3.697 \(\int \frac{x^3}{\left (2+3 x^4\right )^2} \, dx\)

Optimal. Leaf size=13 \[ -\frac{1}{12 \left (3 x^4+2\right )} \]

[Out]

-1/(12*(2 + 3*x^4))

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Rubi [A]  time = 0.00775095, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{12 \left (3 x^4+2\right )} \]

Antiderivative was successfully verified.

[In]  Int[x^3/(2 + 3*x^4)^2,x]

[Out]

-1/(12*(2 + 3*x^4))

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Rubi in Sympy [A]  time = 1.92482, size = 8, normalized size = 0.62 \[ - \frac{1}{12 \left (3 x^{4} + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3/(3*x**4+2)**2,x)

[Out]

-1/(12*(3*x**4 + 2))

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Mathematica [A]  time = 0.00601536, size = 13, normalized size = 1. \[ -\frac{1}{12 \left (3 x^4+2\right )} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/(2 + 3*x^4)^2,x]

[Out]

-1/(12*(2 + 3*x^4))

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Maple [A]  time = 0.001, size = 12, normalized size = 0.9 \[ -{\frac{1}{36\,{x}^{4}+24}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(3*x^4+2)^2,x)

[Out]

-1/12/(3*x^4+2)

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Maxima [A]  time = 1.43838, size = 15, normalized size = 1.15 \[ -\frac{1}{12 \,{\left (3 \, x^{4} + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(3*x^4 + 2)^2,x, algorithm="maxima")

[Out]

-1/12/(3*x^4 + 2)

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Fricas [A]  time = 0.217176, size = 15, normalized size = 1.15 \[ -\frac{1}{12 \,{\left (3 \, x^{4} + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(3*x^4 + 2)^2,x, algorithm="fricas")

[Out]

-1/12/(3*x^4 + 2)

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Sympy [A]  time = 0.24916, size = 8, normalized size = 0.62 \[ - \frac{1}{36 x^{4} + 24} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3/(3*x**4+2)**2,x)

[Out]

-1/(36*x**4 + 24)

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GIAC/XCAS [A]  time = 0.224295, size = 15, normalized size = 1.15 \[ -\frac{1}{12 \,{\left (3 \, x^{4} + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^3/(3*x^4 + 2)^2,x, algorithm="giac")

[Out]

-1/12/(3*x^4 + 2)