3.180 \(\int \frac{\left (1-x^4\right )^2}{\left (1+x+x^2+x^3\right )^2} \, dx\)

Optimal. Leaf size=11 \[ -\frac{1}{3} (1-x)^3 \]

[Out]

-(1 - x)^3/3

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Rubi [A]  time = 0.0144015, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ -\frac{1}{3} (1-x)^3 \]

Antiderivative was successfully verified.

[In]  Int[(1 - x^4)^2/(1 + x + x^2 + x^3)^2,x]

[Out]

-(1 - x)^3/3

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Rubi in Sympy [A]  time = 4.0638, size = 7, normalized size = 0.64 \[ - \frac{\left (- x + 1\right )^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-x**4+1)**2/(x**3+x**2+x+1)**2,x)

[Out]

-(-x + 1)**3/3

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Mathematica [A]  time = 0.00123161, size = 14, normalized size = 1.27 \[ \frac{x^3}{3}-x^2+x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - x^4)^2/(1 + x + x^2 + x^3)^2,x]

[Out]

x - x^2 + x^3/3

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Maple [A]  time = 0.002, size = 8, normalized size = 0.7 \[{\frac{ \left ( -1+x \right ) ^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-x^4+1)^2/(x^3+x^2+x+1)^2,x)

[Out]

1/3*(-1+x)^3

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Maxima [A]  time = 1.37128, size = 16, normalized size = 1.45 \[ \frac{1}{3} \, x^{3} - x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 - 1)^2/(x^3 + x^2 + x + 1)^2,x, algorithm="maxima")

[Out]

1/3*x^3 - x^2 + x

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Fricas [A]  time = 0.214174, size = 16, normalized size = 1.45 \[ \frac{1}{3} \, x^{3} - x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 - 1)^2/(x^3 + x^2 + x + 1)^2,x, algorithm="fricas")

[Out]

1/3*x^3 - x^2 + x

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Sympy [A]  time = 0.065068, size = 8, normalized size = 0.73 \[ \frac{x^{3}}{3} - x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-x**4+1)**2/(x**3+x**2+x+1)**2,x)

[Out]

x**3/3 - x**2 + x

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GIAC/XCAS [A]  time = 0.209303, size = 16, normalized size = 1.45 \[ \frac{1}{3} \, x^{3} - x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^4 - 1)^2/(x^3 + x^2 + x + 1)^2,x, algorithm="giac")

[Out]

1/3*x^3 - x^2 + x