3.232 \(\int \frac{-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx\)

Optimal. Leaf size=11 \[ -\frac{x}{x^5+x+1} \]

[Out]

-(x/(1 + x + x^5))

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Rubi [A]  time = 0.00803861, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{x}{x^5+x+1} \]

Antiderivative was successfully verified.

[In]  Int[(-1 + 4*x^5)/(1 + x + x^5)^2,x]

[Out]

-(x/(1 + x + x^5))

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Rubi in Sympy [A]  time = 6.7951, size = 8, normalized size = 0.73 \[ - \frac{x}{x^{5} + x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((4*x**5-1)/(x**5+x+1)**2,x)

[Out]

-x/(x**5 + x + 1)

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Mathematica [A]  time = 0.0106846, size = 11, normalized size = 1. \[ -\frac{x}{x^5+x+1} \]

Antiderivative was successfully verified.

[In]  Integrate[(-1 + 4*x^5)/(1 + x + x^5)^2,x]

[Out]

-(x/(1 + x + x^5))

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Maple [B]  time = 0.013, size = 41, normalized size = 3.7 \[{\frac{-1-3\,x}{7\,{x}^{2}+7\,x+7}}-{\frac{-3\,{x}^{2}+5\,x-1}{7\,{x}^{3}-7\,{x}^{2}+7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((4*x^5-1)/(x^5+x+1)^2,x)

[Out]

1/7*(-1-3*x)/(x^2+x+1)-1/7*(-3*x^2+5*x-1)/(x^3-x^2+1)

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Maxima [A]  time = 0.857491, size = 15, normalized size = 1.36 \[ -\frac{x}{x^{5} + x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^5 - 1)/(x^5 + x + 1)^2,x, algorithm="maxima")

[Out]

-x/(x^5 + x + 1)

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Fricas [A]  time = 0.259103, size = 15, normalized size = 1.36 \[ -\frac{x}{x^{5} + x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^5 - 1)/(x^5 + x + 1)^2,x, algorithm="fricas")

[Out]

-x/(x^5 + x + 1)

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Sympy [A]  time = 0.332222, size = 8, normalized size = 0.73 \[ - \frac{x}{x^{5} + x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x**5-1)/(x**5+x+1)**2,x)

[Out]

-x/(x**5 + x + 1)

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GIAC/XCAS [A]  time = 0.259282, size = 15, normalized size = 1.36 \[ -\frac{x}{x^{5} + x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^5 - 1)/(x^5 + x + 1)^2,x, algorithm="giac")

[Out]

-x/(x^5 + x + 1)