Optimal. Leaf size=21 \[ \frac{3}{4} a x^{4/3}+\frac{3}{7} b x^{7/3} \]
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Rubi [A] time = 0.0035914, 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} \[ \frac{3}{4} a x^{4/3}+\frac{3}{7} b x^{7/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \sqrt [3]{x} (a+b x) \, dx &=\int \left (a \sqrt [3]{x}+b x^{4/3}\right ) \, dx\\ &=\frac{3}{4} a x^{4/3}+\frac{3}{7} b x^{7/3}\\ \end{align*}
Mathematica [A] time = 0.0044191, size = 17, normalized size = 0.81 \[ \frac{3}{28} x^{4/3} (7 a+4 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \begin{align*}{\frac{12\,bx+21\,a}{28}{x}^{{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05329, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{7} \, b x^{\frac{7}{3}} + \frac{3}{4} \, a x^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50137, size = 43, normalized size = 2.05 \begin{align*} \frac{3}{28} \,{\left (4 \, b x^{2} + 7 \, a x\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.24474, size = 19, normalized size = 0.9 \begin{align*} \frac{3 a x^{\frac{4}{3}}}{4} + \frac{3 b x^{\frac{7}{3}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05017, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{7} \, b x^{\frac{7}{3}} + \frac{3}{4} \, a x^{\frac{4}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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