Optimal. Leaf size=13 \[ \frac{4}{\sqrt [8]{1-x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00582945, antiderivative size = 13, 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 \[ \frac{4}{\sqrt [8]{1-x^2}} \]
Antiderivative was successfully verified.
[In] Int[x/(1 - x^2)^(9/8),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.911313, size = 8, normalized size = 0.62 \[ \frac{4}{\sqrt [8]{- x^{2} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-x**2+1)**(9/8),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00365069, size = 13, normalized size = 1. \[ \frac{4}{\sqrt [8]{1-x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 - x^2)^(9/8),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 18, normalized size = 1.4 \[ -4\,{ \left ( -1+x \right ) \left ( 1+x \right ) \left ( -{x}^{2}+1 \right ) ^{-{\frac{9}{8}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-x^2+1)^(9/8),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.3864, size = 15, normalized size = 1.15 \[ \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x^2 + 1)^(9/8),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211273, size = 15, normalized size = 1.15 \[ \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x^2 + 1)^(9/8),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.78034, size = 8, normalized size = 0.62 \[ \frac{4}{\sqrt [8]{- x^{2} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x**2+1)**(9/8),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.201328, size = 15, normalized size = 1.15 \[ \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x^2 + 1)^(9/8),x, algorithm="giac")
[Out]