Optimal. Leaf size=6 \[ \sin ^{-1}\left (\frac{x}{4}\right ) \]
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Rubi [A] time = 0.0012241, antiderivative size = 6, normalized size of antiderivative = 1., 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 = {216} \[ \sin ^{-1}\left (\frac{x}{4}\right ) \]
Antiderivative was successfully verified.
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Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{16-x^2}} \, dx &=\sin ^{-1}\left (\frac{x}{4}\right )\\ \end{align*}
Mathematica [A] time = 0.0041155, size = 6, normalized size = 1. \[ \sin ^{-1}\left (\frac{x}{4}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 5, normalized size = 0.8 \begin{align*} \arcsin \left ({\frac{x}{4}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.40092, size = 5, normalized size = 0.83 \begin{align*} \arcsin \left (\frac{1}{4} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.20828, size = 49, normalized size = 8.17 \begin{align*} -2 \, \arctan \left (\frac{\sqrt{-x^{2} + 16} - 4}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131268, size = 3, normalized size = 0.5 \begin{align*} \operatorname{asin}{\left (\frac{x}{4} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07072, size = 5, normalized size = 0.83 \begin{align*} \arcsin \left (\frac{1}{4} \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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