Optimal. Leaf size=23 \[ \frac{1}{4} \tan ^{-1}\left (x^2\right )-\frac{x^2}{4 \left (x^4+1\right )} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0267787, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{1}{4} \tan ^{-1}\left (x^2\right )-\frac{x^2}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In] Int[x^5/(1 + 2*x^4 + x^8),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.84579, size = 15, normalized size = 0.65 \[ - \frac{x^{2}}{4 \left (x^{4} + 1\right )} + \frac{\operatorname{atan}{\left (x^{2} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(x**8+2*x**4+1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0138274, size = 23, normalized size = 1. \[ \frac{1}{4} \tan ^{-1}\left (x^2\right )-\frac{x^2}{4 \left (x^4+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(1 + 2*x^4 + x^8),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 20, normalized size = 0.9 \[ -{\frac{{x}^{2}}{4\,{x}^{4}+4}}+{\frac{\arctan \left ({x}^{2} \right ) }{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(x^8+2*x^4+1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.844045, size = 26, normalized size = 1.13 \[ -\frac{x^{2}}{4 \,{\left (x^{4} + 1\right )}} + \frac{1}{4} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^8 + 2*x^4 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.245134, size = 32, normalized size = 1.39 \[ -\frac{x^{2} -{\left (x^{4} + 1\right )} \arctan \left (x^{2}\right )}{4 \,{\left (x^{4} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^8 + 2*x^4 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.322669, size = 15, normalized size = 0.65 \[ - \frac{x^{2}}{4 x^{4} + 4} + \frac{\operatorname{atan}{\left (x^{2} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(x**8+2*x**4+1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.288737, size = 26, normalized size = 1.13 \[ -\frac{x^{2}}{4 \,{\left (x^{4} + 1\right )}} + \frac{1}{4} \, \arctan \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^8 + 2*x^4 + 1),x, algorithm="giac")
[Out]