Optimal. Leaf size=18 \[ -\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0295821, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[a + b/x^3]*x^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.11858, size = 15, normalized size = 0.83 \[ - \frac{2 \sqrt{a + \frac{b}{x^{3}}}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(a+b/x**3)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0210587, size = 18, normalized size = 1. \[ -\frac{2 \sqrt{a+\frac{b}{x^3}}}{3 b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[a + b/x^3]*x^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 29, normalized size = 1.6 \[ -{\frac{2\,a{x}^{3}+2\,b}{3\,b{x}^{3}}{\frac{1}{\sqrt{{\frac{a{x}^{3}+b}{{x}^{3}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(a+b/x^3)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42252, size = 19, normalized size = 1.06 \[ -\frac{2 \, \sqrt{a + \frac{b}{x^{3}}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^3)*x^4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.241184, size = 24, normalized size = 1.33 \[ -\frac{2 \, \sqrt{\frac{a x^{3} + b}{x^{3}}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^3)*x^4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 6.28361, size = 29, normalized size = 1.61 \[ \begin{cases} - \frac{2 \sqrt{a + \frac{b}{x^{3}}}}{3 b} & \text{for}\: b \neq 0 \\- \frac{1}{3 \sqrt{a} x^{3}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(a+b/x**3)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.224881, size = 19, normalized size = 1.06 \[ -\frac{2 \, \sqrt{a + \frac{b}{x^{3}}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^3)*x^4),x, algorithm="giac")
[Out]