Optimal. Leaf size=23 \[ \frac{2 \left (a x+b x^{2/3}\right )^{3/2}}{a x} \]
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Rubi [A] time = 0.0404968, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {2014} \[ \frac{2 \left (a x+b x^{2/3}\right )^{3/2}}{a x} \]
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin{align*} \int \frac{\sqrt{b x^{2/3}+a x}}{x} \, dx &=\frac{2 \left (b x^{2/3}+a x\right )^{3/2}}{a x}\\ \end{align*}
Mathematica [A] time = 0.0108147, size = 23, normalized size = 1. \[ \frac{2 \left (a x+b x^{2/3}\right )^{3/2}}{a x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 27, normalized size = 1.2 \begin{align*} 2\,{\frac{\sqrt{b{x}^{2/3}+ax} \left ( b+a\sqrt [3]{x} \right ) }{a\sqrt [3]{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{a x + b x^{\frac{2}{3}}}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{a x + b x^{\frac{2}{3}}}}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.126, size = 31, normalized size = 1.35 \begin{align*} \frac{2 \,{\left (a x^{\frac{1}{3}} + b\right )}^{\frac{3}{2}}}{a} - \frac{2 \, b^{\frac{3}{2}}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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