Integrand size = 11, antiderivative size = 13 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2}{3} \left (-1+x^2\right )^{3/4} \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {267} \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2}{3} \left (x^2-1\right )^{3/4} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {2}{3} \left (-1+x^2\right )^{3/4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2}{3} \left (-1+x^2\right )^{3/4} \]
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Time = 0.79 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {2 \left (x^{2}-1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
default | \(\frac {2 \left (x^{2}-1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
trager | \(\frac {2 \left (x^{2}-1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
risch | \(\frac {2 \left (x^{2}-1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
pseudoelliptic | \(\frac {2 \left (x^{2}-1\right )^{\frac {3}{4}}}{3}\) | \(10\) |
gosper | \(\frac {2 \left (x -1\right ) \left (1+x \right )}{3 \left (x^{2}-1\right )^{\frac {1}{4}}}\) | \(16\) |
meijerg | \(\frac {{\left (-\operatorname {signum}\left (x^{2}-1\right )\right )}^{\frac {1}{4}} x^{2} \operatorname {hypergeom}\left (\left [\frac {1}{4}, 1\right ], \left [2\right ], x^{2}\right )}{2 \operatorname {signum}\left (x^{2}-1\right )^{\frac {1}{4}}}\) | \(33\) |
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none
Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2}{3} \, {\left (x^{2} - 1\right )}^{\frac {3}{4}} \]
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Time = 0.08 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2 \left (x^{2} - 1\right )^{\frac {3}{4}}}{3} \]
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none
Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2}{3} \, {\left (x^{2} - 1\right )}^{\frac {3}{4}} \]
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none
Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2}{3} \, {\left (x^{2} - 1\right )}^{\frac {3}{4}} \]
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Time = 5.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x}{\sqrt [4]{-1+x^2}} \, dx=\frac {2\,{\left (x^2-1\right )}^{3/4}}{3} \]
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