3.1553 \(\int \frac{a+\frac{b}{x}}{x^3} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{2 x^2}-\frac{b}{3 x^3} \]

[Out]

-b/(3*x^3) - a/(2*x^2)

_______________________________________________________________________________________

Rubi [A]  time = 0.0159288, antiderivative size = 17, 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 \[ -\frac{a}{2 x^2}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)/x^3,x]

[Out]

-b/(3*x^3) - a/(2*x^2)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.9507, size = 14, normalized size = 0.82 \[ - \frac{a}{2 x^{2}} - \frac{b}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)/x**3,x)

[Out]

-a/(2*x**2) - b/(3*x**3)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00337294, size = 17, normalized size = 1. \[ -\frac{a}{2 x^2}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)/x^3,x]

[Out]

-b/(3*x^3) - a/(2*x^2)

_______________________________________________________________________________________

Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{b}{3\,{x}^{3}}}-{\frac{a}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)/x^3,x)

[Out]

-1/3*b/x^3-1/2*a/x^2

_______________________________________________________________________________________

Maxima [A]  time = 1.4564, size = 18, normalized size = 1.06 \[ -\frac{3 \, a x + 2 \, b}{6 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x^3,x, algorithm="maxima")

[Out]

-1/6*(3*a*x + 2*b)/x^3

_______________________________________________________________________________________

Fricas [A]  time = 0.218678, size = 18, normalized size = 1.06 \[ -\frac{3 \, a x + 2 \, b}{6 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x^3,x, algorithm="fricas")

[Out]

-1/6*(3*a*x + 2*b)/x^3

_______________________________________________________________________________________

Sympy [A]  time = 1.06811, size = 14, normalized size = 0.82 \[ - \frac{3 a x + 2 b}{6 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)/x**3,x)

[Out]

-(3*a*x + 2*b)/(6*x**3)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.229957, size = 18, normalized size = 1.06 \[ -\frac{3 \, a x + 2 \, b}{6 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x)/x^3,x, algorithm="giac")

[Out]

-1/6*(3*a*x + 2*b)/x^3