Integrand size = 25, antiderivative size = 41 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=-\frac {133}{8 (3-x)^2}+\frac {407}{16 (3-x)}+\frac {313}{64} \log (3-x)+\frac {7}{64} \log (1+x) \]
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Time = 0.03 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2099} \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=\frac {407}{16 (3-x)}-\frac {133}{8 (3-x)^2}+\frac {313}{64} \log (3-x)+\frac {7}{64} \log (x+1) \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {133}{4 (-3+x)^3}+\frac {407}{16 (-3+x)^2}+\frac {313}{64 (-3+x)}+\frac {7}{64 (1+x)}\right ) \, dx \\ & = -\frac {133}{8 (3-x)^2}+\frac {407}{16 (3-x)}+\frac {313}{64} \log (3-x)+\frac {7}{64} \log (1+x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.90 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=-\frac {133}{8 (-3+x)^2}-\frac {407}{16 (-3+x)}+\frac {313}{64} \log (3-x)+\frac {7}{64} \log (1+x) \]
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Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.61
method | result | size |
norman | \(\frac {-\frac {407 x}{16}+\frac {955}{16}}{\left (-3+x \right )^{2}}+\frac {313 \ln \left (-3+x \right )}{64}+\frac {7 \ln \left (1+x \right )}{64}\) | \(25\) |
default | \(\frac {7 \ln \left (1+x \right )}{64}-\frac {133}{8 \left (-3+x \right )^{2}}-\frac {407}{16 \left (-3+x \right )}+\frac {313 \ln \left (-3+x \right )}{64}\) | \(28\) |
risch | \(\frac {-\frac {407 x}{16}+\frac {955}{16}}{x^{2}-6 x +9}+\frac {313 \ln \left (-3+x \right )}{64}+\frac {7 \ln \left (1+x \right )}{64}\) | \(30\) |
parallelrisch | \(\frac {7 \ln \left (1+x \right ) x^{2}+313 \ln \left (-3+x \right ) x^{2}+3820-42 \ln \left (1+x \right ) x -1878 \ln \left (-3+x \right ) x +63 \ln \left (1+x \right )+2817 \ln \left (-3+x \right )-1628 x}{64 x^{2}-384 x +576}\) | \(62\) |
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Time = 0.24 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.10 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=\frac {7 \, {\left (x^{2} - 6 \, x + 9\right )} \log \left (x + 1\right ) + 313 \, {\left (x^{2} - 6 \, x + 9\right )} \log \left (x - 3\right ) - 1628 \, x + 3820}{64 \, {\left (x^{2} - 6 \, x + 9\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.76 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=\frac {955 - 407 x}{16 x^{2} - 96 x + 144} + \frac {313 \log {\left (x - 3 \right )}}{64} + \frac {7 \log {\left (x + 1 \right )}}{64} \]
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Time = 0.22 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.73 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=-\frac {407 \, x - 955}{16 \, {\left (x^{2} - 6 \, x + 9\right )}} + \frac {7}{64} \, \log \left (x + 1\right ) + \frac {313}{64} \, \log \left (x - 3\right ) \]
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Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.66 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=-\frac {407 \, x - 955}{16 \, {\left (x - 3\right )}^{2}} + \frac {7}{64} \, \log \left ({\left | x + 1 \right |}\right ) + \frac {313}{64} \, \log \left ({\left | x - 3 \right |}\right ) \]
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Time = 0.07 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.73 \[ \int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx=\frac {7\,\ln \left (x+1\right )}{64}+\frac {313\,\ln \left (x-3\right )}{64}-\frac {\frac {407\,x}{16}-\frac {955}{16}}{x^2-6\,x+9} \]
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