Optimal. Leaf size=28 \[ \frac{x^3}{3}+\frac{1}{6} \log \left (x^3+1\right )-\frac{3}{2} \log \left (x^3+3\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0469661, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{x^3}{3}+\frac{1}{6} \log \left (x^3+1\right )-\frac{3}{2} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
[In] Int[x^8/(3 + 4*x^3 + x^6),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.1333, size = 22, normalized size = 0.79 \[ \frac{x^{3}}{3} + \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{3 \log{\left (x^{3} + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(x**6+4*x**3+3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00915247, size = 28, normalized size = 1. \[ \frac{x^3}{3}+\frac{1}{6} \log \left (x^3+1\right )-\frac{3}{2} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^8/(3 + 4*x^3 + x^6),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 23, normalized size = 0.8 \[{\frac{{x}^{3}}{3}}+{\frac{\ln \left ({x}^{3}+1 \right ) }{6}}-{\frac{3\,\ln \left ({x}^{3}+3 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(x^6+4*x^3+3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.779735, size = 30, normalized size = 1.07 \[ \frac{1}{3} \, x^{3} - \frac{3}{2} \, \log \left (x^{3} + 3\right ) + \frac{1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(x^6 + 4*x^3 + 3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.263143, size = 30, normalized size = 1.07 \[ \frac{1}{3} \, x^{3} - \frac{3}{2} \, \log \left (x^{3} + 3\right ) + \frac{1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(x^6 + 4*x^3 + 3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.266127, size = 22, normalized size = 0.79 \[ \frac{x^{3}}{3} + \frac{\log{\left (x^{3} + 1 \right )}}{6} - \frac{3 \log{\left (x^{3} + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(x**6+4*x**3+3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.277353, size = 32, normalized size = 1.14 \[ \frac{1}{3} \, x^{3} - \frac{3}{2} \,{\rm ln}\left ({\left | x^{3} + 3 \right |}\right ) + \frac{1}{6} \,{\rm ln}\left ({\left | x^{3} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(x^6 + 4*x^3 + 3),x, algorithm="giac")
[Out]