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

Optimal. Leaf size=14 \[ \frac{3}{5} x \sqrt [3]{b x^2} \]

[Out]

(3*x*(b*x^2)^(1/3))/5

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Rubi [A]  time = 0.00720474, 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 \[ \frac{3}{5} x \sqrt [3]{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(1/3),x]

[Out]

(3*x*(b*x^2)^(1/3))/5

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Rubi in Sympy [A]  time = 1.22868, size = 12, normalized size = 0.86 \[ \frac{3 x \sqrt [3]{b x^{2}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*x*(b*x**2)**(1/3)/5

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Mathematica [A]  time = 0.00205365, size = 14, normalized size = 1. \[ \frac{3}{5} x \sqrt [3]{b x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(1/3),x]

[Out]

(3*x*(b*x^2)^(1/3))/5

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Maple [A]  time = 0.002, size = 11, normalized size = 0.8 \[{\frac{3\,x}{5}\sqrt [3]{b{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(1/3),x)

[Out]

3/5*x*(b*x^2)^(1/3)

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Maxima [A]  time = 1.44057, size = 14, normalized size = 1. \[ \frac{3}{5} \, \left (b x^{2}\right )^{\frac{1}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*(b*x^2)^(1/3)*x

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Fricas [A]  time = 0.222534, size = 18, normalized size = 1.29 \[ \frac{3 \, b x^{3}}{5 \, \left (b x^{2}\right )^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/5*b*x^3/(b*x^2)^(2/3)

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Sympy [A]  time = 0.493636, size = 15, normalized size = 1.07 \[ \frac{3 \sqrt [3]{b} x \sqrt [3]{x^{2}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(1/3),x)

[Out]

3*b**(1/3)*x*(x**2)**(1/3)/5

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

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)