Optimal. Leaf size=16 \[ -\frac{1}{3 x \sqrt{c x^4}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00762296, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ -\frac{1}{3 x \sqrt{c x^4}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*Sqrt[2 + 2*a - 2*(1 + a) + c*x^4]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.13506, size = 15, normalized size = 0.94 \[ - \frac{\sqrt{c x^{4}}}{3 c x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(c*x**4)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00365389, size = 16, normalized size = 1. \[ -\frac{1}{3 x \sqrt{c x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*Sqrt[2 + 2*a - 2*(1 + a) + c*x^4]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 13, normalized size = 0.8 \[ -{\frac{1}{3\,x}{\frac{1}{\sqrt{c{x}^{4}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(c*x^4)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.708985, size = 16, normalized size = 1. \[ -\frac{1}{3 \, \sqrt{c x^{4}} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(c*x^4)*x^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.263154, size = 20, normalized size = 1.25 \[ -\frac{\sqrt{c x^{4}}}{3 \, c x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(c*x^4)*x^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.67977, size = 17, normalized size = 1.06 \[ - \frac{1}{3 \sqrt{c} x \sqrt{x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(c*x**4)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.261782, size = 11, normalized size = 0.69 \[ -\frac{1}{3 \, \sqrt{c} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(c*x^4)*x^2),x, algorithm="giac")
[Out]