Optimal. Leaf size=10 \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
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Rubi [A] time = 0.0136073, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[2 - 3*x]*Sqrt[2 + 3*x]),x]
[Out]
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Rubi in Sympy [A] time = 1.50161, 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/(2-3*x)**(1/2)/(2+3*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00696571, size = 10, normalized size = 1. \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[2 - 3*x]*Sqrt[2 + 3*x]),x]
[Out]
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Maple [B] time = 0.01, size = 34, normalized size = 3.4 \[{\frac{1}{3}\sqrt{ \left ( 2-3\,x \right ) \left ( 2+3\,x \right ) }\arcsin \left ({\frac{3\,x}{2}} \right ){\frac{1}{\sqrt{2-3\,x}}}{\frac{1}{\sqrt{2+3\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2-3*x)^(1/2)/(2+3*x)^(1/2),x)
[Out]
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Maxima [A] time = 0.8093, 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(3*x + 2)*sqrt(-3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265899, size = 34, normalized size = 3.4 \[ -\frac{2}{3} \, \arctan \left (\frac{\sqrt{3 \, x + 2} \sqrt{-3 \, x + 2} - 2}{3 \, x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(3*x + 2)*sqrt(-3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.8553, size = 51, normalized size = 5.1 \[ \begin{cases} - \frac{2 i \operatorname{acosh}{\left (\frac{\sqrt{3} \sqrt{x + \frac{2}{3}}}{2} \right )}}{3} & \text{for}\: \frac{3 \left |{x + \frac{2}{3}}\right |}{4} > 1 \\\frac{2 \operatorname{asin}{\left (\frac{\sqrt{3} \sqrt{x + \frac{2}{3}}}{2} \right )}}{3} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2-3*x)**(1/2)/(2+3*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.267658, size = 16, normalized size = 1.6 \[ \frac{2}{3} \, \arcsin \left (\frac{1}{2} \, \sqrt{3 \, x + 2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(3*x + 2)*sqrt(-3*x + 2)),x, algorithm="giac")
[Out]