Optimal. Leaf size=14 \[ \sqrt {2 x^4-2 x-1} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {1588} \begin {gather*} \sqrt {2 x^4-2 x-1} \end {gather*}
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx &=\sqrt {-1-2 x+2 x^4}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \sqrt {2 x^4-2 x-1} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \sqrt {-1-2 x+2 x^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 12, normalized size = 0.86 \begin {gather*} \sqrt {2 \, x^{4} - 2 \, x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 12, normalized size = 0.86 \begin {gather*} \sqrt {2 \, x^{4} - 2 \, x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.90, size = 13, normalized size = 0.93
method | result | size |
gosper | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
default | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
trager | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
risch | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
elliptic | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 12, normalized size = 0.86 \begin {gather*} \sqrt {2 \, x^{4} - 2 \, x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 12, normalized size = 0.86 \begin {gather*} \sqrt {2\,x^4-2\,x-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 12, normalized size = 0.86 \begin {gather*} \sqrt {2 x^{4} - 2 x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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