Integrand size = 13, antiderivative size = 19 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=-\frac {3 b}{7 x^{7/3}}-\frac {a}{2 x^2} \]
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Time = 0.00 (sec) , antiderivative size = 19, 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 = {14} \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=-\frac {a}{2 x^2}-\frac {3 b}{7 x^{7/3}} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {b}{x^{10/3}}+\frac {a}{x^3}\right ) \, dx \\ & = -\frac {3 b}{7 x^{7/3}}-\frac {a}{2 x^2} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=\frac {-6 b-7 a \sqrt [3]{x}}{14 x^{7/3}} \]
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Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74
method | result | size |
derivativedivides | \(-\frac {3 b}{7 x^{\frac {7}{3}}}-\frac {a}{2 x^{2}}\) | \(14\) |
default | \(-\frac {3 b}{7 x^{\frac {7}{3}}}-\frac {a}{2 x^{2}}\) | \(14\) |
trager | \(\frac {\left (-1+x \right ) a \left (1+x \right )}{2 x^{2}}-\frac {3 b}{7 x^{\frac {7}{3}}}\) | \(20\) |
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none
Time = 0.31 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=-\frac {7 \, a x + 6 \, b x^{\frac {2}{3}}}{14 \, x^{3}} \]
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Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=- \frac {a}{2 x^{2}} - \frac {3 b}{7 x^{\frac {7}{3}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 98 vs. \(2 (13) = 26\).
Time = 0.20 (sec) , antiderivative size = 98, normalized size of antiderivative = 5.16 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=-\frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{7}}{7 \, b^{6}} + \frac {5 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{6} a}{2 \, b^{6}} - \frac {6 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{5} a^{2}}{b^{6}} + \frac {15 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{4} a^{3}}{2 \, b^{6}} - \frac {5 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{3} a^{4}}{b^{6}} + \frac {3 \, {\left (a + \frac {b}{x^{\frac {1}{3}}}\right )}^{2} a^{5}}{2 \, b^{6}} \]
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none
Time = 0.29 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=-\frac {7 \, a x^{\frac {1}{3}} + 6 \, b}{14 \, x^{\frac {7}{3}}} \]
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Time = 0.04 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {a+\frac {b}{\sqrt [3]{x}}}{x^3} \, dx=-\frac {a}{2\,x^2}-\frac {3\,b}{7\,x^{7/3}} \]
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