Integrand size = 30, antiderivative size = 35 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=-2 x+\frac {x^2}{2}+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (2+x)+20 \log (3+x) \]
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Time = 0.02 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2099} \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=\frac {x^2}{2}-2 x+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (x+2)+20 \log (x+3) \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-2+\frac {13}{3 (-4+x)}+x-\frac {22}{3 (2+x)}+\frac {20}{3+x}\right ) \, dx \\ & = -2 x+\frac {x^2}{2}+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (2+x)+20 \log (3+x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=-2 x+\frac {x^2}{2}+\frac {13}{3} \log (4-x)-\frac {22}{3} \log (2+x)+20 \log (3+x) \]
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Time = 0.06 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.80
method | result | size |
default | \(\frac {x^{2}}{2}-2 x -\frac {22 \ln \left (x +2\right )}{3}+20 \ln \left (3+x \right )+\frac {13 \ln \left (x -4\right )}{3}\) | \(28\) |
norman | \(\frac {x^{2}}{2}-2 x -\frac {22 \ln \left (x +2\right )}{3}+20 \ln \left (3+x \right )+\frac {13 \ln \left (x -4\right )}{3}\) | \(28\) |
risch | \(\frac {x^{2}}{2}-2 x -\frac {22 \ln \left (x +2\right )}{3}+20 \ln \left (3+x \right )+\frac {13 \ln \left (x -4\right )}{3}\) | \(28\) |
parallelrisch | \(\frac {x^{2}}{2}-2 x -\frac {22 \ln \left (x +2\right )}{3}+20 \ln \left (3+x \right )+\frac {13 \ln \left (x -4\right )}{3}\) | \(28\) |
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Time = 0.28 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=\frac {1}{2} \, x^{2} - 2 \, x + 20 \, \log \left (x + 3\right ) - \frac {22}{3} \, \log \left (x + 2\right ) + \frac {13}{3} \, \log \left (x - 4\right ) \]
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Time = 0.07 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.89 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=\frac {x^{2}}{2} - 2 x + \frac {13 \log {\left (x - 4 \right )}}{3} - \frac {22 \log {\left (x + 2 \right )}}{3} + 20 \log {\left (x + 3 \right )} \]
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Time = 0.18 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=\frac {1}{2} \, x^{2} - 2 \, x + 20 \, \log \left (x + 3\right ) - \frac {22}{3} \, \log \left (x + 2\right ) + \frac {13}{3} \, \log \left (x - 4\right ) \]
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Time = 0.27 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.86 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=\frac {1}{2} \, x^{2} - 2 \, x + 20 \, \log \left ({\left | x + 3 \right |}\right ) - \frac {22}{3} \, \log \left ({\left | x + 2 \right |}\right ) + \frac {13}{3} \, \log \left ({\left | x - 4 \right |}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int \frac {2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx=20\,\ln \left (x+3\right )-\frac {22\,\ln \left (x+2\right )}{3}-2\,x+\frac {13\,\ln \left (x-4\right )}{3}+\frac {x^2}{2} \]
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