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

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

[Out]

1/(3*(1 - x)^3)

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Rubi [A]  time = 0.0154507, 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 + x^2 + x^3)^4/(1 - x^4)^4,x]

[Out]

1/(3*(1 - x)^3)

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Rubi in Sympy [A]  time = 4.29994, size = 7, normalized size = 0.64 \[ \frac{1}{3 \left (- x + 1\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/(3*(-x + 1)**3)

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Mathematica [A]  time = 0.00227476, size = 9, normalized size = 0.82 \[ -\frac{1}{3 (x-1)^3} \]

Antiderivative was successfully verified.

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

[Out]

-1/(3*(-1 + x)^3)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Maxima [A]  time = 1.39801, size = 23, normalized size = 2.09 \[ -\frac{1}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3/(x^3 - 3*x^2 + 3*x - 1)

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Fricas [A]  time = 0.21031, size = 23, normalized size = 2.09 \[ -\frac{1}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3/(x^3 - 3*x^2 + 3*x - 1)

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Sympy [A]  time = 0.1231, size = 17, normalized size = 1.55 \[ - \frac{1}{3 x^{3} - 9 x^{2} + 9 x - 3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(3*x**3 - 9*x**2 + 9*x - 3)

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GIAC/XCAS [A]  time = 0.209831, size = 9, normalized size = 0.82 \[ -\frac{1}{3 \,{\left (x - 1\right )}^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3/(x - 1)^3