Integrand size = 13, antiderivative size = 13 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3}{25} \left (1+x^5\right )^{5/3} \]
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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} \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3}{25} \left (x^5+1\right )^{5/3} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {3}{25} \left (1+x^5\right )^{5/3} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3}{25} \left (1+x^5\right )^{5/3} \]
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Time = 0.84 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {3 \left (x^{5}+1\right )^{\frac {5}{3}}}{25}\) | \(10\) |
default | \(\frac {3 \left (x^{5}+1\right )^{\frac {5}{3}}}{25}\) | \(10\) |
risch | \(\frac {3 \left (x^{5}+1\right )^{\frac {5}{3}}}{25}\) | \(10\) |
pseudoelliptic | \(\frac {3 \left (x^{5}+1\right )^{\frac {5}{3}}}{25}\) | \(10\) |
trager | \(\left (\frac {3}{25}+\frac {3 x^{5}}{25}\right ) \left (x^{5}+1\right )^{\frac {2}{3}}\) | \(16\) |
meijerg | \(\frac {x^{5} \operatorname {hypergeom}\left (\left [-\frac {2}{3}, 1\right ], \left [2\right ], -x^{5}\right )}{5}\) | \(17\) |
gosper | \(\frac {3 \left (1+x \right ) \left (x^{4}-x^{3}+x^{2}-x +1\right ) \left (x^{5}+1\right )^{\frac {2}{3}}}{25}\) | \(29\) |
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Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3}{25} \, {\left (x^{5} + 1\right )}^{\frac {5}{3}} \]
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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 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3 x^{5} \left (x^{5} + 1\right )^{\frac {2}{3}}}{25} + \frac {3 \left (x^{5} + 1\right )^{\frac {2}{3}}}{25} \]
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Time = 0.18 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3}{25} \, {\left (x^{5} + 1\right )}^{\frac {5}{3}} \]
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Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3}{25} \, {\left (x^{5} + 1\right )}^{\frac {5}{3}} \]
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Time = 4.96 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^4 \left (1+x^5\right )^{2/3} \, dx=\frac {3\,{\left (x^5+1\right )}^{5/3}}{25} \]
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