Optimal. Leaf size=21 \[ \frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3} \]
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Rubi [A] time = 0.0038604, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{\sqrt [3]{x}} \, dx &=\int \left (\frac{a}{\sqrt [3]{x}}+b x^{2/3}\right ) \, dx\\ &=\frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3}\\ \end{align*}
Mathematica [A] time = 0.0045825, size = 17, normalized size = 0.81 \[ \frac{3}{10} x^{2/3} (5 a+2 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \begin{align*}{\frac{6\,bx+15\,a}{10}{x}^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06304, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{5} \, b x^{\frac{5}{3}} + \frac{3}{2} \, a x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53034, size = 38, normalized size = 1.81 \begin{align*} \frac{3}{10} \,{\left (2 \, b x + 5 \, a\right )} x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.32003, size = 19, normalized size = 0.9 \begin{align*} \frac{3 a x^{\frac{2}{3}}}{2} + \frac{3 b x^{\frac{5}{3}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07289, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{5} \, b x^{\frac{5}{3}} + \frac{3}{2} \, a x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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