Optimal. Leaf size=13 \[ \frac {1}{20} \left (1-x^2\right )^{10} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {261} \[ \frac {1}{20} \left (1-x^2\right )^{10} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \left (-1+x^2\right )^9 \, dx &=\frac {1}{20} \left (1-x^2\right )^{10}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.85 \[ \frac {1}{20} \left (x^2-1\right )^{10} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.35, size = 51, normalized size = 3.92 \[ \frac {1}{20} x^{20} - \frac {1}{2} x^{18} + \frac {9}{4} x^{16} - 6 x^{14} + \frac {21}{2} x^{12} - \frac {63}{5} x^{10} + \frac {21}{2} x^{8} - 6 x^{6} + \frac {9}{4} x^{4} - \frac {1}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 9, normalized size = 0.69 \[ \frac {1}{20} \, {\left (x^{2} - 1\right )}^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 52, normalized size = 4.00 \[ \frac {1}{20} x^{20}-\frac {1}{2} x^{18}+\frac {9}{4} x^{16}-6 x^{14}+\frac {21}{2} x^{12}-\frac {63}{5} x^{10}+\frac {21}{2} x^{8}-6 x^{6}+\frac {9}{4} x^{4}-\frac {1}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 9, normalized size = 0.69 \[ \frac {1}{20} \, {\left (x^{2} - 1\right )}^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 9, normalized size = 0.69 \[ \frac {{\left (x^2-1\right )}^{10}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.06, size = 58, normalized size = 4.46 \[ \frac {x^{20}}{20} - \frac {x^{18}}{2} + \frac {9 x^{16}}{4} - 6 x^{14} + \frac {21 x^{12}}{2} - \frac {63 x^{10}}{5} + \frac {21 x^{8}}{2} - 6 x^{6} + \frac {9 x^{4}}{4} - \frac {x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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