Optimal. Leaf size=16 \[ -\frac{1}{3} (4-\sin (2 x))^{3/2} \]
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Rubi [A] time = 0.0230421, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {2668, 32} \[ -\frac{1}{3} (4-\sin (2 x))^{3/2} \]
Antiderivative was successfully verified.
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Rule 2668
Rule 32
Rubi steps
\begin{align*} \int \cos (2 x) \sqrt{4-\sin (2 x)} \, dx &=-\left (\frac{1}{2} \operatorname{Subst}\left (\int \sqrt{4+x} \, dx,x,-\sin (2 x)\right )\right )\\ &=-\frac{1}{3} (4-\sin (2 x))^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0119864, size = 16, normalized size = 1. \[ -\frac{1}{3} (4-\sin (2 x))^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.013, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{3} \left ( 4-\sin \left ( 2\,x \right ) \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946658, size = 16, normalized size = 1. \begin{align*} -\frac{1}{3} \,{\left (-\sin \left (2 \, x\right ) + 4\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.46015, size = 54, normalized size = 3.38 \begin{align*} \frac{1}{3} \,{\left (\sin \left (2 \, x\right ) - 4\right )} \sqrt{-\sin \left (2 \, x\right ) + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.29622, size = 29, normalized size = 1.81 \begin{align*} \frac{\sqrt{4 - \sin{\left (2 x \right )}} \sin{\left (2 x \right )}}{3} - \frac{4 \sqrt{4 - \sin{\left (2 x \right )}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08493, size = 16, normalized size = 1. \begin{align*} -\frac{1}{3} \,{\left (-\sin \left (2 \, x\right ) + 4\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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