Integrand size = 11, antiderivative size = 19 \[ \int \frac {a+b x}{x^{5/3}} \, dx=-\frac {3 a}{2 x^{2/3}}+3 b \sqrt [3]{x} \]
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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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45} \[ \int \frac {a+b x}{x^{5/3}} \, dx=3 b \sqrt [3]{x}-\frac {3 a}{2 x^{2/3}} \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a}{x^{5/3}}+\frac {b}{x^{2/3}}\right ) \, dx \\ & = -\frac {3 a}{2 x^{2/3}}+3 b \sqrt [3]{x} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {a+b x}{x^{5/3}} \, dx=-\frac {3 (a-2 b x)}{2 x^{2/3}} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63
method | result | size |
gosper | \(-\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}}\) | \(12\) |
trager | \(-\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}}\) | \(12\) |
risch | \(-\frac {3 \left (-2 b x +a \right )}{2 x^{\frac {2}{3}}}\) | \(12\) |
derivativedivides | \(-\frac {3 a}{2 x^{\frac {2}{3}}}+3 b \,x^{\frac {1}{3}}\) | \(14\) |
default | \(-\frac {3 a}{2 x^{\frac {2}{3}}}+3 b \,x^{\frac {1}{3}}\) | \(14\) |
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Time = 0.22 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {a+b x}{x^{5/3}} \, dx=\frac {3 \, {\left (2 \, b x - a\right )}}{2 \, x^{\frac {2}{3}}} \]
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Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {a+b x}{x^{5/3}} \, dx=- \frac {3 a}{2 x^{\frac {2}{3}}} + 3 b \sqrt [3]{x} \]
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none
Time = 0.20 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {a+b x}{x^{5/3}} \, dx=3 \, b x^{\frac {1}{3}} - \frac {3 \, a}{2 \, x^{\frac {2}{3}}} \]
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Time = 0.30 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {a+b x}{x^{5/3}} \, dx=3 \, b x^{\frac {1}{3}} - \frac {3 \, a}{2 \, x^{\frac {2}{3}}} \]
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Time = 0.03 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {a+b x}{x^{5/3}} \, dx=-\frac {3\,a-6\,b\,x}{2\,x^{2/3}} \]
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