3.11.34 \(\int \frac {1}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx\) [1034]

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

[Out]

x/a^(1/2)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2, 8} \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

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 = 0.01, size = 6, normalized size = 0.86

method	result	size
default	\(\frac {x}{\sqrt {a}}\)	\(6\)
norman	\(\frac {x}{\sqrt {a}}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/a^(1/2),x,method=_RETURNVERBOSE)

[Out]

x/a^(1/2)

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Maxima [A]
time = 0.28, size = 5, normalized size = 0.71 \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

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 = 0.33, size = 5, normalized size = 0.71 \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

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 = 0.02, size = 5, normalized size = 0.71 \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

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 = 4.46, size = 5, normalized size = 0.71 \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/sqrt(a)

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Mupad [B]
time = 0.00, size = 5, normalized size = 0.71 \begin {gather*} \frac {x}{\sqrt {a}} \end {gather*}

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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