Optimal. Leaf size=21 \[ \frac{1}{2} \log \left (x^3+3\right )-\frac{1}{6} \log \left (x^3+1\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0360109, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{1}{2} \log \left (x^3+3\right )-\frac{1}{6} \log \left (x^3+1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^5/(3 + 4*x^3 + x^6),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.919, size = 15, normalized size = 0.71 \[ - \frac{\log{\left (x^{3} + 1 \right )}}{6} + \frac{\log{\left (x^{3} + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(x**6+4*x**3+3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00720602, size = 21, normalized size = 1. \[ \frac{1}{2} \log \left (x^3+3\right )-\frac{1}{6} \log \left (x^3+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(3 + 4*x^3 + x^6),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 18, normalized size = 0.9 \[ -{\frac{\ln \left ({x}^{3}+1 \right ) }{6}}+{\frac{\ln \left ({x}^{3}+3 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(x^6+4*x^3+3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.795143, size = 23, normalized size = 1.1 \[ \frac{1}{2} \, \log \left (x^{3} + 3\right ) - \frac{1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^6 + 4*x^3 + 3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.25847, size = 23, normalized size = 1.1 \[ \frac{1}{2} \, \log \left (x^{3} + 3\right ) - \frac{1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^6 + 4*x^3 + 3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.23647, size = 15, normalized size = 0.71 \[ - \frac{\log{\left (x^{3} + 1 \right )}}{6} + \frac{\log{\left (x^{3} + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(x**6+4*x**3+3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.300991, size = 26, normalized size = 1.24 \[ \frac{1}{2} \,{\rm ln}\left ({\left | x^{3} + 3 \right |}\right ) - \frac{1}{6} \,{\rm ln}\left ({\left | x^{3} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(x^6 + 4*x^3 + 3),x, algorithm="giac")
[Out]