3.1023 \(\int \frac{x^2}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx\)

Optimal. Leaf size=13 \[ \frac{x^3}{\sqrt{c x^4}} \]

[Out]

x^3/Sqrt[c*x^4]

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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]

x^3/Sqrt[c*x^4]

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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]

sqrt(c*x**4)/(c*x)

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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]

x^3/Sqrt[c*x^4]

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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]

x^3/(c*x^4)^(1/2)

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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]

x^3/sqrt(c*x^4)

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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]

sqrt(c*x^4)/(c*x)

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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]

x**3/(sqrt(c)*sqrt(x**4))

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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]

x/sqrt(c)