Integrand size = 9, antiderivative size = 14 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=\frac {3}{2} b x^{2/3}+a x \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x+\frac {3}{2} b x^{2/3} \]
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Rubi steps \begin{align*} \text {integral}& = \frac {3}{2} b x^{2/3}+a x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=\frac {3}{2} b x^{2/3}+a x \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79
method | result | size |
derivativedivides | \(\frac {3 b \,x^{\frac {2}{3}}}{2}+a x\) | \(11\) |
default | \(\frac {3 b \,x^{\frac {2}{3}}}{2}+a x\) | \(11\) |
risch | \(\frac {3 b \,x^{\frac {2}{3}}}{2}+a x\) | \(11\) |
trager | \(a \left (-1+x \right )+\frac {3 b \,x^{\frac {2}{3}}}{2}\) | \(13\) |
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3 b x^{\frac {2}{3}}}{2} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx=a\,x+\frac {3\,b\,x^{2/3}}{2} \]
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