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

Optimal. Leaf size=7 \[ \frac{1}{1-x} \]

[Out]

(1 - x)^(-1)

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Rubi [A]  time = 0.0133343, antiderivative size = 7, 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 \[ \frac{1}{1-x} \]

Antiderivative was successfully verified.

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

[Out]

(1 - x)^(-1)

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Rubi in Sympy [A]  time = 4.16705, size = 3, normalized size = 0.43 \[ \frac{1}{- x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/(-x + 1)

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Mathematica [A]  time = 0.00190998, size = 7, normalized size = 1. \[ -\frac{1}{x-1} \]

Antiderivative was successfully verified.

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

[Out]

-(-1 + x)^(-1)

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Maple [A]  time = 0.002, size = 8, normalized size = 1.1 \[ - \left ( -1+x \right ) ^{-1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(-1+x)

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Maxima [A]  time = 6.69503, size = 9, normalized size = 1.29 \[ -\frac{1}{x - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(x - 1)

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Fricas [A]  time = 0.214316, size = 9, normalized size = 1.29 \[ -\frac{1}{x - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(x - 1)

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Sympy [A]  time = 0.085161, size = 5, normalized size = 0.71 \[ - \frac{1}{x - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(x - 1)

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GIAC/XCAS [A]  time = 0.209931, size = 9, normalized size = 1.29 \[ -\frac{1}{x - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(x - 1)