Optimal. Leaf size=8 \[ \log (x (b+c x)) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0265935, antiderivative size = 9, normalized size of antiderivative = 1.12, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \log (b+c x)+\log (x) \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x)/(x*(b + c*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.3167, size = 8, normalized size = 1. \[ \log{\left (x \right )} + \log{\left (b + c x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x+b)/x/(c*x+b),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00814933, size = 9, normalized size = 1.12 \[ \log (b+c x)+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x)/(x*(b + c*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 9, normalized size = 1.1 \[ \ln \left ( x \left ( cx+b \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x+b)/x/(c*x+b),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.40142, size = 12, normalized size = 1.5 \[ \log \left (c x + b\right ) + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/((c*x + b)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.208297, size = 14, normalized size = 1.75 \[ \log \left (c x^{2} + b x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/((c*x + b)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.560487, size = 8, normalized size = 1. \[ \log{\left (b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x+b)/x/(c*x+b),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.206336, size = 15, normalized size = 1.88 \[{\rm ln}\left ({\left | c x + b \right |}\right ) +{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/((c*x + b)*x),x, algorithm="giac")
[Out]