Optimal. Leaf size=13 \[ \frac{2 \sqrt{x^3-1}}{3} \]
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Rubi [A] time = 0.0024092, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{2 \sqrt{x^3-1}}{3} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^2}{\sqrt{-1+x^3}} \, dx &=\frac{2}{3} \sqrt{-1+x^3}\\ \end{align*}
Mathematica [A] time = 0.0019403, size = 13, normalized size = 1. \[ \frac{2 \sqrt{x^3-1}}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 19, normalized size = 1.5 \begin{align*}{\frac{ \left ( -2+2\,x \right ) \left ({x}^{2}+x+1 \right ) }{3}{\frac{1}{\sqrt{{x}^{3}-1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04036, size = 12, normalized size = 0.92 \begin{align*} \frac{2}{3} \, \sqrt{x^{3} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.76337, size = 26, normalized size = 2. \begin{align*} \frac{2}{3} \, \sqrt{x^{3} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.134299, size = 10, normalized size = 0.77 \begin{align*} \frac{2 \sqrt{x^{3} - 1}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13629, size = 12, normalized size = 0.92 \begin{align*} \frac{2}{3} \, \sqrt{x^{3} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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