Optimal. Leaf size=21 \[ -\frac{\sqrt{a+b x^4}}{2 a x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0199967, antiderivative size = 21, 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 \[ -\frac{\sqrt{a+b x^4}}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*Sqrt[a + b*x^4]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.78694, size = 17, normalized size = 0.81 \[ - \frac{\sqrt{a + b x^{4}}}{2 a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(b*x**4+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0146616, size = 21, normalized size = 1. \[ -\frac{\sqrt{a+b x^4}}{2 a x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*Sqrt[a + b*x^4]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 18, normalized size = 0.9 \[ -{\frac{1}{2\,a{x}^{2}}\sqrt{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(b*x^4+a)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43725, size = 23, normalized size = 1.1 \[ -\frac{\sqrt{b x^{4} + a}}{2 \, a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.23168, size = 23, normalized size = 1.1 \[ -\frac{\sqrt{b x^{4} + a}}{2 \, a x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.03931, size = 20, normalized size = 0.95 \[ - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} + 1}}{2 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(b*x**4+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.223031, size = 19, normalized size = 0.9 \[ -\frac{\sqrt{b + \frac{a}{x^{4}}}}{2 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^3),x, algorithm="giac")
[Out]