Optimal. Leaf size=18 \[ \frac{x^2}{2 \sqrt{1-x^4}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0127446, antiderivative size = 18, 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 \[ \frac{x^2}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Int[x/(1 - x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.26679, size = 12, normalized size = 0.67 \[ \frac{x^{2}}{2 \sqrt{- x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0112336, size = 18, normalized size = 1. \[ \frac{x^2}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 - x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 26, normalized size = 1.4 \[ -{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ){x}^{2}}{2} \left ( -{x}^{4}+1 \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-x^4+1)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43034, size = 19, normalized size = 1.06 \[ \frac{x^{2}}{2 \, \sqrt{-x^{4} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.26828, size = 50, normalized size = 2.78 \[ -\frac{\sqrt{-x^{4} + 1} x^{2} - x^{2}}{2 \,{\left (x^{4} + \sqrt{-x^{4} + 1} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.66813, size = 32, normalized size = 1.78 \[ \begin{cases} - \frac{i x^{2}}{2 \sqrt{x^{4} - 1}} & \text{for}\: \left |{x^{4}}\right | > 1 \\\frac{x^{2}}{2 \sqrt{- x^{4} + 1}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.218817, size = 28, normalized size = 1.56 \[ -\frac{\sqrt{-x^{4} + 1} x^{2}}{2 \,{\left (x^{4} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x^4 + 1)^(3/2),x, algorithm="giac")
[Out]