Optimal. Leaf size=16 \[ \frac{3 (a+b x)^{4/3}}{4 b} \]
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Rubi [A] time = 0.001431, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ \frac{3 (a+b x)^{4/3}}{4 b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \sqrt [3]{a+b x} \, dx &=\frac{3 (a+b x)^{4/3}}{4 b}\\ \end{align*}
Mathematica [A] time = 0.0210137, size = 16, normalized size = 1. \[ \frac{3 (a+b x)^{4/3}}{4 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*}{\frac{3}{4\,b} \left ( bx+a \right ) ^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02454, size = 16, normalized size = 1. \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{4}{3}}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77857, size = 31, normalized size = 1.94 \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{4}{3}}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074832, size = 12, normalized size = 0.75 \begin{align*} \frac{3 \left (a + b x\right )^{\frac{4}{3}}}{4 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2059, size = 16, normalized size = 1. \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{4}{3}}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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