Integrand size = 13, antiderivative size = 13 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2}{15} \left (1+x^6\right )^{5/4} \]
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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} \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2}{15} \left (x^6+1\right )^{5/4} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {2}{15} \left (1+x^6\right )^{5/4} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2}{15} \left (1+x^6\right )^{5/4} \]
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Time = 0.78 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {2 \left (x^{6}+1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
default | \(\frac {2 \left (x^{6}+1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
risch | \(\frac {2 \left (x^{6}+1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
pseudoelliptic | \(\frac {2 \left (x^{6}+1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
trager | \(\left (\frac {2}{15}+\frac {2 x^{6}}{15}\right ) \left (x^{6}+1\right )^{\frac {1}{4}}\) | \(16\) |
meijerg | \(\frac {x^{6} \operatorname {hypergeom}\left (\left [-\frac {1}{4}, 1\right ], \left [2\right ], -x^{6}\right )}{6}\) | \(17\) |
gosper | \(\frac {2 \left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right ) \left (x^{6}+1\right )^{\frac {1}{4}}}{15}\) | \(25\) |
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Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2}{15} \, {\left (x^{6} + 1\right )}^{\frac {5}{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 26 vs. \(2 (10) = 20\).
Time = 0.11 (sec) , antiderivative size = 26, normalized size of antiderivative = 2.00 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2 x^{6} \sqrt [4]{x^{6} + 1}}{15} + \frac {2 \sqrt [4]{x^{6} + 1}}{15} \]
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Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2}{15} \, {\left (x^{6} + 1\right )}^{\frac {5}{4}} \]
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Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2}{15} \, {\left (x^{6} + 1\right )}^{\frac {5}{4}} \]
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Time = 4.96 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^5 \sqrt [4]{1+x^6} \, dx=\frac {2\,{\left (x^6+1\right )}^{5/4}}{15} \]
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