Optimal. Leaf size=10 \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
[Out]
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Rubi [A] time = 0.00580065, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[4 - 9*x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.54615, size = 7, normalized size = 0.7 \[ \frac{\operatorname{asin}{\left (\frac{3 x}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-9*x**2+4)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00670908, size = 10, normalized size = 1. \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[4 - 9*x^2],x]
[Out]
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Maple [A] time = 0.005, size = 7, normalized size = 0.7 \[{\frac{1}{3}\arcsin \left ({\frac{3\,x}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-9*x^2+4)^(1/2),x)
[Out]
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Maxima [A] time = 0.798958, size = 8, normalized size = 0.8 \[ \frac{1}{3} \, \arcsin \left (\frac{3}{2} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-9*x^2 + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264605, size = 26, normalized size = 2.6 \[ -\frac{2}{3} \, \arctan \left (\frac{\sqrt{-9 \, x^{2} + 4} - 2}{3 \, x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-9*x^2 + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.337213, size = 7, normalized size = 0.7 \[ \frac{\operatorname{asin}{\left (\frac{3 x}{2} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-9*x**2+4)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.272269, size = 8, normalized size = 0.8 \[ \frac{1}{3} \, \arcsin \left (\frac{3}{2} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-9*x^2 + 4),x, algorithm="giac")
[Out]