Optimal. Leaf size=16 \[ -\frac {1}{3} (4-\sin (2 x))^{3/2} \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.00, 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 32
Rule 2668
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*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ -\frac {1}{3} (4-\sin (2 x))^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 18, normalized size = 1.12 \[ \frac {1}{3} \, {\left (\sin \left (2 \, x\right ) - 4\right )} \sqrt {-\sin \left (2 \, x\right ) + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 0.81 \[ -\frac {\left (-\sin \left (2 x \right )+4\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 12, normalized size = 0.75 \[ -\frac {1}{3} \, {\left (-\sin \left (2 \, x\right ) + 4\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 12, normalized size = 0.75 \[ -\frac {{\left (4-\sin \left (2\,x\right )\right )}^{3/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.34, size = 29, normalized size = 1.81 \[ \frac {\sqrt {4 - \sin {\left (2 x \right )}} \sin {\left (2 x \right )}}{3} - \frac {4 \sqrt {4 - \sin {\left (2 x \right )}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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