Optimal. Leaf size=13 \[ \frac{x^3}{\sqrt{c x^4}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00588769, antiderivative size = 13, 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 \[ \frac{x^3}{\sqrt{c x^4}} \]
Antiderivative was successfully verified.
[In] Int[x^2/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.12478, size = 10, normalized size = 0.77 \[ \frac{\sqrt{c x^{4}}}{c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(c*x**4)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00237811, size = 13, normalized size = 1. \[ \frac{x^3}{\sqrt{c x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/Sqrt[2 + 2*a - 2*(1 + a) + c*x^4],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 12, normalized size = 0.9 \[{{x}^{3}{\frac{1}{\sqrt{c{x}^{4}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(c*x^4)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.708495, size = 15, normalized size = 1.15 \[ \frac{x^{3}}{\sqrt{c x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(c*x^4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.2659, size = 19, normalized size = 1.46 \[ \frac{\sqrt{c x^{4}}}{c x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(c*x^4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.52269, size = 14, normalized size = 1.08 \[ \frac{x^{3}}{\sqrt{c} \sqrt{x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(c*x**4)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.264578, size = 7, normalized size = 0.54 \[ \frac{x}{\sqrt{c}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(c*x^4),x, algorithm="giac")
[Out]