Optimal. Leaf size=34 \[ -\frac{2 a}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0572949, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2 a}{b^2 \sqrt{a+\frac{b}{x}}}-\frac{2 \sqrt{a+\frac{b}{x}}}{b^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)^(3/2)*x^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.74981, size = 29, normalized size = 0.85 \[ - \frac{2 a}{b^{2} \sqrt{a + \frac{b}{x}}} - \frac{2 \sqrt{a + \frac{b}{x}}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**(3/2)/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0340849, size = 29, normalized size = 0.85 \[ -\frac{2 \sqrt{a+\frac{b}{x}} (2 a x+b)}{b^2 (a x+b)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)^(3/2)*x^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 31, normalized size = 0.9 \[ -2\,{\frac{ \left ( ax+b \right ) \left ( 2\,ax+b \right ) }{{b}^{2}{x}^{2}} \left ({\frac{ax+b}{x}} \right ) ^{-3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^(3/2)/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43811, size = 41, normalized size = 1.21 \[ -\frac{2 \, \sqrt{a + \frac{b}{x}}}{b^{2}} - \frac{2 \, a}{\sqrt{a + \frac{b}{x}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(3/2)*x^3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.233898, size = 34, normalized size = 1. \[ -\frac{2 \,{\left (2 \, a x + b\right )}}{b^{2} x \sqrt{\frac{a x + b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(3/2)*x^3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 5.73243, size = 42, normalized size = 1.24 \[ \begin{cases} - \frac{4 a}{b^{2} \sqrt{a + \frac{b}{x}}} - \frac{2}{b x \sqrt{a + \frac{b}{x}}} & \text{for}\: b \neq 0 \\- \frac{1}{2 a^{\frac{3}{2}} x^{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**(3/2)/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.256332, size = 47, normalized size = 1.38 \[ -2 \, b{\left (\frac{a}{b^{3} \sqrt{\frac{a x + b}{x}}} + \frac{\sqrt{\frac{a x + b}{x}}}{b^{3}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)^(3/2)*x^3),x, algorithm="giac")
[Out]