Optimal. Leaf size=14 \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]
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Rubi [A] time = 0.0014176, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (b x^2\right )^{2/3} \, dx &=\frac{\left (b x^2\right )^{2/3} \int x^{4/3} \, dx}{x^{4/3}}\\ &=\frac{3}{7} x \left (b x^2\right )^{2/3}\\ \end{align*}
Mathematica [A] time = 0.0011185, size = 14, normalized size = 1. \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,x}{7} \left ( b{x}^{2} \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981949, size = 14, normalized size = 1. \begin{align*} \frac{3}{7} \, \left (b x^{2}\right )^{\frac{2}{3}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72182, size = 28, normalized size = 2. \begin{align*} \frac{3}{7} \, \left (b x^{2}\right )^{\frac{2}{3}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.374301, size = 15, normalized size = 1.07 \begin{align*} \frac{3 b^{\frac{2}{3}} x \left (x^{2}\right )^{\frac{2}{3}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (b x^{2}\right )^{\frac{2}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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