Integrand size = 19, antiderivative size = 15 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3}{2} \left (-x+x^3\right )^{2/3} \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {1602} \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3}{2} \left (x^3-x\right )^{2/3} \]
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Rule 1602
Rubi steps \begin{align*} \text {integral}& = \frac {3}{2} \left (-x+x^3\right )^{2/3} \\ \end{align*}
Time = 0.91 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3}{2} \left (x \left (-1+x^2\right )\right )^{2/3} \]
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Time = 0.84 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80
method | result | size |
derivativedivides | \(\frac {3 \left (x^{3}-x \right )^{\frac {2}{3}}}{2}\) | \(12\) |
default | \(\frac {3 \left (x^{3}-x \right )^{\frac {2}{3}}}{2}\) | \(12\) |
trager | \(\frac {3 \left (x^{3}-x \right )^{\frac {2}{3}}}{2}\) | \(12\) |
pseudoelliptic | \(\frac {3 \left (x^{3}-x \right )^{\frac {2}{3}}}{2}\) | \(12\) |
risch | \(\frac {3 x \left (x^{2}-1\right )}{2 {\left (x \left (x^{2}-1\right )\right )}^{\frac {1}{3}}}\) | \(18\) |
gosper | \(\frac {3 \left (1+x \right ) x \left (x -1\right )}{2 \left (x^{3}-x \right )^{\frac {1}{3}}}\) | \(19\) |
meijerg | \(-\frac {3 {\left (-\operatorname {signum}\left (x^{2}-1\right )\right )}^{\frac {1}{3}} x^{\frac {2}{3}} \operatorname {hypergeom}\left (\left [\frac {1}{3}, \frac {1}{3}\right ], \left [\frac {4}{3}\right ], x^{2}\right )}{2 \operatorname {signum}\left (x^{2}-1\right )^{\frac {1}{3}}}+\frac {9 {\left (-\operatorname {signum}\left (x^{2}-1\right )\right )}^{\frac {1}{3}} x^{\frac {8}{3}} \operatorname {hypergeom}\left (\left [\frac {1}{3}, \frac {4}{3}\right ], \left [\frac {7}{3}\right ], x^{2}\right )}{8 \operatorname {signum}\left (x^{2}-1\right )^{\frac {1}{3}}}\) | \(66\) |
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none
Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3}{2} \, {\left (x^{3} - x\right )}^{\frac {2}{3}} \]
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Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3 \left (x^{3} - x\right )^{\frac {2}{3}}}{2} \]
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none
Time = 0.17 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3}{2} \, {\left (x^{3} - x\right )}^{\frac {2}{3}} \]
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none
Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3}{2} \, {\left (x^{3} - x\right )}^{\frac {2}{3}} \]
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Time = 5.29 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {-1+3 x^2}{\sqrt [3]{-x+x^3}} \, dx=\frac {3\,{\left (x^3-x\right )}^{2/3}}{2} \]
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