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

Optimal. Leaf size=11 \[ -\frac{1}{4} (1-x)^4 \]

[Out]

-(1 - x)^4/4

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Rubi [A]  time = 0.012919, 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 \[ -\frac{1}{4} (1-x)^4 \]

Antiderivative was successfully verified.

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

[Out]

-(1 - x)^4/4

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Rubi in Sympy [A]  time = 4.0795, size = 7, normalized size = 0.64 \[ - \frac{\left (- x + 1\right )^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(-x + 1)**4/4

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Mathematica [A]  time = 0.00281969, size = 9, normalized size = 0.82 \[ -\frac{1}{4} (x-1)^4 \]

Antiderivative was successfully verified.

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

[Out]

-(-1 + x)^4/4

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Maple [A]  time = 0.001, size = 8, normalized size = 0.7 \[ -{\frac{ \left ( -1+x \right ) ^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4*(-1+x)^4

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Maxima [A]  time = 1.42326, size = 20, normalized size = 1.82 \[ -\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4*x^4 + x^3 - 3/2*x^2 + x

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Fricas [A]  time = 0.207356, size = 20, normalized size = 1.82 \[ -\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4*x^4 + x^3 - 3/2*x^2 + x

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Sympy [A]  time = 0.073051, size = 15, normalized size = 1.36 \[ - \frac{x^{4}}{4} + x^{3} - \frac{3 x^{2}}{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-x**4/4 + x**3 - 3*x**2/2 + x

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GIAC/XCAS [A]  time = 0.210623, size = 20, normalized size = 1.82 \[ -\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/4*x^4 + x^3 - 3/2*x^2 + x