Optimal. Leaf size=17 \[ \frac{\sin ^{-1}\left (\frac{\sqrt{b} x}{3}\right )}{\sqrt{b}} \]
[Out]
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Rubi [A] time = 0.0113191, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{\sin ^{-1}\left (\frac{\sqrt{b} x}{3}\right )}{\sqrt{b}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[9 - b*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.97757, size = 14, normalized size = 0.82 \[ \frac{\operatorname{asin}{\left (\frac{\sqrt{b} x}{3} \right )}}{\sqrt{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-b*x**2+9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0127152, size = 17, normalized size = 1. \[ \frac{\sin ^{-1}\left (\frac{\sqrt{b} x}{3}\right )}{\sqrt{b}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[9 - b*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 21, normalized size = 1.2 \[{1\arctan \left ({x\sqrt{b}{\frac{1}{\sqrt{-b{x}^{2}+9}}}} \right ){\frac{1}{\sqrt{b}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-b*x^2+9)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-b*x^2 + 9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244151, size = 1, normalized size = 0.06 \[ \left [\frac{\log \left (\frac{\sqrt{-b x^{2} + 9} b x - 3 \, b x +{\left (b x^{2} + 3 \, \sqrt{-b x^{2} + 9} - 9\right )} \sqrt{-b}}{\sqrt{-b x^{2} + 9} - 3}\right )}{\sqrt{-b}}, -\frac{2 \, \arctan \left (\frac{\sqrt{-b x^{2} + 9} - 3}{\sqrt{b} x}\right )}{\sqrt{b}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-b*x^2 + 9),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.52015, size = 39, normalized size = 2.29 \[ \begin{cases} - \frac{i \operatorname{acosh}{\left (\frac{\sqrt{b} x}{3} \right )}}{\sqrt{b}} & \text{for}\: \frac{\left |{b x^{2}}\right |}{9} > 1 \\\frac{\operatorname{asin}{\left (\frac{\sqrt{b} x}{3} \right )}}{\sqrt{b}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-b*x**2+9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217633, size = 36, normalized size = 2.12 \[ -\frac{{\rm ln}\left (-\sqrt{-b} x + \sqrt{-b x^{2} + 9}\right )}{\sqrt{-b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-b*x^2 + 9),x, algorithm="giac")
[Out]