Optimal. Leaf size=34 \[ -\frac{a}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0646196, 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 \[ -\frac{a}{b^2 \sqrt{a+\frac{b}{x^2}}}-\frac{\sqrt{a+\frac{b}{x^2}}}{b^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x^2)^(3/2)*x^5),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.94936, size = 29, normalized size = 0.85 \[ - \frac{a}{b^{2} \sqrt{a + \frac{b}{x^{2}}}} - \frac{\sqrt{a + \frac{b}{x^{2}}}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x**2)**(3/2)/x**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0276238, size = 28, normalized size = 0.82 \[ \frac{-2 a x^2-b}{b^2 x^2 \sqrt{a+\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x^2)^(3/2)*x^5),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 37, normalized size = 1.1 \[ -{\frac{ \left ( a{x}^{2}+b \right ) \left ( 2\,a{x}^{2}+b \right ) }{{b}^{2}{x}^{4}} \left ({\frac{a{x}^{2}+b}{{x}^{2}}} \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x^2)^(3/2)/x^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42762, size = 41, normalized size = 1.21 \[ -\frac{\sqrt{a + \frac{b}{x^{2}}}}{b^{2}} - \frac{a}{\sqrt{a + \frac{b}{x^{2}}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^5),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.235011, size = 50, normalized size = 1.47 \[ -\frac{{\left (2 \, a x^{2} + b\right )} \sqrt{\frac{a x^{2} + b}{x^{2}}}}{a b^{2} x^{2} + b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^5),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 11.1242, size = 48, normalized size = 1.41 \[ \begin{cases} - \frac{2 a}{b^{2} \sqrt{a + \frac{b}{x^{2}}}} - \frac{1}{b x^{2} \sqrt{a + \frac{b}{x^{2}}}} & \text{for}\: b \neq 0 \\- \frac{1}{4 a^{\frac{3}{2}} x^{4}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x**2)**(3/2)/x**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (a + \frac{b}{x^{2}}\right )}^{\frac{3}{2}} x^{5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x^2)^(3/2)*x^5),x, algorithm="giac")
[Out]