3.2391 \(\int \left (a+\frac{b}{\sqrt [3]{x}}\right ) \, dx\)

Optimal. Leaf size=14 \[ a x+\frac{3}{2} b x^{2/3} \]

[Out]

(3*b*x^(2/3))/2 + a*x

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Rubi [A]  time = 0.0108887, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+\frac{3}{2} b x^{2/3} \]

Antiderivative was successfully verified.

[In]  Int[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{3 b x^{\frac{2}{3}}}{2} + \int a\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(a+b/x**(1/3),x)

[Out]

3*b*x**(2/3)/2 + Integral(a, x)

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Mathematica [A]  time = 0.00256594, size = 14, normalized size = 1. \[ a x+\frac{3}{2} b x^{2/3} \]

Antiderivative was successfully verified.

[In]  Integrate[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

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Maple [A]  time = 0.001, size = 11, normalized size = 0.8 \[{\frac{3\,b}{2}{x}^{{\frac{2}{3}}}}+ax \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(a+b/x^(1/3),x)

[Out]

3/2*b*x^(2/3)+a*x

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Maxima [A]  time = 1.42328, size = 14, normalized size = 1. \[ a x + \frac{3}{2} \, b x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x + 3/2*b*x^(2/3)

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Fricas [A]  time = 0.215945, size = 14, normalized size = 1. \[ a x + \frac{3}{2} \, b x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x + 3/2*b*x^(2/3)

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Sympy [A]  time = 0.066027, size = 12, normalized size = 0.86 \[ a x + \frac{3 b x^{\frac{2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a+b/x**(1/3),x)

[Out]

a*x + 3*b*x**(2/3)/2

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GIAC/XCAS [A]  time = 0.220599, size = 14, normalized size = 1. \[ a x + \frac{3}{2} \, b x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x + 3/2*b*x^(2/3)