Optimal. Leaf size=19 \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{x}} \]
[Out]
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Rubi [A] time = 0.01252, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(3/2)*Sqrt[a + b*x]),x]
[Out]
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Rubi in Sympy [A] time = 2.36496, size = 17, normalized size = 0.89 \[ - \frac{2 \sqrt{a + b x}}{a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(3/2)/(b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0139484, size = 19, normalized size = 1. \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(3/2)*Sqrt[a + b*x]),x]
[Out]
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Maple [A] time = 0.006, size = 16, normalized size = 0.8 \[ -2\,{\frac{\sqrt{bx+a}}{a\sqrt{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(3/2)/(b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.33884, size = 20, normalized size = 1.05 \[ -\frac{2 \, \sqrt{b x + a}}{a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*x^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211005, size = 20, normalized size = 1.05 \[ -\frac{2 \, \sqrt{b x + a}}{a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*x^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.60177, size = 19, normalized size = 1. \[ - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(3/2)/(b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.222354, size = 45, normalized size = 2.37 \[ -\frac{2 \, \sqrt{b x + a} b^{2}}{\sqrt{{\left (b x + a\right )} b - a b} a{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + a)*x^(3/2)),x, algorithm="giac")
[Out]