Optimal. Leaf size=48 \[ \frac{2 x^{3/2} \sqrt{a+\frac{b}{x}}}{3 a}-\frac{4 b \sqrt{x} \sqrt{a+\frac{b}{x}}}{3 a^2} \]
[Out]
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Rubi [A] time = 0.0518068, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2 x^{3/2} \sqrt{a+\frac{b}{x}}}{3 a}-\frac{4 b \sqrt{x} \sqrt{a+\frac{b}{x}}}{3 a^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/Sqrt[a + b/x],x]
[Out]
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Rubi in Sympy [A] time = 4.36381, size = 39, normalized size = 0.81 \[ \frac{2 x^{\frac{3}{2}} \sqrt{a + \frac{b}{x}}}{3 a} - \frac{4 b \sqrt{x} \sqrt{a + \frac{b}{x}}}{3 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)/(a+b/x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0356013, size = 30, normalized size = 0.62 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}} (a x-2 b)}{3 a^2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/Sqrt[a + b/x],x]
[Out]
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Maple [A] time = 0.003, size = 32, normalized size = 0.7 \[{\frac{ \left ( 2\,ax+2\,b \right ) \left ( ax-2\,b \right ) }{3\,{a}^{2}}{\frac{1}{\sqrt{x}}}{\frac{1}{\sqrt{{\frac{ax+b}{x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)/(a+b/x)^(1/2),x)
[Out]
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Maxima [A] time = 1.44007, size = 46, normalized size = 0.96 \[ \frac{2 \,{\left ({\left (a + \frac{b}{x}\right )}^{\frac{3}{2}} x^{\frac{3}{2}} - 3 \, \sqrt{a + \frac{b}{x}} b \sqrt{x}\right )}}{3 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/sqrt(a + b/x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231161, size = 35, normalized size = 0.73 \[ \frac{2 \,{\left (a x - 2 \, b\right )} \sqrt{x} \sqrt{\frac{a x + b}{x}}}{3 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/sqrt(a + b/x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.74571, size = 42, normalized size = 0.88 \[ \frac{2 \sqrt{b} x \sqrt{\frac{a x}{b} + 1}}{3 a} - \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a x}{b} + 1}}{3 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)/(a+b/x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227837, size = 43, normalized size = 0.9 \[ \frac{4 \, b^{\frac{3}{2}}}{3 \, a^{2}} + \frac{2 \,{\left ({\left (a x + b\right )}^{\frac{3}{2}} - 3 \, \sqrt{a x + b} b\right )}}{3 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/sqrt(a + b/x),x, algorithm="giac")
[Out]