Optimal. Leaf size=21 \[ \frac{2 x^{3/2}}{3}-\frac{2}{3} (x-1)^{3/2} \]
[Out]
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Rubi [A] time = 0.0144696, antiderivative size = 21, 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 \[ \frac{2 x^{3/2}}{3}-\frac{2}{3} (x-1)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[-1 + x] + Sqrt[x])^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.46981, size = 17, normalized size = 0.81 \[ \frac{2 x^{\frac{3}{2}}}{3} - \frac{2 \left (x - 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((-1+x)**(1/2)+x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0234333, size = 19, normalized size = 0.9 \[ \frac{2}{3} \left (x^{3/2}-(x-1)^{3/2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[-1 + x] + Sqrt[x])^(-1),x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \[ -{\frac{2}{3} \left ( -1+x \right ) ^{{\frac{3}{2}}}}+{\frac{2}{3}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((-1+x)^(1/2)+x^(1/2)),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 1} + \sqrt{x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 1) + sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.27261, size = 18, normalized size = 0.86 \[ -\frac{2}{3} \,{\left (x - 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 1) + sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.44117, size = 63, normalized size = 3. \[ \frac{2 \sqrt{x} \sqrt{x - 1}}{3 \sqrt{x} + 3 \sqrt{x - 1}} + \frac{4 x}{3 \sqrt{x} + 3 \sqrt{x - 1}} - \frac{2}{3 \sqrt{x} + 3 \sqrt{x - 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-1+x)**(1/2)+x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.278179, size = 18, normalized size = 0.86 \[ -\frac{2}{3} \,{\left (x - 1\right )}^{\frac{3}{2}} + \frac{2}{3} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 1) + sqrt(x)),x, algorithm="giac")
[Out]