3.119 \(\int \frac{1}{\sqrt [3]{b x^2}} \, dx\)

Optimal. Leaf size=12 \[ \frac{3 x}{\sqrt [3]{b x^2}} \]

[Out]

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

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Rubi [A]  time = 0.00692539, 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 \[ \frac{3 x}{\sqrt [3]{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(-1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.57355, size = 12, normalized size = 1. \[ \frac{3 \left (b x^{2}\right )^{\frac{2}{3}}}{b x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00214037, size = 12, normalized size = 1. \[ \frac{3 x}{\sqrt [3]{b x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(-1/3),x]

[Out]

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

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Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ 3\,{\frac{x}{\sqrt [3]{b{x}^{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x^2)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.44015, size = 14, normalized size = 1.17 \[ \frac{3 \, x}{\left (b x^{2}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.213629, size = 14, normalized size = 1.17 \[ \frac{3 \, x}{\left (b x^{2}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.46492, size = 14, normalized size = 1.17 \[ \frac{3 x}{\sqrt [3]{b} \sqrt [3]{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x**2)**(1/3),x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((b*x^2)^(-1/3), x)