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

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

[Out]

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

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Rubi [A]  time = 0.00658077, 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 \[ -\frac{3 x}{\left (b x^2\right )^{2/3}} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(-2/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.54412, size = 14, normalized size = 1.17 \[ - \frac{3 \sqrt [3]{b x^{2}}}{b x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00275569, size = 12, normalized size = 1. \[ -\frac{3 x}{\left (b x^2\right )^{2/3}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(-2/3),x]

[Out]

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

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Maple [A]  time = 0.001, size = 11, normalized size = 0.9 \[ -3\,{\frac{x}{ \left ( b{x}^{2} \right ) ^{2/3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x^2)^(2/3),x)

[Out]

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

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Maxima [A]  time = 1.42898, size = 14, normalized size = 1.17 \[ -\frac{3 \, x}{\left (b x^{2}\right )^{\frac{2}{3}}} \]

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)

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Fricas [A]  time = 0.251385, size = 20, normalized size = 1.67 \[ -\frac{3 \, \left (b x^{2}\right )^{\frac{1}{3}}}{b x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.61082, size = 15, normalized size = 1.25 \[ - \frac{3 x}{b^{\frac{2}{3}} \left (x^{2}\right )^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x**2)**(2/3),x)

[Out]

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

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

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)