Integrand size = 13, antiderivative size = 27 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=-\frac {51}{16} (3-2 x)^{4/3}+\frac {3}{28} (3-2 x)^{7/3} \]
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Time = 0.00 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45} \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=\frac {3}{28} (3-2 x)^{7/3}-\frac {51}{16} (3-2 x)^{4/3} \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {17}{2} \sqrt [3]{3-2 x}-\frac {1}{2} (3-2 x)^{4/3}\right ) \, dx \\ & = -\frac {51}{16} (3-2 x)^{4/3}+\frac {3}{28} (3-2 x)^{7/3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.67 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=-\frac {3}{112} (3-2 x)^{4/3} (107+8 x) \]
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Time = 0.29 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56
method | result | size |
gosper | \(-\frac {3 \left (8 x +107\right ) \left (3-2 x \right )^{\frac {4}{3}}}{112}\) | \(15\) |
trager | \(\left (\frac {3}{7} x^{2}+\frac {285}{56} x -\frac {963}{112}\right ) \left (3-2 x \right )^{\frac {1}{3}}\) | \(19\) |
derivativedivides | \(-\frac {51 \left (3-2 x \right )^{\frac {4}{3}}}{16}+\frac {3 \left (3-2 x \right )^{\frac {7}{3}}}{28}\) | \(20\) |
default | \(-\frac {51 \left (3-2 x \right )^{\frac {4}{3}}}{16}+\frac {3 \left (3-2 x \right )^{\frac {7}{3}}}{28}\) | \(20\) |
pseudoelliptic | \(\frac {3 \left (3-2 x \right )^{\frac {1}{3}} \left (16 x^{2}+190 x -321\right )}{112}\) | \(20\) |
risch | \(-\frac {3 \left (16 x^{2}+190 x -321\right ) \left (-3+2 x \right )}{112 \left (3-2 x \right )^{\frac {2}{3}}}\) | \(25\) |
meijerg | \(7 \,3^{\frac {1}{3}} x {}_{2}^{}{\moversetsp {}{\mundersetsp {}{F_{1}^{}}}}\left (-\frac {1}{3},1;2;\frac {2 x}{3}\right )+\frac {3^{\frac {1}{3}} x^{2} {}_{2}^{}{\moversetsp {}{\mundersetsp {}{F_{1}^{}}}}\left (-\frac {1}{3},2;3;\frac {2 x}{3}\right )}{2}\) | \(34\) |
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Time = 0.22 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=\frac {3}{112} \, {\left (16 \, x^{2} + 190 \, x - 321\right )} {\left (-2 \, x + 3\right )}^{\frac {1}{3}} \]
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Result contains complex when optimal does not.
Time = 0.70 (sec) , antiderivative size = 112, normalized size of antiderivative = 4.15 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=\begin {cases} \frac {3 \left (x + 7\right )^{2} \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{7} - \frac {51 \left (x + 7\right ) \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{56} - \frac {2601 \sqrt [3]{2 x - 3} e^{\frac {i \pi }{3}}}{112} & \text {for}\: \left |{x + 7}\right | > \frac {17}{2} \\\frac {3 \sqrt [3]{3 - 2 x} \left (x + 7\right )^{2}}{7} - \frac {51 \sqrt [3]{3 - 2 x} \left (x + 7\right )}{56} - \frac {2601 \sqrt [3]{3 - 2 x}}{112} & \text {otherwise} \end {cases} \]
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Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=\frac {3}{28} \, {\left (-2 \, x + 3\right )}^{\frac {7}{3}} - \frac {51}{16} \, {\left (-2 \, x + 3\right )}^{\frac {4}{3}} \]
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Time = 0.32 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=\frac {3}{28} \, {\left (2 \, x - 3\right )}^{2} {\left (-2 \, x + 3\right )}^{\frac {1}{3}} - \frac {51}{16} \, {\left (-2 \, x + 3\right )}^{\frac {4}{3}} \]
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.52 \[ \int \sqrt [3]{3-2 x} (7+x) \, dx=-\frac {3\,{\left (3-2\,x\right )}^{4/3}\,\left (8\,x+107\right )}{112} \]
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