Optimal. Leaf size=7 \[ \sin ^{-1}\left (\frac{\sin (x)}{2}\right ) \]
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Rubi [A] time = 0.0249788, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {3190, 216} \[ \sin ^{-1}\left (\frac{\sin (x)}{2}\right ) \]
Antiderivative was successfully verified.
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Rule 3190
Rule 216
Rubi steps
\begin{align*} \int \frac{\cos (x)}{\sqrt{4-\sin ^2(x)}} \, dx &=\operatorname{Subst}\left (\int \frac{1}{\sqrt{4-x^2}} \, dx,x,\sin (x)\right )\\ &=\sin ^{-1}\left (\frac{\sin (x)}{2}\right )\\ \end{align*}
Mathematica [A] time = 0.0089002, size = 7, normalized size = 1. \[ \sin ^{-1}\left (\frac{\sin (x)}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.026, size = 6, normalized size = 0.9 \begin{align*} \arcsin \left ({\frac{\sin \left ( x \right ) }{2}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.44222, size = 7, normalized size = 1. \begin{align*} \arcsin \left (\frac{1}{2} \, \sin \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.21549, size = 176, normalized size = 25.14 \begin{align*} \frac{1}{2} \, \arctan \left (\frac{\sqrt{\cos \left (x\right )^{2} + 3}{\left (\cos \left (x\right )^{2} + 1\right )} \sin \left (x\right ) - 4 \, \cos \left (x\right ) \sin \left (x\right )}{\cos \left (x\right )^{4} + 6 \, \cos \left (x\right )^{2} - 3}\right ) + \frac{1}{2} \, \arctan \left (\frac{\sin \left (x\right )}{\cos \left (x\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10703, size = 7, normalized size = 1. \begin{align*} \arcsin \left (\frac{1}{2} \, \sin \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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