Integrand size = 11, antiderivative size = 22 \[ \int \frac {1+x^3}{-2+x} \, dx=4 x+x^2+\frac {x^3}{3}+9 \log (2-x) \]
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Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1864} \[ \int \frac {1+x^3}{-2+x} \, dx=\frac {x^3}{3}+x^2+4 x+9 \log (2-x) \]
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Rule 1864
Rubi steps \begin{align*} \text {integral}& = \int \left (4+\frac {9}{-2+x}+2 x+x^2\right ) \, dx \\ & = 4 x+x^2+\frac {x^3}{3}+9 \log (2-x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {1+x^3}{-2+x} \, dx=-\frac {44}{3}+4 x+x^2+\frac {x^3}{3}+9 \log (-2+x) \]
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Time = 0.74 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86
method | result | size |
default | \(\frac {x^{3}}{3}+x^{2}+4 x +9 \ln \left (x -2\right )\) | \(19\) |
norman | \(\frac {x^{3}}{3}+x^{2}+4 x +9 \ln \left (x -2\right )\) | \(19\) |
risch | \(\frac {x^{3}}{3}+x^{2}+4 x +9 \ln \left (x -2\right )\) | \(19\) |
parallelrisch | \(\frac {x^{3}}{3}+x^{2}+4 x +9 \ln \left (x -2\right )\) | \(19\) |
meijerg | \(9 \ln \left (1-\frac {x}{2}\right )+\frac {x \left (x^{2}+3 x +12\right )}{3}\) | \(21\) |
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none
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {1+x^3}{-2+x} \, dx=\frac {1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left (x - 2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {1+x^3}{-2+x} \, dx=\frac {x^{3}}{3} + x^{2} + 4 x + 9 \log {\left (x - 2 \right )} \]
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none
Time = 0.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {1+x^3}{-2+x} \, dx=\frac {1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left (x - 2\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {1+x^3}{-2+x} \, dx=\frac {1}{3} \, x^{3} + x^{2} + 4 \, x + 9 \, \log \left ({\left | x - 2 \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \frac {1+x^3}{-2+x} \, dx=4\,x+9\,\ln \left (x-2\right )+x^2+\frac {x^3}{3} \]
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