Optimal. Leaf size=46 \[ -\frac{5}{63} \left (1-x^3\right )^{21/5}+\frac{5}{24} \left (1-x^3\right )^{16/5}-\frac{5}{33} \left (1-x^3\right )^{11/5} \]
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Rubi [A] time = 0.019694, antiderivative size = 46, 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} \[ -\frac{5}{63} \left (1-x^3\right )^{21/5}+\frac{5}{24} \left (1-x^3\right )^{16/5}-\frac{5}{33} \left (1-x^3\right )^{11/5} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^8 \left (1-x^3\right )^{6/5} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int (1-x)^{6/5} x^2 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left ((1-x)^{6/5}-2 (1-x)^{11/5}+(1-x)^{16/5}\right ) \, dx,x,x^3\right )\\ &=-\frac{5}{33} \left (1-x^3\right )^{11/5}+\frac{5}{24} \left (1-x^3\right )^{16/5}-\frac{5}{63} \left (1-x^3\right )^{21/5}\\ \end{align*}
Mathematica [A] time = 0.0134046, size = 27, normalized size = 0.59 \[ -\frac{5 \left (1-x^3\right )^{11/5} \left (88 x^6+55 x^3+25\right )}{5544} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 33, normalized size = 0.7 \begin{align*}{\frac{ \left ( -5+5\,x \right ) \left ({x}^{2}+x+1 \right ) \left ( 88\,{x}^{6}+55\,{x}^{3}+25 \right ) }{5544} \left ( -{x}^{3}+1 \right ) ^{{\frac{6}{5}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02281, size = 46, normalized size = 1. \begin{align*} -\frac{5}{63} \,{\left (-x^{3} + 1\right )}^{\frac{21}{5}} + \frac{5}{24} \,{\left (-x^{3} + 1\right )}^{\frac{16}{5}} - \frac{5}{33} \,{\left (-x^{3} + 1\right )}^{\frac{11}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73452, size = 90, normalized size = 1.96 \begin{align*} -\frac{5}{5544} \,{\left (88 \, x^{12} - 121 \, x^{9} + 3 \, x^{6} + 5 \, x^{3} + 25\right )}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 12.2684, size = 71, normalized size = 1.54 \begin{align*} - \frac{5 x^{12} \sqrt [5]{1 - x^{3}}}{63} + \frac{55 x^{9} \sqrt [5]{1 - x^{3}}}{504} - \frac{5 x^{6} \sqrt [5]{1 - x^{3}}}{1848} - \frac{25 x^{3} \sqrt [5]{1 - x^{3}}}{5544} - \frac{125 \sqrt [5]{1 - x^{3}}}{5544} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14739, size = 74, normalized size = 1.61 \begin{align*} -\frac{5}{63} \,{\left (x^{3} - 1\right )}^{4}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} - \frac{5}{24} \,{\left (x^{3} - 1\right )}^{3}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} - \frac{5}{33} \,{\left (x^{3} - 1\right )}^{2}{\left (-x^{3} + 1\right )}^{\frac{1}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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