Optimal. Leaf size=11 \[ \frac{1}{3 (1-x)^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0154507, antiderivative size = 11, 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 \[ \frac{1}{3 (1-x)^3} \]
Antiderivative was successfully verified.
[In] Int[(1 + x + x^2 + x^3)^4/(1 - x^4)^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.29994, size = 7, normalized size = 0.64 \[ \frac{1}{3 \left (- x + 1\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3+x**2+x+1)**4/(-x**4+1)**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00227476, size = 9, normalized size = 0.82 \[ -\frac{1}{3 (x-1)^3} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x + x^2 + x^3)^4/(1 - x^4)^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 8, normalized size = 0.7 \[ -{\frac{1}{3\, \left ( -1+x \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3+x^2+x+1)^4/(-x^4+1)^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.39801, size = 23, normalized size = 2.09 \[ -\frac{1}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + x^2 + x + 1)^4/(x^4 - 1)^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21031, size = 23, normalized size = 2.09 \[ -\frac{1}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + x^2 + x + 1)^4/(x^4 - 1)^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.1231, size = 17, normalized size = 1.55 \[ - \frac{1}{3 x^{3} - 9 x^{2} + 9 x - 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3+x**2+x+1)**4/(-x**4+1)**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209831, size = 9, normalized size = 0.82 \[ -\frac{1}{3 \,{\left (x - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 + x^2 + x + 1)^4/(x^4 - 1)^4,x, algorithm="giac")
[Out]