Optimal. Leaf size=20 \[ -\frac{2 \sqrt{a-b x}}{a \sqrt{x}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0131849, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{2 \sqrt{a-b x}}{a \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(3/2)*Sqrt[a - b*x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.65643, size = 17, normalized size = 0.85 \[ - \frac{2 \sqrt{a - b x}}{a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(3/2)/(-b*x+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.014332, size = 20, 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]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 17, normalized size = 0.9 \[ -2\,{\frac{\sqrt{-bx+a}}{a\sqrt{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(3/2)/(-b*x+a)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.38745, size = 22, normalized size = 1.1 \[ -\frac{2 \, \sqrt{-b x + a}}{a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + a)*x^(3/2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211522, size = 22, normalized size = 1.1 \[ -\frac{2 \, \sqrt{-b x + a}}{a \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + a)*x^(3/2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.64539, size = 46, normalized size = 2.3 \[ \begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{a} & \text{for}\: \left |{\frac{a}{b x}}\right | > 1 \\- \frac{2 i \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{a} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(3/2)/(-b*x+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.230662, size = 47, normalized size = 2.35 \[ -\frac{2 \, \sqrt{-b x + a} b^{2}}{\sqrt{{\left (b x - a\right )} b + a b} a{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + a)*x^(3/2)),x, algorithm="giac")
[Out]