3.130 \(\int \frac{1}{\left (\frac{b}{x^3}\right )^{2/3}} \, dx\)

Optimal. Leaf size=14 \[ \frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}} \]

[Out]

x/(3*(b/x^3)^(2/3))

_______________________________________________________________________________________

Rubi [A]  time = 0.00676988, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^3)^(-2/3),x]

[Out]

x/(3*(b/x^3)^(2/3))

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.54476, size = 14, normalized size = 1. \[ \frac{x^{4} \sqrt [3]{\frac{b}{x^{3}}}}{3 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**4*(b/x**3)**(1/3)/(3*b)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00309968, size = 14, normalized size = 1. \[ \frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^3)^(-2/3),x]

[Out]

x/(3*(b/x^3)^(2/3))

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[{\frac{x}{3} \left ({\frac{b}{{x}^{3}}} \right ) ^{-{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b/x^3)^(2/3),x)

[Out]

1/3*x/(b/x^3)^(2/3)

_______________________________________________________________________________________

Maxima [A]  time = 1.44673, size = 14, normalized size = 1. \[ \frac{x}{3 \, \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^3)^(-2/3),x, algorithm="maxima")

[Out]

1/3*x/(b/x^3)^(2/3)

_______________________________________________________________________________________

Fricas [A]  time = 0.216707, size = 20, normalized size = 1.43 \[ \frac{x^{4} \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}}}{3 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^3)^(-2/3),x, algorithm="fricas")

[Out]

1/3*x^4*(b/x^3)^(1/3)/b

_______________________________________________________________________________________

Sympy [A]  time = 1.66463, size = 15, normalized size = 1.07 \[ \frac{x}{3 b^{\frac{2}{3}} \left (\frac{1}{x^{3}}\right )^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b/x**3)**(2/3),x)

[Out]

x/(3*b**(2/3)*(x**(-3))**(2/3))

_______________________________________________________________________________________

GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (\frac{b}{x^{3}}\right )^{\frac{2}{3}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^3)^(-2/3),x, algorithm="giac")

[Out]

integrate((b/x^3)^(-2/3), x)