3.1033 \(\int \frac{x}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx\)

Optimal. Leaf size=12 \[ \frac{x^2}{2 \sqrt{a}} \]

[Out]

x^2/(2*Sqrt[a])

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Rubi [A]  time = 0.00579073, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.136 \[ \frac{x^2}{2 \sqrt{a}} \]

Antiderivative was successfully verified.

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

[Out]

x^2/(2*Sqrt[a])

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/a**(1/2),x)

[Out]

Integral(x, x)/sqrt(a)

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Mathematica [A]  time = 0.000953549, size = 12, normalized size = 1. \[ \frac{x^2}{2 \sqrt{a}} \]

Antiderivative was successfully verified.

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

[Out]

x^2/(2*Sqrt[a])

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Maple [A]  time = 0., size = 9, normalized size = 0.8 \[{\frac{{x}^{2}}{2}{\frac{1}{\sqrt{a}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/a^(1/2),x)

[Out]

1/2*x^2/a^(1/2)

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Maxima [A]  time = 0.737804, size = 11, normalized size = 0.92 \[ \frac{x^{2}}{2 \, \sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2/sqrt(a)

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Fricas [A]  time = 0.266192, size = 11, normalized size = 0.92 \[ \frac{x^{2}}{2 \, \sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2/sqrt(a)

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Sympy [A]  time = 0.051983, size = 8, normalized size = 0.67 \[ \frac{x^{2}}{2 \sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/a**(1/2),x)

[Out]

x**2/(2*sqrt(a))

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GIAC/XCAS [A]  time = 0.260769, size = 11, normalized size = 0.92 \[ \frac{x^{2}}{2 \, \sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2/sqrt(a)