Integrand size = 72, antiderivative size = 27 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=4-\log \left (-1+\frac {1}{x}+\frac {3 x^2}{\left (4-x-2 x^2\right )^2}\right ) \]
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Time = 0.11 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {2099, 642, 1601} \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=2 \log \left (-2 x^2-x+4\right )-\log \left (-4 x^5+22 x^3-7 x^2-24 x+16\right )+\log (x) \]
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Rule 642
Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{x}+\frac {2 (1+4 x)}{-4+x+2 x^2}-\frac {2 \left (12+7 x-33 x^2+10 x^4\right )}{-16+24 x+7 x^2-22 x^3+4 x^5}\right ) \, dx \\ & = \log (x)+2 \int \frac {1+4 x}{-4+x+2 x^2} \, dx-2 \int \frac {12+7 x-33 x^2+10 x^4}{-16+24 x+7 x^2-22 x^3+4 x^5} \, dx \\ & = \log (x)+2 \log \left (4-x-2 x^2\right )-\log \left (16-24 x-7 x^2+22 x^3-4 x^5\right ) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=\log (x)+2 \log \left (4-x-2 x^2\right )-\log \left (16-24 x-7 x^2+22 x^3-4 x^5\right ) \]
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Time = 0.06 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33
method | result | size |
parallelrisch | \(\ln \left (x \right )+2 \ln \left (x^{2}+\frac {1}{2} x -2\right )-\ln \left (x^{5}-\frac {11}{2} x^{3}+\frac {7}{4} x^{2}+6 x -4\right )\) | \(36\) |
default | \(\ln \left (x \right )-\ln \left (4 x^{5}-22 x^{3}+7 x^{2}+24 x -16\right )+2 \ln \left (2 x^{2}+x -4\right )\) | \(38\) |
norman | \(\ln \left (x \right )-\ln \left (4 x^{5}-22 x^{3}+7 x^{2}+24 x -16\right )+2 \ln \left (2 x^{2}+x -4\right )\) | \(38\) |
risch | \(\ln \left (x \right )-\ln \left (4 x^{5}-22 x^{3}+7 x^{2}+24 x -16\right )+2 \ln \left (2 x^{2}+x -4\right )\) | \(38\) |
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Time = 0.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=-\log \left (4 \, x^{5} - 22 \, x^{3} + 7 \, x^{2} + 24 \, x - 16\right ) + 2 \, \log \left (2 \, x^{2} + x - 4\right ) + \log \left (x\right ) \]
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Time = 0.08 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=\log {\left (x \right )} + 2 \log {\left (2 x^{2} + x - 4 \right )} - \log {\left (4 x^{5} - 22 x^{3} + 7 x^{2} + 24 x - 16 \right )} \]
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Time = 0.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=-\log \left (4 \, x^{5} - 22 \, x^{3} + 7 \, x^{2} + 24 \, x - 16\right ) + 2 \, \log \left (2 \, x^{2} + x - 4\right ) + \log \left (x\right ) \]
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Time = 0.27 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.48 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=-\log \left ({\left | 4 \, x^{5} - 22 \, x^{3} + 7 \, x^{2} + 24 \, x - 16 \right |}\right ) + 2 \, \log \left ({\left | 2 \, x^{2} + x - 4 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 0.17 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.30 \[ \int \frac {64-48 x-84 x^2+23 x^3+42 x^4-24 x^5-8 x^6}{64 x-112 x^2-36 x^3+143 x^4-8 x^5-60 x^6+4 x^7+8 x^8} \, dx=2\,\ln \left (2\,x^2+x-4\right )+\ln \left (x\right )-\ln \left (x^5-\frac {11\,x^3}{2}+\frac {7\,x^2}{4}+6\,x-4\right ) \]
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