Optimal. Leaf size=10 \[ -\frac{1}{2} \log (3-2 x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0158625, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 35, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.057 \[ -\frac{1}{2} \log (3-2 x) \]
Antiderivative was successfully verified.
[In] Int[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.47107, size = 8, normalized size = 0.8 \[ - \frac{\log{\left (- 2 x + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00179574, size = 10, normalized size = 1. \[ -\frac{1}{2} \log (3-2 x) \]
Antiderivative was successfully verified.
[In] Integrate[(243 + 162*x + 108*x^2 + 72*x^3 + 48*x^4 + 32*x^5)/(729 - 64*x^6),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 9, normalized size = 0.9 \[ -{\frac{\ln \left ( -3+2\,x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.40774, size = 11, normalized size = 1.1 \[ -\frac{1}{2} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.20057, size = 11, normalized size = 1.1 \[ -\frac{1}{2} \, \log \left (2 \, x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.062623, size = 8, normalized size = 0.8 \[ - \frac{\log{\left (2 x - 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((32*x**5+48*x**4+72*x**3+108*x**2+162*x+243)/(-64*x**6+729),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.217028, size = 12, normalized size = 1.2 \[ -\frac{1}{2} \,{\rm ln}\left ({\left | 2 \, x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(32*x^5 + 48*x^4 + 72*x^3 + 108*x^2 + 162*x + 243)/(64*x^6 - 729),x, algorithm="giac")
[Out]