Optimal. Leaf size=10 \[ \frac{\log (a x+b)}{a} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0159448, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{\log (a x+b)}{a} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b/x)*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.21303, size = 7, normalized size = 0.7 \[ \frac{\log{\left (a x + b \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0018095, size = 10, normalized size = 1. \[ \frac{\log (a x+b)}{a} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b/x)*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 11, normalized size = 1.1 \[{\frac{\ln \left ( ax+b \right ) }{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)/x,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43688, size = 14, normalized size = 1.4 \[ \frac{\log \left (a x + b\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221061, size = 14, normalized size = 1.4 \[ \frac{\log \left (a x + b\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.0943, size = 7, normalized size = 0.7 \[ \frac{\log{\left (a x + b \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.225743, size = 15, normalized size = 1.5 \[ \frac{{\rm ln}\left ({\left | a x + b \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + b/x)*x),x, algorithm="giac")
[Out]