Optimal. Leaf size=16 \[ -\frac{1}{3} (4-\sin (2 x))^{3/2} \]
[Out]
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Rubi [A] time = 0.0363133, 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 \[ -\frac{1}{3} (4-\sin (2 x))^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Cos[2*x]*Sqrt[4 - Sin[2*x]],x]
[Out]
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Rubi in Sympy [A] time = 1.88455, size = 12, normalized size = 0.75 \[ - \frac{\left (- \sin{\left (2 x \right )} + 4\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(2*x)*(4-sin(2*x))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0184198, size = 16, normalized size = 1. \[ -\frac{1}{3} (4-\sin (2 x))^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[Cos[2*x]*Sqrt[4 - Sin[2*x]],x]
[Out]
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Maple [A] time = 0.021, size = 13, normalized size = 0.8 \[ -{\frac{1}{3} \left ( 4-\sin \left ( 2\,x \right ) \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(2*x)*(4-sin(2*x))^(1/2),x)
[Out]
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Maxima [A] time = 1.35489, size = 16, normalized size = 1. \[ -\frac{1}{3} \,{\left (-\sin \left (2 \, x\right ) + 4\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-sin(2*x) + 4)*cos(2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233611, size = 24, normalized size = 1.5 \[ \frac{1}{3} \,{\left (\sin \left (2 \, x\right ) - 4\right )} \sqrt{-\sin \left (2 \, x\right ) + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-sin(2*x) + 4)*cos(2*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.399012, size = 29, normalized size = 1.81 \[ \frac{\sqrt{- \sin{\left (2 x \right )} + 4} \sin{\left (2 x \right )}}{3} - \frac{4 \sqrt{- \sin{\left (2 x \right )} + 4}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(2*x)*(4-sin(2*x))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219949, size = 16, normalized size = 1. \[ -\frac{1}{3} \,{\left (-\sin \left (2 \, x\right ) + 4\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-sin(2*x) + 4)*cos(2*x),x, algorithm="giac")
[Out]