
norman | \(\frac {16+x^{2}+\frac {40 \ln \left (\frac {14 x}{3}\right )^{2}}{3}+\frac {25 \ln \left (\frac {14 x}{3}\right )^{4}}{9}+\frac {10 x \ln \left (\frac {14 x}{3}\right )^{2}}{3}}{x}\) | \(35\) |
risch | \(\frac {25 \ln \left (\frac {14 x}{3}\right )^{4}}{9 x}+\frac {10 \left (4+x \right ) \ln \left (\frac {14 x}{3}\right )^{2}}{3 x}+\frac {x^{2}+16}{x}\) | \(36\) |
derivativedivides | \(\frac {25 \ln \left (\frac {14 x}{3}\right )^{4}}{9 x}+\frac {40 \ln \left (\frac {14 x}{3}\right )^{2}}{3 x}+\frac {16}{x}+\frac {10 \ln \left (\frac {14 x}{3}\right )^{2}}{3}+x\) | \(38\) |
default | \(\frac {25 \ln \left (\frac {14 x}{3}\right )^{4}}{9 x}+\frac {40 \ln \left (\frac {14 x}{3}\right )^{2}}{3 x}+\frac {16}{x}+\frac {10 \ln \left (\frac {14 x}{3}\right )^{2}}{3}+x\) | \(38\) |
parallelrisch | \(\frac {25 \ln \left (\frac {14 x}{3}\right )^{4}+144+30 x \ln \left (\frac {14 x}{3}\right )^{2}+9 x^{2}+120 \ln \left (\frac {14 x}{3}\right )^{2}}{9 x}\) | \(38\) |
parts | \(\frac {25 \ln \left (\frac {14 x}{3}\right )^{4}}{9 x}+\frac {40 \ln \left (\frac {14 x}{3}\right )^{2}}{3 x}+\frac {16}{x}+\frac {10 \ln \left (\frac {14 x}{3}\right )^{2}}{3}+x\) | \(38\) |
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Time = 0.27 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.48 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=\frac {25 \, \log \left (\frac {14}{3} \, x\right )^{4} + 30 \, {\left (x + 4\right )} \log \left (\frac {14}{3} \, x\right )^{2} + 9 \, x^{2} + 144}{9 \, x} \]
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Time = 0.10 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.62 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=x + \frac {\left (10 x + 40\right ) \log {\left (\frac {14 x}{3} \right )}^{2}}{3 x} + \frac {25 \log {\left (\frac {14 x}{3} \right )}^{4}}{9 x} + \frac {16}{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (20) = 40\).
Time = 0.18 (sec) , antiderivative size = 105, normalized size of antiderivative = 5.00 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=\frac {10}{3} \, \log \left (\frac {14}{3} \, x\right )^{2} + x + \frac {25 \, {\left (\log \left (\frac {14}{3} \, x\right )^{4} + 4 \, \log \left (\frac {14}{3} \, x\right )^{3} + 12 \, \log \left (\frac {14}{3} \, x\right )^{2} + 24 \, \log \left (\frac {14}{3} \, x\right ) + 24\right )}}{9 \, x} - \frac {100 \, {\left (\log \left (\frac {14}{3} \, x\right )^{3} + 3 \, \log \left (\frac {14}{3} \, x\right )^{2} + 6 \, \log \left (\frac {14}{3} \, x\right ) + 6\right )}}{9 \, x} + \frac {40 \, {\left (\log \left (\frac {14}{3} \, x\right )^{2} + 2 \, \log \left (\frac {14}{3} \, x\right ) + 2\right )}}{3 \, x} - \frac {80 \, \log \left (\frac {14}{3} \, x\right )}{3 \, x} - \frac {32}{3 \, x} \]
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Time = 0.26 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.57 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=\frac {10}{3} \, {\left (\frac {4}{x} + 1\right )} \log \left (\frac {14}{3} \, x\right )^{2} + \frac {25 \, \log \left (\frac {14}{3} \, x\right )^{4}}{9 \, x} + x + \frac {16}{x} \]
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Time = 14.29 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.52 \[ \int \frac {-144+9 x^2+(240+60 x) \log \left (\frac {14 x}{3}\right )-120 \log ^2\left (\frac {14 x}{3}\right )+100 \log ^3\left (\frac {14 x}{3}\right )-25 \log ^4\left (\frac {14 x}{3}\right )}{9 x^2} \, dx=x+\frac {\frac {25\,{\ln \left (\frac {14\,x}{3}\right )}^4}{9}+\frac {40\,{\ln \left (\frac {14\,x}{3}\right )}^2}{3}+16}{x}+\frac {10\,{\ln \left (\frac {14\,x}{3}\right )}^2}{3} \]
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