Optimal. Leaf size=12 \[ \frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right ) \]
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Rubi [A] time = 0.0041662, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {275, 216} \[ \frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right ) \]
Antiderivative was successfully verified.
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Rule 275
Rule 216
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{16-x^4}} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{1}{\sqrt{16-x^2}} \, dx,x,x^2\right )\\ &=\frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right )\\ \end{align*}
Mathematica [A] time = 0.0021365, size = 12, normalized size = 1. \[ \frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 9, normalized size = 0.8 \begin{align*}{\frac{1}{2}\arcsin \left ({\frac{{x}^{2}}{4}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.46221, size = 22, normalized size = 1.83 \begin{align*} -\frac{1}{2} \, \arctan \left (\frac{\sqrt{-x^{4} + 16}}{x^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.4885, size = 49, normalized size = 4.08 \begin{align*} -\arctan \left (\frac{\sqrt{-x^{4} + 16} - 4}{x^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.29352, size = 24, normalized size = 2. \begin{align*} \begin{cases} - \frac{i \operatorname{acosh}{\left (\frac{x^{2}}{4} \right )}}{2} & \text{for}\: \frac{\left |{x^{4}}\right |}{16} > 1 \\\frac{\operatorname{asin}{\left (\frac{x^{2}}{4} \right )}}{2} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2018, size = 11, normalized size = 0.92 \begin{align*} \frac{1}{2} \, \arcsin \left (\frac{1}{4} \, x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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