Integrand size = 55, antiderivative size = 23 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=\log \left (16 x \left (-3+\frac {3 \left (3+x+x^2\right )^2}{12-x}\right )\right ) \]
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Time = 0.07 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {2099, 1601} \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=\log \left (-x^4-2 x^3-7 x^2-7 x+3\right )-\log (12-x)+\log (x) \]
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Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{12-x}+\frac {1}{x}+\frac {7+14 x+6 x^2+4 x^3}{-3+7 x+7 x^2+2 x^3+x^4}\right ) \, dx \\ & = -\log (12-x)+\log (x)+\int \frac {7+14 x+6 x^2+4 x^3}{-3+7 x+7 x^2+2 x^3+x^4} \, dx \\ & = -\log (12-x)+\log (x)+\log \left (3-7 x-7 x^2-2 x^3-x^4\right ) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=-\log (12-x)+\log (x)+\log \left (3-7 x-7 x^2-2 x^3-x^4\right ) \]
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Time = 0.08 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.26
method | result | size |
default | \(\ln \left (x \right )-\ln \left (x -12\right )+\ln \left (x^{4}+2 x^{3}+7 x^{2}+7 x -3\right )\) | \(29\) |
norman | \(\ln \left (x \right )-\ln \left (x -12\right )+\ln \left (x^{4}+2 x^{3}+7 x^{2}+7 x -3\right )\) | \(29\) |
parallelrisch | \(\ln \left (x \right )-\ln \left (x -12\right )+\ln \left (x^{4}+2 x^{3}+7 x^{2}+7 x -3\right )\) | \(29\) |
risch | \(-\ln \left (x -12\right )+\ln \left (x^{5}+2 x^{4}+7 x^{3}+7 x^{2}-3 x \right )\) | \(31\) |
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Time = 0.25 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=\log \left (x^{5} + 2 \, x^{4} + 7 \, x^{3} + 7 \, x^{2} - 3 \, x\right ) - \log \left (x - 12\right ) \]
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Time = 0.09 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=- \log {\left (x - 12 \right )} + \log {\left (x^{5} + 2 x^{4} + 7 x^{3} + 7 x^{2} - 3 x \right )} \]
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Time = 0.22 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=\log \left (x^{4} + 2 \, x^{3} + 7 \, x^{2} + 7 \, x - 3\right ) - \log \left (x - 12\right ) + \log \left (x\right ) \]
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Time = 0.27 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.35 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=\log \left ({\left | x^{4} + 2 \, x^{3} + 7 \, x^{2} + 7 \, x - 3 \right |}\right ) - \log \left ({\left | x - 12 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 0.15 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22 \[ \int \frac {36-168 x-245 x^2-82 x^3-54 x^4+4 x^5}{36 x-87 x^2-77 x^3-17 x^4-10 x^5+x^6} \, dx=\ln \left (x\,\left (x^4+2\,x^3+7\,x^2+7\,x-3\right )\right )-\ln \left (x-12\right ) \]
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