Integrand size = 39, antiderivative size = 33 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {9}{2} \log (a-x)-17 \log (2 a-x)+\frac {35}{2} \log (3 a-x) \]
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Time = 0.04 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {2099} \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {9}{2} \log (a-x)-17 \log (2 a-x)+\frac {35}{2} \log (3 a-x) \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {9}{2 (a-x)}+\frac {17}{2 a-x}-\frac {35}{2 (3 a-x)}\right ) \, dx \\ & = \frac {9}{2} \log (a-x)-17 \log (2 a-x)+\frac {35}{2} \log (3 a-x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.88 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {35}{2} \log (-3 a+x)-17 \log (-2 a+x)+\frac {9}{2} \log (-a+x) \]
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Time = 0.05 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.79
method | result | size |
risch | \(\frac {35 \ln \left (-3 a +x \right )}{2}-17 \ln \left (x -2 a \right )+\frac {9 \ln \left (-a +x \right )}{2}\) | \(26\) |
parallelrisch | \(\frac {35 \ln \left (-3 a +x \right )}{2}-17 \ln \left (x -2 a \right )+\frac {9 \ln \left (-a +x \right )}{2}\) | \(26\) |
default | \(\frac {9 \ln \left (a -x \right )}{2}-17 \ln \left (-x +2 a \right )+\frac {35 \ln \left (3 a -x \right )}{2}\) | \(30\) |
norman | \(\frac {9 \ln \left (a -x \right )}{2}-17 \ln \left (-x +2 a \right )+\frac {35 \ln \left (3 a -x \right )}{2}\) | \(30\) |
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none
Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.76 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {9}{2} \, \log \left (-a + x\right ) - 17 \, \log \left (-2 \, a + x\right ) + \frac {35}{2} \, \log \left (-3 \, a + x\right ) \]
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Time = 0.12 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.79 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {35 \log {\left (- 3 a + x \right )}}{2} - 17 \log {\left (- 2 a + x \right )} + \frac {9 \log {\left (- a + x \right )}}{2} \]
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none
Time = 0.21 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.76 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {9}{2} \, \log \left (-a + x\right ) - 17 \, \log \left (-2 \, a + x\right ) + \frac {35}{2} \, \log \left (-3 \, a + x\right ) \]
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Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.85 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {9}{2} \, \log \left ({\left | -a + x \right |}\right ) - 17 \, \log \left ({\left | -2 \, a + x \right |}\right ) + \frac {35}{2} \, \log \left ({\left | -3 \, a + x \right |}\right ) \]
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Time = 0.11 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.76 \[ \int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx=\frac {9\,\ln \left (x-a\right )}{2}-17\,\ln \left (x-2\,a\right )+\frac {35\,\ln \left (x-3\,a\right )}{2} \]
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