Integrand size = 13, antiderivative size = 13 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4}{21} \left (1+x^3\right )^{7/4} \]
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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} \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4}{21} \left (x^3+1\right )^{7/4} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {4}{21} \left (1+x^3\right )^{7/4} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4}{21} \left (1+x^3\right )^{7/4} \]
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Time = 0.76 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77
method | result | size |
derivativedivides | \(\frac {4 \left (x^{3}+1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
default | \(\frac {4 \left (x^{3}+1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
risch | \(\frac {4 \left (x^{3}+1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
pseudoelliptic | \(\frac {4 \left (x^{3}+1\right )^{\frac {7}{4}}}{21}\) | \(10\) |
trager | \(\left (\frac {4}{21}+\frac {4 x^{3}}{21}\right ) \left (x^{3}+1\right )^{\frac {3}{4}}\) | \(16\) |
meijerg | \(\frac {x^{3} \operatorname {hypergeom}\left (\left [-\frac {3}{4}, 1\right ], \left [2\right ], -x^{3}\right )}{3}\) | \(17\) |
gosper | \(\frac {4 \left (1+x \right ) \left (x^{2}-x +1\right ) \left (x^{3}+1\right )^{\frac {3}{4}}}{21}\) | \(21\) |
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Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4}{21} \, {\left (x^{3} + 1\right )}^{\frac {7}{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 26 vs. \(2 (10) = 20\).
Time = 0.13 (sec) , antiderivative size = 26, normalized size of antiderivative = 2.00 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4 x^{3} \left (x^{3} + 1\right )^{\frac {3}{4}}}{21} + \frac {4 \left (x^{3} + 1\right )^{\frac {3}{4}}}{21} \]
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none
Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4}{21} \, {\left (x^{3} + 1\right )}^{\frac {7}{4}} \]
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Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4}{21} \, {\left (x^{3} + 1\right )}^{\frac {7}{4}} \]
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Time = 4.81 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int x^2 \left (1+x^3\right )^{3/4} \, dx=\frac {4\,{\left (x^3+1\right )}^{7/4}}{21} \]
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