Optimal. Leaf size=32 \[ -\tan ^{-1}\left (\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right ) \]
[Out]
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Rubi [A] time = 0.0263628, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\tan ^{-1}\left (\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[(b - x)*(-a + x)],x]
[Out]
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Rubi in Sympy [A] time = 1.19132, size = 26, normalized size = 0.81 \[ - \operatorname{atan}{\left (\frac{a + b - 2 x}{2 \sqrt{- a b - x^{2} + x \left (a + b\right )}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((b-x)*(-a+x))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0385634, size = 64, normalized size = 2. \[ -\frac{\sqrt{x-a} \sqrt{b-x} \tan ^{-1}\left (\frac{a+b-2 x}{2 \sqrt{x-a} \sqrt{b-x}}\right )}{\sqrt{(a-x) (x-b)}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[(b - x)*(-a + x)],x]
[Out]
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \[ \arctan \left ({1 \left ( x-{\frac{a}{2}}-{\frac{b}{2}} \right ){\frac{1}{\sqrt{-ab+ \left ( a+b \right ) x-{x}^{2}}}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((b-x)*(-a+x))^(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(-(a - x)*(b - x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207562, size = 35, normalized size = 1.09 \[ \arctan \left (-\frac{a + b - 2 \, x}{2 \, \sqrt{-a b +{\left (a + b\right )} x - x^{2}}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-(a - x)*(b - x)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{\left (- a + x\right ) \left (b - x\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b-x)*(-a+x))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.24245, size = 30, normalized size = 0.94 \[ \arcsin \left (\frac{a + b - 2 \, x}{a - b}\right ){\rm sign}\left (-a + b\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-(a - x)*(b - x)),x, algorithm="giac")
[Out]