3.215 \(\int \frac{a+b x^3}{x^6} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{5 x^5}-\frac{b}{2 x^2} \]

[Out]

-a/(5*x^5) - b/(2*x^2)

_______________________________________________________________________________________

Rubi [A]  time = 0.0128473, 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 \[ -\frac{a}{5 x^5}-\frac{b}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^6,x]

[Out]

-a/(5*x^5) - b/(2*x^2)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.9771, size = 14, normalized size = 0.82 \[ - \frac{a}{5 x^{5}} - \frac{b}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x**6,x)

[Out]

-a/(5*x**5) - b/(2*x**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00342574, size = 17, normalized size = 1. \[ -\frac{a}{5 x^5}-\frac{b}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^6,x]

[Out]

-a/(5*x^5) - b/(2*x^2)

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{a}{5\,{x}^{5}}}-{\frac{b}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^6,x)

[Out]

-1/5*a/x^5-1/2*b/x^2

_______________________________________________________________________________________

Maxima [A]  time = 1.41984, size = 20, normalized size = 1.18 \[ -\frac{5 \, b x^{3} + 2 \, a}{10 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^6,x, algorithm="maxima")

[Out]

-1/10*(5*b*x^3 + 2*a)/x^5

_______________________________________________________________________________________

Fricas [A]  time = 0.213696, size = 20, normalized size = 1.18 \[ -\frac{5 \, b x^{3} + 2 \, a}{10 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^6,x, algorithm="fricas")

[Out]

-1/10*(5*b*x^3 + 2*a)/x^5

_______________________________________________________________________________________

Sympy [A]  time = 1.19228, size = 15, normalized size = 0.88 \[ - \frac{2 a + 5 b x^{3}}{10 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**6,x)

[Out]

-(2*a + 5*b*x**3)/(10*x**5)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.21805, size = 20, normalized size = 1.18 \[ -\frac{5 \, b x^{3} + 2 \, a}{10 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^6,x, algorithm="giac")

[Out]

-1/10*(5*b*x^3 + 2*a)/x^5