Optimal. Leaf size=21 \[ -\frac{2}{a \sqrt{x} \sqrt{a+\frac{b}{x}}} \]
[Out]
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Rubi [A] time = 0.025686, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{2}{a \sqrt{x} \sqrt{a+\frac{b}{x}}} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^(3/2)*x^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.73657, size = 17, normalized size = 0.81 \[ - \frac{2}{a \sqrt{x} \sqrt{a + \frac{b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**(3/2)/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.0339656, size = 30, normalized size = 1.43 \[ -\frac{2 \sqrt{x} \sqrt{\frac{a x+b}{x}}}{a (a x+b)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^(3/2)*x^(3/2)),x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 1.2 \[ -2\,{\frac{ax+b}{a{x}^{3/2}} \left ({\frac{ax+b}{x}} \right ) ^{-3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^(3/2)/x^(3/2),x)
[Out]
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Maxima [A] time = 1.43356, size = 23, normalized size = 1.1 \[ -\frac{2}{\sqrt{a + \frac{b}{x}} a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(3/2)*x^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234193, size = 26, normalized size = 1.24 \[ -\frac{2}{a \sqrt{x} \sqrt{\frac{a x + b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(3/2)*x^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 107.435, size = 19, normalized size = 0.9 \[ - \frac{2}{a \sqrt{b} \sqrt{\frac{a x}{b} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**(3/2)/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.232329, size = 28, normalized size = 1.33 \[ -\frac{2}{\sqrt{a x + b} a} + \frac{2}{a \sqrt{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(3/2)*x^(3/2)),x, algorithm="giac")
[Out]