Optimal. Leaf size=11 \[ 2 \sqrt [4]{x^2-1} \]
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Rubi [A] time = 0.02, antiderivative size = 11, 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*} 2 \sqrt [4]{x^2-1} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x}{\left (-1+x^2\right )^{3/4}} \, dx &=2 \sqrt [4]{-1+x^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} 2 \sqrt [4]{x^2-1} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 11, normalized size = 1.00 \begin {gather*} 2 \sqrt [4]{-1+x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 9, normalized size = 0.82 \begin {gather*} 2 \, {\left (x^{2} - 1\right )}^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.49, size = 9, normalized size = 0.82 \begin {gather*} 2 \, {\left (x^{2} - 1\right )}^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 10, normalized size = 0.91
method | result | size |
derivativedivides | \(2 \left (x^{2}-1\right )^{\frac {1}{4}}\) | \(10\) |
default | \(2 \left (x^{2}-1\right )^{\frac {1}{4}}\) | \(10\) |
trager | \(2 \left (x^{2}-1\right )^{\frac {1}{4}}\) | \(10\) |
risch | \(2 \left (x^{2}-1\right )^{\frac {1}{4}}\) | \(10\) |
gosper | \(\frac {2 \left (-1+x \right ) \left (1+x \right )}{\left (x^{2}-1\right )^{\frac {3}{4}}}\) | \(16\) |
meijerg | \(\frac {\left (-\mathrm {signum}\left (x^{2}-1\right )\right )^{\frac {3}{4}} x^{2} \hypergeom \left (\left [\frac {3}{4}, 1\right ], \relax [2], x^{2}\right )}{2 \mathrm {signum}\left (x^{2}-1\right )^{\frac {3}{4}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 9, normalized size = 0.82 \begin {gather*} 2 \, {\left (x^{2} - 1\right )}^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 9, normalized size = 0.82 \begin {gather*} 2\,{\left (x^2-1\right )}^{1/4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 8, normalized size = 0.73 \begin {gather*} 2 \sqrt [4]{x^{2} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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