Optimal. Leaf size=12 \[ \frac {1}{2} F\left (\left .\sin ^{-1}\left (\frac {x}{2}\right )\right |-1\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, 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 = {221} \[ \frac {1}{2} F\left (\left .\sin ^{-1}\left (\frac {x}{2}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
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Rule 221
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {16-x^4}} \, dx &=\frac {1}{2} F\left (\left .\sin ^{-1}\left (\frac {x}{2}\right )\right |-1\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ \frac {1}{2} F\left (\left .\sin ^{-1}\left (\frac {x}{2}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
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fricas [F] time = 0.94, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-x^{4} + 16}}{x^{4} - 16}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-x^{4} + 16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 34, normalized size = 2.83 \[ \frac {\sqrt {-x^{2}+4}\, \sqrt {x^{2}+4}\, \EllipticF \left (\frac {x}{2}, i\right )}{2 \sqrt {-x^{4}+16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-x^{4} + 16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 13, normalized size = 1.08 \[ \frac {x\,{{}}_2{\mathrm {F}}_1\left (\frac {1}{4},\frac {1}{2};\ \frac {5}{4};\ \frac {x^4}{16}\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.92, size = 31, normalized size = 2.58 \[ \frac {x \Gamma \left (\frac {1}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} \frac {1}{4}, \frac {1}{2} \\ \frac {5}{4} \end {matrix}\middle | {\frac {x^{4} e^{2 i \pi }}{16}} \right )}}{16 \Gamma \left (\frac {5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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