Optimal. Leaf size=39 \[ \frac{\sqrt{x}}{3 \sqrt{2-b x}}+\frac{\sqrt{x}}{3 (2-b x)^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0233741, antiderivative size = 39, 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 \[ \frac{\sqrt{x}}{3 \sqrt{2-b x}}+\frac{\sqrt{x}}{3 (2-b x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[x]*(2 - b*x)^(5/2)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.71283, size = 29, normalized size = 0.74 \[ \frac{\sqrt{x}}{3 \sqrt{- b x + 2}} + \frac{\sqrt{x}}{3 \left (- b x + 2\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-b*x+2)**(5/2)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0223988, size = 24, normalized size = 0.62 \[ -\frac{\sqrt{x} (b x-3)}{3 (2-b x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[x]*(2 - b*x)^(5/2)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 19, normalized size = 0.5 \[ -{\frac{bx-3}{3}\sqrt{x} \left ( -bx+2 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-b*x+2)^(5/2)/x^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34482, size = 34, normalized size = 0.87 \[ \frac{{\left (b - \frac{3 \,{\left (b x - 2\right )}}{x}\right )} x^{\frac{3}{2}}}{6 \,{\left (-b x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x + 2)^(5/2)*sqrt(x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228981, size = 39, normalized size = 1. \[ \frac{b x^{2} - 3 \, x}{3 \,{\left (b x - 2\right )} \sqrt{-b x + 2} \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x + 2)^(5/2)*sqrt(x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 23.8281, size = 165, normalized size = 4.23 \[ \begin{cases} \frac{b x}{3 b^{\frac{3}{2}} x \sqrt{-1 + \frac{2}{b x}} - 6 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}} - \frac{3}{3 b^{\frac{3}{2}} x \sqrt{-1 + \frac{2}{b x}} - 6 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}} & \text{for}\: 2 \left |{\frac{1}{b x}}\right | > 1 \\- \frac{i b^{2} x}{3 b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}} - 6 b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}} + \frac{3 i b}{3 b^{\frac{5}{2}} x \sqrt{1 - \frac{2}{b x}} - 6 b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-b*x+2)**(5/2)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210541, size = 122, normalized size = 3.13 \[ \frac{8 \,{\left (3 \,{\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} - 2 \, b\right )} \sqrt{-b} b^{2}}{3 \,{\left ({\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} - 2 \, b\right )}^{3}{\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x + 2)^(5/2)*sqrt(x)),x, algorithm="giac")
[Out]