Optimal. Leaf size=19 \[ \frac{19}{60} \log \left (2 x^6+5\right )-\frac{2 \log (x)}{5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0529364, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{19}{60} \log \left (2 x^6+5\right )-\frac{2 \log (x)}{5} \]
Antiderivative was successfully verified.
[In] Int[(-2 + 3*x^6)/(x*(5 + 2*x^6)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.06544, size = 17, normalized size = 0.89 \[ - \frac{\log{\left (x^{6} \right )}}{15} + \frac{19 \log{\left (2 x^{6} + 5 \right )}}{60} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*x**6-2)/x/(2*x**6+5),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0083234, size = 19, normalized size = 1. \[ \frac{19}{60} \log \left (2 x^6+5\right )-\frac{2 \log (x)}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(-2 + 3*x^6)/(x*(5 + 2*x^6)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 16, normalized size = 0.8 \[ -{\frac{2\,\ln \left ( x \right ) }{5}}+{\frac{19\,\ln \left ( 2\,{x}^{6}+5 \right ) }{60}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*x^6-2)/x/(2*x^6+5),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.78885, size = 23, normalized size = 1.21 \[ \frac{19}{60} \, \log \left (2 \, x^{6} + 5\right ) - \frac{1}{15} \, \log \left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^6 - 2)/((2*x^6 + 5)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.254399, size = 20, normalized size = 1.05 \[ \frac{19}{60} \, \log \left (2 \, x^{6} + 5\right ) - \frac{2}{5} \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^6 - 2)/((2*x^6 + 5)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.257758, size = 17, normalized size = 0.89 \[ - \frac{2 \log{\left (x \right )}}{5} + \frac{19 \log{\left (2 x^{6} + 5 \right )}}{60} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x**6-2)/x/(2*x**6+5),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.266006, size = 23, normalized size = 1.21 \[ \frac{19}{60} \,{\rm ln}\left (2 \, x^{6} + 5\right ) - \frac{1}{15} \,{\rm ln}\left (x^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^6 - 2)/((2*x^6 + 5)*x),x, algorithm="giac")
[Out]