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 = 0.76 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
gosper | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
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 | \(\frac {3 \left (x^{4}+1\right )^{\frac {2}{3}}}{8}\) | \(10\) |
meijerg | \(\frac {x^{4} \operatorname {hypergeom}\left (\left [\frac {1}{3}, 1\right ], \left [2\right ], -x^{4}\right )}{4}\) | \(17\) |
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none
Time = 0.24 (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 = 0.07 (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 = 4.83 (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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