Optimal. Leaf size=25 \[ \sin ^{-1}\left (\sqrt{x}\right )-\left (\sqrt{x}+2\right ) \sqrt{1-x} \]
[Out]
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Rubi [A] time = 0.0905389, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.19 \[ \sin ^{-1}\left (\sqrt{x}\right )-\left (\sqrt{x}+2\right ) \sqrt{1-x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - x]/(1 - Sqrt[x]),x]
[Out]
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Rubi in Sympy [A] time = 5.61758, size = 26, normalized size = 1.04 \[ - \sqrt{- x + 1} + \operatorname{asin}{\left (\sqrt{x} \right )} - \frac{\left (- x + 1\right )^{\frac{3}{2}}}{- \sqrt{x} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-x)**(1/2)/(1-x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0203013, size = 26, normalized size = 1.04 \[ \sqrt{1-x} \left (-\sqrt{x}-2\right )+\sin ^{-1}\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - x]/(1 - Sqrt[x]),x]
[Out]
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Maple [B] time = 0.004, size = 48, normalized size = 1.9 \[ -2\,\sqrt{1-x}+{\frac{1}{2}\sqrt{1-x}\sqrt{x} \left ( -2\,\sqrt{-x \left ( -1+x \right ) }+\arcsin \left ( 2\,x-1 \right ) \right ){\frac{1}{\sqrt{-x \left ( -1+x \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-x)^(1/2)/(1-x^(1/2)),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ -\int \frac{\sqrt{-x + 1}}{\sqrt{x} - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(-x + 1)/(sqrt(x) - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264293, size = 49, normalized size = 1.96 \[ -\sqrt{x} \sqrt{-x + 1} - 2 \, \sqrt{-x + 1} - \arctan \left (\frac{\sqrt{-x + 1}}{\sqrt{x}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(-x + 1)/(sqrt(x) - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.6973, size = 87, normalized size = 3.48 \[ 2 \left (\begin{cases} - \sqrt{- x + 1} + \frac{i \operatorname{acosh}{\left (\sqrt{- x + 1} \right )}}{2} - \frac{i \left (- x + 1\right )^{\frac{3}{2}}}{2 \sqrt{- x}} + \frac{i \sqrt{- x + 1}}{2 \sqrt{- x}} & \text{for}\: \left |{x - 1}\right | > 1 \\\frac{\sqrt{x} \sqrt{- x + 1}}{2} - \sqrt{- x + 1} + \frac{\operatorname{asin}{\left (\sqrt{- x + 1} \right )}}{2} & \text{otherwise} \end{cases}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-x)**(1/2)/(1-x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.265383, size = 43, normalized size = 1.72 \[ -\sqrt{x} \sqrt{-x + 1} - 2 \, \sqrt{-x + 1} - \arcsin \left (\sqrt{-x + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(-x + 1)/(sqrt(x) - 1),x, algorithm="giac")
[Out]