Integrand size = 57, antiderivative size = 17 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=\log \left (-5-\frac {73}{60 x (-5+x+\log (9))}\right ) \]
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Time = 0.07 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.65, number of steps used = 7, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {6, 1694, 12, 1121, 630, 31} \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=\log \left (300 x^2-300 x (5-\log (9))+73\right )-\log (x (x-5+\log (9))) \]
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Rule 6
Rule 12
Rule 31
Rule 630
Rule 1121
Rule 1694
Rubi steps \begin{align*} \text {integral}& = \int \frac {365-146 x-73 \log (9)}{-365 x-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+x^2 \left (7573+300 \log ^2(9)\right )} \, dx \\ & = \text {Subst}\left (\int \frac {584 x}{-1200 x^4-(-5+\log (9))^2 \left (1802-750 \log (9)+75 \log ^2(9)\right )+4 x^2 \left (3677-1500 \log (9)+150 \log ^2(9)\right )} \, dx,x,x+\frac {-3000+600 \log (9)}{1200}\right ) \\ & = 584 \text {Subst}\left (\int \frac {x}{-1200 x^4-(-5+\log (9))^2 \left (1802-750 \log (9)+75 \log ^2(9)\right )+4 x^2 \left (3677-1500 \log (9)+150 \log ^2(9)\right )} \, dx,x,x+\frac {-3000+600 \log (9)}{1200}\right ) \\ & = 292 \text {Subst}\left (\int \frac {1}{-1200 x^2-(-5+\log (9))^2 \left (1802-750 \log (9)+75 \log ^2(9)\right )+4 x \left (3677-1500 \log (9)+150 \log ^2(9)\right )} \, dx,x,\left (x+\frac {-3000+600 \log (9)}{1200}\right )^2\right ) \\ & = 1200 \text {Subst}\left (\int \frac {1}{-1200 x+300 (5-\log (9))^2} \, dx,x,\left (x+\frac {-3000+600 \log (9)}{1200}\right )^2\right )-1200 \text {Subst}\left (\int \frac {1}{-1200 x+4 \left (1802-750 \log (9)+75 \log ^2(9)\right )} \, dx,x,\left (x+\frac {-3000+600 \log (9)}{1200}\right )^2\right ) \\ & = \log \left (73+300 x^2-300 x (5-\log (9))\right )-\log (-x (5-x-\log (9))) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(43\) vs. \(2(17)=34\).
Time = 0.03 (sec) , antiderivative size = 43, normalized size of antiderivative = 2.53 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=-73 \left (\frac {\log (x)}{73}+\frac {1}{73} \log (5-x-\log (9))-\frac {1}{73} \log \left (73-1500 x+300 x^2+300 x \log (9)\right )\right ) \]
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Time = 0.08 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.76
method | result | size |
parallelrisch | \(-\ln \left (x \right )-\ln \left (2 \ln \left (3\right )+x -5\right )+\ln \left (2 x \ln \left (3\right )+x^{2}-5 x +\frac {73}{300}\right )\) | \(30\) |
default | \(-\ln \left (x \right )-\ln \left (2 \ln \left (3\right )+x -5\right )+\ln \left (600 x \ln \left (3\right )+300 x^{2}-1500 x +73\right )\) | \(32\) |
norman | \(-\ln \left (x \right )-\ln \left (2 \ln \left (3\right )+x -5\right )+\ln \left (600 x \ln \left (3\right )+300 x^{2}-1500 x +73\right )\) | \(32\) |
risch | \(-\ln \left (x^{2}+\left (2 \ln \left (3\right )-5\right ) x \right )+\ln \left (-300 x^{2}+\left (-600 \ln \left (3\right )+1500\right ) x -73\right )\) | \(33\) |
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Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.88 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=\log \left (300 \, x^{2} + 600 \, x \log \left (3\right ) - 1500 \, x + 73\right ) - \log \left (x^{2} + 2 \, x \log \left (3\right ) - 5 \, x\right ) \]
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Time = 0.56 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.71 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=- \log {\left (x^{2} + x \left (-5 + 2 \log {\left (3 \right )}\right ) \right )} + \log {\left (x^{2} + x \left (-5 + 2 \log {\left (3 \right )}\right ) + \frac {73}{300} \right )} \]
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Time = 0.18 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.88 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=\log \left (300 \, x^{2} + 300 \, x {\left (2 \, \log \left (3\right ) - 5\right )} + 73\right ) - \log \left (x + 2 \, \log \left (3\right ) - 5\right ) - \log \left (x\right ) \]
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Time = 0.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 2.00 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=\log \left ({\left | 300 \, x^{2} + 600 \, x \log \left (3\right ) - 1500 \, x + 73 \right |}\right ) - \log \left ({\left | x^{2} + 2 \, x \log \left (3\right ) - 5 \, x \right |}\right ) \]
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Time = 0.31 (sec) , antiderivative size = 88, normalized size of antiderivative = 5.18 \[ \int \frac {365-146 x-73 \log (9)}{-365 x+7573 x^2-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+300 x^2 \log ^2(9)} \, dx=-\mathrm {atan}\left (\frac {-\ln \left (3\right )\,525600000{}\mathrm {i}+x\,\left (105120000\,\ln \left (3\right )-262800000\right )\,2{}\mathrm {i}+{\ln \left (3\right )}^2\,105120000{}\mathrm {i}+x^2\,105120000{}\mathrm {i}+657000000{}\mathrm {i}}{2\,x^2\,\left (432000000\,{\ln \left (3\right )}^2-2160000000\,\ln \left (3\right )+2647440000\right )-525600000\,\ln \left (3\right )+105120000\,{\ln \left (3\right )}^2+2\,x\,\left (16094880000\,\ln \left (3\right )-6480000000\,{\ln \left (3\right )}^2+864000000\,{\ln \left (3\right )}^3-13237200000\right )+657000000}\right )\,2{}\mathrm {i} \]
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