3.1034 \(\int \frac{1}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx\)

Optimal. Leaf size=7 \[ \frac{x}{\sqrt{a}} \]

[Out]

x/Sqrt[a]

_______________________________________________________________________________________

Rubi [A]  time = 0.00440841, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{x}{\sqrt{a}} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]

[Out]

x/Sqrt[a]

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{a}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/a**(1/2),x)

[Out]

Integral(1/sqrt(a), x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.000984268, size = 7, normalized size = 1. \[ \frac{x}{\sqrt{a}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4],x]

[Out]

x/Sqrt[a]

_______________________________________________________________________________________

Maple [A]  time = 0., size = 6, normalized size = 0.9 \[{x{\frac{1}{\sqrt{a}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/a^(1/2),x)

[Out]

x/a^(1/2)

_______________________________________________________________________________________

Maxima [A]  time = 0.737945, size = 7, normalized size = 1. \[ \frac{x}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(a),x, algorithm="maxima")

[Out]

x/sqrt(a)

_______________________________________________________________________________________

Fricas [A]  time = 0.262916, size = 7, normalized size = 1. \[ \frac{x}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(a),x, algorithm="fricas")

[Out]

x/sqrt(a)

_______________________________________________________________________________________

Sympy [A]  time = 0.040289, size = 5, normalized size = 0.71 \[ \frac{x}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/a**(1/2),x)

[Out]

x/sqrt(a)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.260934, size = 7, normalized size = 1. \[ \frac{x}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(a),x, algorithm="giac")

[Out]

x/sqrt(a)