3.123 \(\int \frac{1}{\sqrt [3]{\frac{b}{x^3}}} \, dx\)

Optimal. Leaf size=14 \[ \frac{x}{2 \sqrt [3]{\frac{b}{x^3}}} \]

[Out]

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

_______________________________________________________________________________________

Rubi [A]  time = 0.0064643, 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 \[ \frac{x}{2 \sqrt [3]{\frac{b}{x^3}}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^3)^(-1/3),x]

[Out]

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

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x^{2} \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}} \int x\, dx}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**2*(b/x**3)**(2/3)*Integral(x, x)/b

_______________________________________________________________________________________

Mathematica [A]  time = 0.00306992, size = 14, normalized size = 1. \[ \frac{x}{2 \sqrt [3]{\frac{b}{x^3}}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^3)^(-1/3),x]

[Out]

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

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 11, normalized size = 0.8 \[{\frac{x}{2}{\frac{1}{\sqrt [3]{{\frac{b}{{x}^{3}}}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b/x^3)^(1/3),x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 1.43781, size = 14, normalized size = 1. \[ \frac{x}{2 \, \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^3)^(-1/3),x, algorithm="maxima")

[Out]

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

_______________________________________________________________________________________

Fricas [A]  time = 0.214957, size = 20, normalized size = 1.43 \[ \frac{x^{4} \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}}}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^3)^(-1/3),x, algorithm="fricas")

[Out]

1/2*x^4*(b/x^3)^(2/3)/b

_______________________________________________________________________________________

Sympy [A]  time = 1.54985, size = 15, normalized size = 1.07 \[ \frac{x}{2 \sqrt [3]{b} \sqrt [3]{\frac{1}{x^{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b/x**3)**(1/3),x)

[Out]

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

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^3)^(-1/3),x, algorithm="giac")

[Out]

integrate((b/x^3)^(-1/3), x)