3.1985 \(\int \frac{1}{\left (a+\frac{b}{x^3}\right )^2 x^4} \, dx\)

Optimal. Leaf size=16 \[ \frac{1}{3 b \left (a+\frac{b}{x^3}\right )} \]

[Out]

1/(3*b*(a + b/x^3))

_______________________________________________________________________________________

Rubi [A]  time = 0.018871, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{1}{3 b \left (a+\frac{b}{x^3}\right )} \]

Antiderivative was successfully verified.

[In]  Int[1/((a + b/x^3)^2*x^4),x]

[Out]

1/(3*b*(a + b/x^3))

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.1281, size = 10, normalized size = 0.62 \[ \frac{1}{3 b \left (a + \frac{b}{x^{3}}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(a+b/x**3)**2/x**4,x)

[Out]

1/(3*b*(a + b/x**3))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0087141, size = 16, normalized size = 1. \[ -\frac{1}{3 a \left (a x^3+b\right )} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((a + b/x^3)^2*x^4),x]

[Out]

-1/(3*a*(b + a*x^3))

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{ \left ( 3\,a{x}^{3}+3\,b \right ) a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(a+b/x^3)^2/x^4,x)

[Out]

-1/3/(a*x^3+b)/a

_______________________________________________________________________________________

Maxima [A]  time = 1.43496, size = 19, normalized size = 1.19 \[ \frac{1}{3 \,{\left (a + \frac{b}{x^{3}}\right )} b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((a + b/x^3)^2*x^4),x, algorithm="maxima")

[Out]

1/3/((a + b/x^3)*b)

_______________________________________________________________________________________

Fricas [A]  time = 0.221356, size = 20, normalized size = 1.25 \[ -\frac{1}{3 \,{\left (a^{2} x^{3} + a b\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((a + b/x^3)^2*x^4),x, algorithm="fricas")

[Out]

-1/3/(a^2*x^3 + a*b)

_______________________________________________________________________________________

Sympy [A]  time = 1.38853, size = 15, normalized size = 0.94 \[ - \frac{1}{3 a^{2} x^{3} + 3 a b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(a+b/x**3)**2/x**4,x)

[Out]

-1/(3*a**2*x**3 + 3*a*b)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.233998, size = 19, normalized size = 1.19 \[ -\frac{1}{3 \,{\left (a x^{3} + b\right )} a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/((a + b/x^3)^2*x^4),x, algorithm="giac")

[Out]

-1/3/((a*x^3 + b)*a)