3.542 \(\int \frac{1+x+x^2+x^3+x^4}{1-x^5} \, dx\)

Optimal. Leaf size=8 \[ -\log (1-x) \]

[Out]

-Log[1 - x]

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Rubi [A]  time = 0.012767, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\log (1-x) \]

Antiderivative was successfully verified.

[In]  Int[(1 + x + x^2 + x^3 + x^4)/(1 - x^5),x]

[Out]

-Log[1 - x]

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Rubi in Sympy [A]  time = 4.34625, size = 5, normalized size = 0.62 \[ - \log{\left (- x + 1 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**4+x**3+x**2+x+1)/(-x**5+1),x)

[Out]

-log(-x + 1)

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Mathematica [A]  time = 0.00143416, size = 8, normalized size = 1. \[ -\log (1-x) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + x + x^2 + x^3 + x^4)/(1 - x^5),x]

[Out]

-Log[1 - x]

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Maple [A]  time = 0.002, size = 7, normalized size = 0.9 \[ -\ln \left ( -1+x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^4+x^3+x^2+x+1)/(-x^5+1),x)

[Out]

-ln(-1+x)

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Maxima [A]  time = 1.42934, size = 8, normalized size = 1. \[ -\log \left (x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x^4 + x^3 + x^2 + x + 1)/(x^5 - 1),x, algorithm="maxima")

[Out]

-log(x - 1)

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Fricas [A]  time = 0.201494, size = 8, normalized size = 1. \[ -\log \left (x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x^4 + x^3 + x^2 + x + 1)/(x^5 - 1),x, algorithm="fricas")

[Out]

-log(x - 1)

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Sympy [A]  time = 0.045877, size = 5, normalized size = 0.62 \[ - \log{\left (x - 1 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**4+x**3+x**2+x+1)/(-x**5+1),x)

[Out]

-log(x - 1)

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GIAC/XCAS [A]  time = 0.218168, size = 9, normalized size = 1.12 \[ -{\rm ln}\left ({\left | x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(x^4 + x^3 + x^2 + x + 1)/(x^5 - 1),x, algorithm="giac")

[Out]

-ln(abs(x - 1))