Optimal. Leaf size=13 \[ \frac {2}{5} \left (x^2-1\right )^{5/4} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {261} \begin {gather*} \frac {2}{5} \left (x^2-1\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \sqrt [4]{-1+x^2} \, dx &=\frac {2}{5} \left (-1+x^2\right )^{5/4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{5} \left (x^2-1\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{5} \left (x^2-1\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{5} \, {\left (x^{2} - 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{5} \, {\left (x^{2} - 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 1.23 \begin {gather*} \frac {2 \left (-1+x \right ) \left (1+x \right ) \left (x^{2}-1\right )^{\frac {1}{4}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{5} \, {\left (x^{2} - 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 9, normalized size = 0.69 \begin {gather*} \frac {2\,{\left (x^2-1\right )}^{5/4}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 26, normalized size = 2.00 \begin {gather*} \frac {2 x^{2} \sqrt [4]{x^{2} - 1}}{5} - \frac {2 \sqrt [4]{x^{2} - 1}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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