Integrand size = 13, antiderivative size = 13 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2}{21} \left (-1+x^6\right )^{7/4} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267} \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2}{21} \left (x^6-1\right )^{7/4} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {2}{21} \left (-1+x^6\right )^{7/4} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2}{21} \left (-1+x^6\right )^{7/4} \]
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Time = 0.78 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {2 \left (x^{6}-1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
default | \(\frac {2 \left (x^{6}-1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
risch | \(\frac {2 \left (x^{6}-1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
pseudoelliptic | \(\frac {2 \left (x^{6}-1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
trager | \(\left (\frac {2 x^{6}}{21}-\frac {2}{21}\right ) \left (x^{6}-1\right )^{\frac {3}{4}}\) | \(16\) |
gosper | \(\frac {2 \left (x -1\right ) \left (1+x \right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right ) \left (x^{6}-1\right )^{\frac {3}{4}}}{21}\) | \(30\) |
meijerg | \(\frac {\operatorname {signum}\left (x^{6}-1\right )^{\frac {3}{4}} x^{6} \operatorname {hypergeom}\left (\left [-\frac {3}{4}, 1\right ], \left [2\right ], x^{6}\right )}{6 {\left (-\operatorname {signum}\left (x^{6}-1\right )\right )}^{\frac {3}{4}}}\) | \(33\) |
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Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2}{21} \, {\left (x^{6} - 1\right )}^{\frac {7}{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 26 vs. \(2 (10) = 20\).
Time = 0.19 (sec) , antiderivative size = 26, normalized size of antiderivative = 2.00 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2 x^{6} \left (x^{6} - 1\right )^{\frac {3}{4}}}{21} - \frac {2 \left (x^{6} - 1\right )^{\frac {3}{4}}}{21} \]
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Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2}{21} \, {\left (x^{6} - 1\right )}^{\frac {7}{4}} \]
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Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2}{21} \, {\left (x^{6} - 1\right )}^{\frac {7}{4}} \]
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Time = 5.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \left (-1+x^6\right )^{3/4} \, dx=\frac {2\,{\left (x^6-1\right )}^{7/4}}{21} \]
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