Integrand size = 13, antiderivative size = 13 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3}{8} \left (-1+x^4\right )^{2/3} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267} \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3}{8} \left (x^4-1\right )^{2/3} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {3}{8} \left (-1+x^4\right )^{2/3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3}{8} \left (-1+x^4\right )^{2/3} \]
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Time = 0.78 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {3 \left (x^{4}-1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
default | \(\frac {3 \left (x^{4}-1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
trager | \(\frac {3 \left (x^{4}-1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
risch | \(\frac {3 \left (x^{4}-1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
pseudoelliptic | \(\frac {3 \left (x^{4}-1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
gosper | \(\frac {3 \left (x -1\right ) \left (1+x \right ) \left (x^{2}+1\right )}{8 \left (x^{4}-1\right )^{\frac {1}{3}}}\) | \(21\) |
meijerg | \(\frac {{\left (-\operatorname {signum}\left (x^{4}-1\right )\right )}^{\frac {1}{3}} x^{4} \operatorname {hypergeom}\left (\left [\frac {1}{3}, 1\right ], \left [2\right ], x^{4}\right )}{4 \operatorname {signum}\left (x^{4}-1\right )^{\frac {1}{3}}}\) | \(33\) |
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Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3}{8} \, {\left (x^{4} - 1\right )}^{\frac {2}{3}} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3 \left (x^{4} - 1\right )^{\frac {2}{3}}}{8} \]
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none
Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3}{8} \, {\left (x^{4} - 1\right )}^{\frac {2}{3}} \]
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none
Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3}{8} \, {\left (x^{4} - 1\right )}^{\frac {2}{3}} \]
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Time = 5.09 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \frac {x^3}{\sqrt [3]{-1+x^4}} \, dx=\frac {3\,{\left (x^4-1\right )}^{2/3}}{8} \]
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