Optimal. Leaf size=13 \[ \frac{3}{20} \left (x^2-1\right )^{10/3} \]
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Rubi [A] time = 0.0021335, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \frac{3}{20} \left (x^2-1\right )^{10/3} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \left (-1+x^2\right )^{7/3} \, dx &=\frac{3}{20} \left (-1+x^2\right )^{10/3}\\ \end{align*}
Mathematica [A] time = 0.0044398, size = 13, normalized size = 1. \[ \frac{3}{20} \left (x^2-1\right )^{10/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 16, normalized size = 1.2 \begin{align*}{\frac{ \left ( 3+3\,x \right ) \left ( -1+x \right ) }{20} \left ({x}^{2}-1 \right ) ^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.84928, size = 12, normalized size = 0.92 \begin{align*} \frac{3}{20} \,{\left (x^{2} - 1\right )}^{\frac{10}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.65653, size = 65, normalized size = 5. \begin{align*} \frac{3}{20} \,{\left (x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1\right )}{\left (x^{2} - 1\right )}^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.75557, size = 56, normalized size = 4.31 \begin{align*} \frac{3 x^{6} \sqrt [3]{x^{2} - 1}}{20} - \frac{9 x^{4} \sqrt [3]{x^{2} - 1}}{20} + \frac{9 x^{2} \sqrt [3]{x^{2} - 1}}{20} - \frac{3 \sqrt [3]{x^{2} - 1}}{20} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.7084, size = 12, normalized size = 0.92 \begin{align*} \frac{3}{20} \,{\left (x^{2} - 1\right )}^{\frac{10}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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