Integrand size = 47, antiderivative size = 23 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\log \left (x-12 \left (1+\frac {2 x}{5}\right ) x^2-\frac {x}{8+x}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2099, 1601} \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\log \left (-24 x^3-252 x^2-475 x+35\right )+\log (x)-\log (x+8) \]
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Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{-8-x}+\frac {1}{x}+\frac {475+504 x+72 x^2}{-35+475 x+252 x^2+24 x^3}\right ) \, dx \\ & = \log (x)-\log (8+x)+\int \frac {475+504 x+72 x^2}{-35+475 x+252 x^2+24 x^3} \, dx \\ & = \log (x)-\log (8+x)+\log \left (35-475 x-252 x^2-24 x^3\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\log (x)-\log (8+x)+\log \left (35-475 x-252 x^2-24 x^3\right ) \]
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Time = 0.05 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04
method | result | size |
parallelrisch | \(\ln \left (x \right )-\ln \left (x +8\right )+\ln \left (x^{3}+\frac {21}{2} x^{2}+\frac {475}{24} x -\frac {35}{24}\right )\) | \(24\) |
default | \(\ln \left (24 x^{3}+252 x^{2}+475 x -35\right )+\ln \left (x \right )-\ln \left (x +8\right )\) | \(26\) |
norman | \(\ln \left (24 x^{3}+252 x^{2}+475 x -35\right )+\ln \left (x \right )-\ln \left (x +8\right )\) | \(26\) |
risch | \(-\ln \left (x +8\right )+\ln \left (24 x^{4}+252 x^{3}+475 x^{2}-35 x \right )\) | \(28\) |
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none
Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\log \left (24 \, x^{4} + 252 \, x^{3} + 475 \, x^{2} - 35 \, x\right ) - \log \left (x + 8\right ) \]
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Time = 0.08 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=- \log {\left (x + 8 \right )} + \log {\left (24 x^{4} + 252 x^{3} + 475 x^{2} - 35 x \right )} \]
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none
Time = 0.18 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\log \left (24 \, x^{3} + 252 \, x^{2} + 475 \, x - 35\right ) - \log \left (x + 8\right ) + \log \left (x\right ) \]
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Time = 0.29 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\log \left ({\left | 24 \, x^{3} + 252 \, x^{2} + 475 \, x - 35 \right |}\right ) - \log \left ({\left | x + 8 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 10.77 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {-280+7600 x+6523 x^2+1272 x^3+72 x^4}{-280 x+3765 x^2+2491 x^3+444 x^4+24 x^5} \, dx=\ln \left (x\,\left (24\,x^3+252\,x^2+475\,x-35\right )\right )-\ln \left (x+8\right ) \]
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