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

Optimal. Leaf size=9 \[ x-\frac{x^2}{2} \]

[Out]

x - x^2/2

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Rubi [A]  time = 0.0123478, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ x-\frac{x^2}{2} \]

Antiderivative was successfully verified.

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

[Out]

x - x^2/2

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ x - \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - Integral(x, x)

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Mathematica [A]  time = 0.0010825, size = 9, normalized size = 1. \[ x-\frac{x^2}{2} \]

Antiderivative was successfully verified.

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

[Out]

x - x^2/2

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Maple [A]  time = 0.003, size = 8, normalized size = 0.9 \[ x-{\frac{{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-x^4+1)/(x^3+x^2+x+1),x)

[Out]

x-1/2*x^2

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Maxima [A]  time = 1.38845, size = 9, normalized size = 1. \[ -\frac{1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2*x^2 + x

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Fricas [A]  time = 0.209718, size = 9, normalized size = 1. \[ -\frac{1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2*x^2 + x

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Sympy [A]  time = 0.043413, size = 5, normalized size = 0.56 \[ - \frac{x^{2}}{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-x**2/2 + x

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GIAC/XCAS [A]  time = 0.21047, size = 9, normalized size = 1. \[ -\frac{1}{2} \, x^{2} + x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2*x^2 + x