Integrand size = 29, antiderivative size = 15 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=-1209 \log (x)+\log \left (-5-x+\log ^2(4)\right ) \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {6, 645} \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=\log \left (x+5-\log ^2(4)\right )-1209 \log (x) \]
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Rule 6
Rule 645
Rubi steps \begin{align*} \text {integral}& = \int \frac {6045+1208 x-1209 \log ^2(4)}{-x^2+x \left (-5+\log ^2(4)\right )} \, dx \\ & = \int \left (-\frac {1209}{x}+\frac {1}{5+x-\log ^2(4)}\right ) \, dx \\ & = -1209 \log (x)+\log \left (5+x-\log ^2(4)\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=-1209 \log (x)+\log \left (5+x-\log ^2(4)\right ) \]
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Time = 0.12 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07
method | result | size |
default | \(-1209 \ln \left (x \right )+\ln \left (-4 \ln \left (2\right )^{2}+5+x \right )\) | \(16\) |
risch | \(-1209 \ln \left (x \right )+\ln \left (-4 \ln \left (2\right )^{2}+5+x \right )\) | \(16\) |
parallelrisch | \(-1209 \ln \left (x \right )+\ln \left (-4 \ln \left (2\right )^{2}+5+x \right )\) | \(16\) |
norman | \(\ln \left (4 \ln \left (2\right )^{2}-5-x \right )-1209 \ln \left (x \right )\) | \(18\) |
meijerg | \(\frac {4836 \ln \left (2\right )^{2} \left (-4 \ln \left (2\right )^{2}+5\right ) \left (\ln \left (x \right )+\ln \left (-\frac {1}{4 \ln \left (2\right )^{2}-5}\right )-\ln \left (1-\frac {x}{4 \ln \left (2\right )^{2}-5}\right )\right )}{\left (4 \ln \left (2\right )^{2}-5\right )^{2}}+\frac {1208 \left (-4 \ln \left (2\right )^{2}+5\right ) \ln \left (1-\frac {x}{4 \ln \left (2\right )^{2}-5}\right )}{4 \ln \left (2\right )^{2}-5}-\frac {6045 \left (-4 \ln \left (2\right )^{2}+5\right ) \left (\ln \left (x \right )+\ln \left (-\frac {1}{4 \ln \left (2\right )^{2}-5}\right )-\ln \left (1-\frac {x}{4 \ln \left (2\right )^{2}-5}\right )\right )}{\left (4 \ln \left (2\right )^{2}-5\right )^{2}}\) | \(150\) |
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none
Time = 0.41 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=\log \left (-4 \, \log \left (2\right )^{2} + x + 5\right ) - 1209 \, \log \left (x\right ) \]
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Time = 0.31 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=- 1209 \log {\left (x \right )} + \log {\left (x - 4 \log {\left (2 \right )}^{2} + 5 \right )} \]
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Time = 0.20 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=\log \left (-4 \, \log \left (2\right )^{2} + x + 5\right ) - 1209 \, \log \left (x\right ) \]
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Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=\log \left ({\left | -4 \, \log \left (2\right )^{2} + x + 5 \right |}\right ) - 1209 \, \log \left ({\left | x \right |}\right ) \]
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Time = 13.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {6045+1208 x-1209 \log ^2(4)}{-5 x-x^2+x \log ^2(4)} \, dx=\ln \left (x-4\,{\ln \left (2\right )}^2+5\right )-1209\,\ln \left (x\right ) \]
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