3.1551 \(\int \frac{a+\frac{b}{x}}{x} \, dx\)

Optimal. Leaf size=11 \[ a \log (x)-\frac{b}{x} \]

[Out]

-(b/x) + a*Log[x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0144776, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ a \log (x)-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)/x,x]

[Out]

-(b/x) + a*Log[x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 3.01052, size = 7, normalized size = 0.64 \[ a \log{\left (x \right )} - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)/x,x)

[Out]

a*log(x) - b/x

_______________________________________________________________________________________

Mathematica [A]  time = 0.00338766, size = 11, normalized size = 1. \[ a \log (x)-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)/x,x]

[Out]

-(b/x) + a*Log[x]

_______________________________________________________________________________________

Maple [A]  time = 0.007, size = 12, normalized size = 1.1 \[ -{\frac{b}{x}}+a\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)/x,x)

[Out]

-b/x+a*ln(x)

_______________________________________________________________________________________

Maxima [A]  time = 1.46568, size = 15, normalized size = 1.36 \[ a \log \left (x\right ) - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x,x, algorithm="maxima")

[Out]

a*log(x) - b/x

_______________________________________________________________________________________

Fricas [A]  time = 0.221038, size = 18, normalized size = 1.64 \[ \frac{a x \log \left (x\right ) - b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x,x, algorithm="fricas")

[Out]

(a*x*log(x) - b)/x

_______________________________________________________________________________________

Sympy [A]  time = 1.0379, size = 7, normalized size = 0.64 \[ a \log{\left (x \right )} - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)/x,x)

[Out]

a*log(x) - b/x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.227991, size = 16, normalized size = 1.45 \[ a{\rm ln}\left ({\left | x \right |}\right ) - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x,x, algorithm="giac")

[Out]

a*ln(abs(x)) - b/x