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

Optimal. Leaf size=12 \[ -3 x \left (\frac{b}{x^2}\right )^{2/3} \]

[Out]

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

_______________________________________________________________________________________

Rubi [A]  time = 0.00705723, antiderivative size = 12, 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 \[ -3 x \left (\frac{b}{x^2}\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^2)^(2/3),x]

[Out]

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

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.27232, size = 12, normalized size = 1. \[ - 3 x \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.00251667, size = 12, normalized size = 1. \[ -3 x \left (\frac{b}{x^2}\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^2)^(2/3),x]

[Out]

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

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ -3\, \left ({\frac{b}{{x}^{2}}} \right ) ^{2/3}x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^2)^(2/3),x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 1.43588, size = 14, normalized size = 1.17 \[ -3 \, x \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

_______________________________________________________________________________________

Fricas [A]  time = 0.24798, size = 18, normalized size = 1.5 \[ -\frac{3 \, b}{x \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

_______________________________________________________________________________________

Sympy [A]  time = 1.69643, size = 17, normalized size = 1.42 \[ - 3 b^{\frac{2}{3}} x \left (\frac{1}{x^{2}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**2)**(2/3),x)

[Out]

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

_______________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((b/x^2)^(2/3), x)