Optimal. Leaf size=11 \[ -\sin ^{-1}\left (\frac{\cos ^2(x)}{3}\right ) \]
[Out]
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Rubi [A] time = 0.082698, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.235 \[ -\sin ^{-1}\left (\frac{\cos ^2(x)}{3}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sin[2*x]/Sqrt[9 - Cos[x]^4],x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sin(2*x)/(9-cos(x)**4)**(1/2),x)
[Out]
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Mathematica [C] time = 0.120085, size = 26, normalized size = 2.36 \[ i \log \left (\sqrt{9-\cos ^4(x)}+i \cos ^2(x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sin[2*x]/Sqrt[9 - Cos[x]^4],x]
[Out]
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Maple [A] time = 0.045, size = 10, normalized size = 0.9 \[ -\arcsin \left ({\frac{ \left ( \cos \left ( x \right ) \right ) ^{2}}{3}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sin(2*x)/(9-cos(x)^4)^(1/2),x)
[Out]
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Maxima [A] time = 6.50359, size = 61, normalized size = 5.55 \[ \log \left (\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} + 2 \, \sin \left (2 \, x\right ) + 1\right ) - \log \left (\cos \left (2 \, x\right )^{2} + \sin \left (2 \, x\right )^{2} - 2 \, \sin \left (2 \, x\right ) + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(2*x)/sqrt(-cos(x)^4 + 9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271522, size = 24, normalized size = 2.18 \[ -\arctan \left (\frac{\cos \left (x\right )^{2}}{\sqrt{-\cos \left (x\right )^{4} + 9}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(2*x)/sqrt(-cos(x)^4 + 9),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(2*x)/(9-cos(x)**4)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sin \left (2 \, x\right )}{\sqrt{-\cos \left (x\right )^{4} + 9}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(2*x)/sqrt(-cos(x)^4 + 9),x, algorithm="giac")
[Out]