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]

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Rubi [A]  time = 0.000861, 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, Rules used = {2, 8} \[ \frac{x}{\sqrt{a}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

x/Sqrt[a]

Rule 2

Int[(u_.)*((a_.) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[u*a^p, x] /; FreeQ[{a, b, n, p}, x] && EqQ[b, 0]

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin{align*} \int \frac{1}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac{1}{\sqrt{a}} \, dx\\ &=\frac{x}{\sqrt{a}}\\ \end{align*}

Mathematica [A]  time = 0.0003813, 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]

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Maple [A]  time = 0.039, size = 6, normalized size = 0.9 \begin{align*}{x{\frac{1}{\sqrt{a}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/a^(1/2),x)

[Out]

x/a^(1/2)

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Maxima [A]  time = 0.949851, size = 7, normalized size = 1. \begin{align*} \frac{x}{\sqrt{a}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/a^(1/2),x, algorithm="maxima")

[Out]

x/sqrt(a)

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Fricas [A]  time = 1.18099, size = 15, normalized size = 2.14 \begin{align*} \frac{x}{\sqrt{a}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/a^(1/2),x, algorithm="fricas")

[Out]

x/sqrt(a)

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Sympy [A]  time = 0.049509, size = 5, normalized size = 0.71 \begin{align*} \frac{x}{\sqrt{a}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/a**(1/2),x)

[Out]

x/sqrt(a)

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Giac [A]  time = 1.15081, size = 7, normalized size = 1. \begin{align*} \frac{x}{\sqrt{a}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/a^(1/2),x, algorithm="giac")

[Out]

x/sqrt(a)