Optimal. Leaf size=31 \[ \frac{2}{9} \left (1-x^3\right )^{3/2}-\frac{2 \sqrt{1-x^3}}{3} \]
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Rubi [A] time = 0.0133722, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ \frac{2}{9} \left (1-x^3\right )^{3/2}-\frac{2 \sqrt{1-x^3}}{3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^5}{\sqrt{1-x^3}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{x}{\sqrt{1-x}} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{1}{\sqrt{1-x}}-\sqrt{1-x}\right ) \, dx,x,x^3\right )\\ &=-\frac{2}{3} \sqrt{1-x^3}+\frac{2}{9} \left (1-x^3\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0058786, size = 20, normalized size = 0.65 \[ -\frac{2}{9} \sqrt{1-x^3} \left (x^3+2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 26, normalized size = 0.8 \begin{align*}{\frac{ \left ( -2+2\,x \right ) \left ({x}^{2}+x+1 \right ) \left ({x}^{3}+2 \right ) }{9}{\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 = 1.03326, size = 31, normalized size = 1. \begin{align*} \frac{2}{9} \,{\left (-x^{3} + 1\right )}^{\frac{3}{2}} - \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 = 1.4915, size = 42, normalized size = 1.35 \begin{align*} -\frac{2}{9} \,{\left (x^{3} + 2\right )} \sqrt{-x^{3} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.348183, size = 27, normalized size = 0.87 \begin{align*} - \frac{2 x^{3} \sqrt{1 - x^{3}}}{9} - \frac{4 \sqrt{1 - x^{3}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11951, size = 31, normalized size = 1. \begin{align*} \frac{2}{9} \,{\left (-x^{3} + 1\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{-x^{3} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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