Optimal. Leaf size=15 \[ -\frac{2}{3} \sqrt{-x^3-1} \]
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Rubi [A] time = 0.0028506, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ -\frac{2}{3} \sqrt{-x^3-1} \]
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 = 0.002075, size = 15, normalized size = 1. \[ -\frac{2}{3} \sqrt{-x^3-1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 23, 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 = 1.04045, size = 15, normalized size = 1. \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 = 1.7077, size = 28, normalized size = 1.87 \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 = 0.136464, size = 14, normalized size = 0.93 \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 = 1.11422, size = 15, normalized size = 1. \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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