3.2389 \(\int \left (a+\frac{b}{\sqrt [3]{x}}\right ) x^2 \, dx\)

Optimal. Leaf size=19 \[ \frac{a x^3}{3}+\frac{3}{8} b x^{8/3} \]

[Out]

(3*b*x^(8/3))/8 + (a*x^3)/3

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Rubi [A]  time = 0.0160699, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a x^3}{3}+\frac{3}{8} b x^{8/3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(1/3))*x^2,x]

[Out]

(3*b*x^(8/3))/8 + (a*x^3)/3

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Rubi in Sympy [A]  time = 2.93624, size = 15, normalized size = 0.79 \[ \frac{a x^{3}}{3} + \frac{3 b x^{\frac{8}{3}}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x**3/3 + 3*b*x**(8/3)/8

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Mathematica [A]  time = 0.00454728, size = 19, normalized size = 1. \[ \frac{a x^3}{3}+\frac{3}{8} b x^{8/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^(1/3))*x^2,x]

[Out]

(3*b*x^(8/3))/8 + (a*x^3)/3

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Maple [A]  time = 0.002, size = 14, normalized size = 0.7 \[{\frac{3\,b}{8}{x}^{{\frac{8}{3}}}}+{\frac{a{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(1/3))*x^2,x)

[Out]

3/8*b*x^(8/3)+1/3*a*x^3

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Maxima [A]  time = 1.42558, size = 20, normalized size = 1.05 \[ \frac{1}{24} \,{\left (8 \, a + \frac{9 \, b}{x^{\frac{1}{3}}}\right )} x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/24*(8*a + 9*b/x^(1/3))*x^3

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Fricas [A]  time = 0.223526, size = 18, normalized size = 0.95 \[ \frac{1}{3} \, a x^{3} + \frac{3}{8} \, b x^{\frac{8}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*a*x^3 + 3/8*b*x^(8/3)

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Sympy [A]  time = 1.38101, size = 15, normalized size = 0.79 \[ \frac{a x^{3}}{3} + \frac{3 b x^{\frac{8}{3}}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**(1/3))*x**2,x)

[Out]

a*x**3/3 + 3*b*x**(8/3)/8

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GIAC/XCAS [A]  time = 0.217181, size = 18, normalized size = 0.95 \[ \frac{1}{3} \, a x^{3} + \frac{3}{8} \, b x^{\frac{8}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*a*x^3 + 3/8*b*x^(8/3)