Optimal. Leaf size=46 \[ -\frac{4 b \sqrt{a-b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a-b x}}{3 a x^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0287786, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{4 b \sqrt{a-b x}}{3 a^2 \sqrt{x}}-\frac{2 \sqrt{a-b x}}{3 a x^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^(5/2)*Sqrt[a - b*x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.19993, size = 41, normalized size = 0.89 \[ - \frac{2 \sqrt{a - b x}}{3 a x^{\frac{3}{2}}} - \frac{4 b \sqrt{a - b x}}{3 a^{2} \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**(5/2)/(-b*x+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0195036, size = 28, normalized size = 0.61 \[ -\frac{2 \sqrt{a-b x} (a+2 b x)}{3 a^2 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^(5/2)*Sqrt[a - b*x]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 23, normalized size = 0.5 \[ -{\frac{4\,bx+2\,a}{3\,{a}^{2}}\sqrt{-bx+a}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^(5/2)/(-b*x+a)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33195, size = 43, normalized size = 0.93 \[ -\frac{2 \,{\left (\frac{3 \, \sqrt{-b x + a} b}{\sqrt{x}} + \frac{{\left (-b x + a\right )}^{\frac{3}{2}}}{x^{\frac{3}{2}}}\right )}}{3 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + a)*x^(5/2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21489, size = 30, normalized size = 0.65 \[ -\frac{2 \,{\left (2 \, b x + a\right )} \sqrt{-b x + a}}{3 \, a^{2} x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + a)*x^(5/2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 23.865, size = 177, normalized size = 3.85 \[ \begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{3 a x} - \frac{4 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} - 1}}{3 a^{2}} & \text{for}\: \left |{\frac{a}{b x}}\right | > 1 \\\frac{2 i a^{2} b^{\frac{3}{2}} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{3} b x + 3 a^{2} b^{2} x^{2}} + \frac{2 i a b^{\frac{5}{2}} x \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{3} b x + 3 a^{2} b^{2} x^{2}} - \frac{4 i b^{\frac{7}{2}} x^{2} \sqrt{- \frac{a}{b x} + 1}}{- 3 a^{3} b x + 3 a^{2} b^{2} x^{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**(5/2)/(-b*x+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21439, size = 73, normalized size = 1.59 \[ -\frac{\sqrt{-b x + a} b{\left (\frac{2 \,{\left (b x - a\right )}}{a^{2} b^{3}} + \frac{3}{a b^{3}}\right )}}{24 \,{\left ({\left (b x - a\right )} b + a b\right )}^{\frac{3}{2}}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-b*x + a)*x^(5/2)),x, algorithm="giac")
[Out]