Integrand size = 15, antiderivative size = 15 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {1}{40} \left (27+8 x^3\right )^{5/3} \]
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Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {267} \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {1}{40} \left (8 x^3+27\right )^{5/3} \]
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Rule 267
Rubi steps \begin{align*} \text {integral}& = \frac {1}{40} \left (27+8 x^3\right )^{5/3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {1}{40} \left (27+8 x^3\right )^{5/3} \]
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Time = 0.09 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80
method | result | size |
derivativedivides | \(\frac {\left (8 x^{3}+27\right )^{\frac {5}{3}}}{40}\) | \(12\) |
default | \(\frac {\left (8 x^{3}+27\right )^{\frac {5}{3}}}{40}\) | \(12\) |
risch | \(\frac {\left (8 x^{3}+27\right )^{\frac {5}{3}}}{40}\) | \(12\) |
pseudoelliptic | \(\frac {\left (8 x^{3}+27\right )^{\frac {5}{3}}}{40}\) | \(12\) |
meijerg | \(3 x^{3} {}_{2}^{}{\moversetsp {}{\mundersetsp {}{F_{1}^{}}}}\left (-\frac {2}{3},1;2;-\frac {8 x^{3}}{27}\right )\) | \(17\) |
trager | \(\left (\frac {x^{3}}{5}+\frac {27}{40}\right ) \left (8 x^{3}+27\right )^{\frac {2}{3}}\) | \(18\) |
gosper | \(\frac {\left (3+2 x \right ) \left (4 x^{2}-6 x +9\right ) \left (8 x^{3}+27\right )^{\frac {2}{3}}}{40}\) | \(27\) |
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none
Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {1}{40} \, {\left (8 \, x^{3} + 27\right )}^{\frac {5}{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 27 vs. \(2 (10) = 20\).
Time = 0.10 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.80 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {x^{3} \left (8 x^{3} + 27\right )^{\frac {2}{3}}}{5} + \frac {27 \left (8 x^{3} + 27\right )^{\frac {2}{3}}}{40} \]
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none
Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {1}{40} \, {\left (8 \, x^{3} + 27\right )}^{\frac {5}{3}} \]
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {1}{40} \, {\left (8 \, x^{3} + 27\right )}^{\frac {5}{3}} \]
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Time = 0.11 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int x^2 \left (27+8 x^3\right )^{2/3} \, dx=\frac {{\left (8\,x^3+27\right )}^{5/3}}{40} \]
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