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

Optimal. Leaf size=14 \[ \frac{1}{2} x \sqrt [3]{b x^3} \]

[Out]

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

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Rubi [A]  time = 0.00681788, 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 \[ \frac{1}{2} x \sqrt [3]{b x^3} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^3)^(1/3),x]

[Out]

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

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\sqrt [3]{b x^{3}} \int x\, dx}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(b*x**3)**(1/3)*Integral(x, x)/x

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Mathematica [A]  time = 0.00215541, size = 14, normalized size = 1. \[ \frac{1}{2} x \sqrt [3]{b x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^3)^(1/3),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.44048, size = 14, normalized size = 1. \[ \frac{1}{2} \, \left (b x^{3}\right )^{\frac{1}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.212435, size = 14, normalized size = 1. \[ \frac{1}{2} \, \left (b x^{3}\right )^{\frac{1}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.491524, size = 14, normalized size = 1. \[ \frac{\sqrt [3]{b} x \sqrt [3]{x^{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3)**(1/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.232182, size = 11, normalized size = 0.79 \[ \frac{1}{2} \, b^{\frac{1}{3}} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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