Integrand size = 20, antiderivative size = 16 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5}{2} \sqrt [5]{1-2 x+x^2} \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {657, 643} \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5}{2} \sqrt [5]{x^2-2 x+1} \]
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Rule 643
Rule 657
Rubi steps \begin{align*} \text {integral}& = \int \frac {1-x}{\left (1-2 x+x^2\right )^{4/5}} \, dx \\ & = -\frac {5}{2} \sqrt [5]{1-2 x+x^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5}{2} \sqrt [5]{(-1+x)^2} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62
method | result | size |
risch | \(-\frac {5 \left (\left (-1+x \right )^{2}\right )^{\frac {1}{5}}}{2}\) | \(10\) |
pseudoelliptic | \(-\frac {5 \left (\left (-1+x \right )^{2}\right )^{\frac {1}{5}}}{2}\) | \(10\) |
gosper | \(-\frac {5 \left (x^{2}-2 x +1\right )^{\frac {1}{5}}}{2}\) | \(13\) |
trager | \(-\frac {5 \left (x^{2}-2 x +1\right )^{\frac {1}{5}}}{2}\) | \(13\) |
meijerg | \(\frac {\operatorname {signum}\left (-1+x \right )^{\frac {2}{5}} x {}_{2}^{}{\moversetsp {}{\mundersetsp {}{F_{1}^{}}}}\left (\frac {3}{5},1;2;x \right )}{\left (-\operatorname {signum}\left (-1+x \right )\right )^{\frac {2}{5}}}\) | \(24\) |
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none
Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5}{2} \, {\left (x^{2} - 2 \, x + 1\right )}^{\frac {1}{5}} \]
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Time = 0.59 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=- \frac {5 \sqrt [5]{x^{2} - 2 x + 1}}{2} \]
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none
Time = 0.17 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5}{2} \, {\left (x - 1\right )}^{\frac {2}{5}} \]
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none
Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5}{2} \, {\left (x^{2} - 2 \, x + 1\right )}^{\frac {1}{5}} \]
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Time = 0.11 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56 \[ \int \frac {\sqrt [5]{1-2 x+x^2}}{1-x} \, dx=-\frac {5\,{\left ({\left (x-1\right )}^2\right )}^{1/5}}{2} \]
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