3.1470 \(\int \frac{x^7}{1-x^8} \, dx\)

Optimal. Leaf size=12 \[ -\frac{1}{8} \log \left (1-x^8\right ) \]

[Out]

-Log[1 - x^8]/8

_______________________________________________________________________________________

Rubi [A]  time = 0.00751128, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{8} \log \left (1-x^8\right ) \]

Antiderivative was successfully verified.

[In]  Int[x^7/(1 - x^8),x]

[Out]

-Log[1 - x^8]/8

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.22334, size = 20, normalized size = 1.67 \[ - \frac{\log{\left (\left (x - 1\right ) \left (x + 1\right ) \left (x^{2} + 1\right ) \left (x^{4} + 1\right ) \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**7/(-x**8+1),x)

[Out]

-log((x - 1)*(x + 1)*(x**2 + 1)*(x**4 + 1))/8

_______________________________________________________________________________________

Mathematica [A]  time = 0.00494406, size = 12, normalized size = 1. \[ -\frac{1}{8} \log \left (1-x^8\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[x^7/(1 - x^8),x]

[Out]

-Log[1 - x^8]/8

_______________________________________________________________________________________

Maple [B]  time = 0.008, size = 30, normalized size = 2.5 \[ -{\frac{\ln \left ( -1+x \right ) }{8}}-{\frac{\ln \left ( 1+x \right ) }{8}}-{\frac{\ln \left ({x}^{2}+1 \right ) }{8}}-{\frac{\ln \left ({x}^{4}+1 \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^7/(-x^8+1),x)

[Out]

-1/8*ln(-1+x)-1/8*ln(1+x)-1/8*ln(x^2+1)-1/8*ln(x^4+1)

_______________________________________________________________________________________

Maxima [A]  time = 1.41372, size = 11, normalized size = 0.92 \[ -\frac{1}{8} \, \log \left (x^{8} - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^7/(x^8 - 1),x, algorithm="maxima")

[Out]

-1/8*log(x^8 - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.209998, size = 11, normalized size = 0.92 \[ -\frac{1}{8} \, \log \left (x^{8} - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^7/(x^8 - 1),x, algorithm="fricas")

[Out]

-1/8*log(x^8 - 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.238359, size = 8, normalized size = 0.67 \[ - \frac{\log{\left (x^{8} - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**7/(-x**8+1),x)

[Out]

-log(x**8 - 1)/8

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.219962, size = 12, normalized size = 1. \[ -\frac{1}{8} \,{\rm ln}\left ({\left | x^{8} - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^7/(x^8 - 1),x, algorithm="giac")

[Out]

-1/8*ln(abs(x^8 - 1))