3.2388 \(\int \left (a+\frac{b}{\sqrt [3]{x}}\right ) x^3 \, dx\)

Optimal. Leaf size=19 \[ \frac{a x^4}{4}+\frac{3}{11} b x^{11/3} \]

[Out]

(3*b*x^(11/3))/11 + (a*x^4)/4

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Rubi [A]  time = 0.0153371, 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 \[ \frac{a x^4}{4}+\frac{3}{11} b x^{11/3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(1/3))*x^3,x]

[Out]

(3*b*x^(11/3))/11 + (a*x^4)/4

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Rubi in Sympy [A]  time = 2.82716, size = 15, normalized size = 0.79 \[ \frac{a x^{4}}{4} + \frac{3 b x^{\frac{11}{3}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x**4/4 + 3*b*x**(11/3)/11

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Mathematica [A]  time = 0.00477479, size = 19, normalized size = 1. \[ \frac{a x^4}{4}+\frac{3}{11} b x^{11/3} \]

Antiderivative was successfully verified.

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

[Out]

(3*b*x^(11/3))/11 + (a*x^4)/4

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Maple [A]  time = 0.002, size = 14, normalized size = 0.7 \[{\frac{3\,b}{11}{x}^{{\frac{11}{3}}}}+{\frac{a{x}^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(1/3))*x^3,x)

[Out]

3/11*b*x^(11/3)+1/4*a*x^4

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Maxima [A]  time = 1.42034, size = 20, normalized size = 1.05 \[ \frac{1}{44} \,{\left (11 \, a + \frac{12 \, b}{x^{\frac{1}{3}}}\right )} x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/44*(11*a + 12*b/x^(1/3))*x^4

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Fricas [A]  time = 0.224965, size = 18, normalized size = 0.95 \[ \frac{1}{4} \, a x^{4} + \frac{3}{11} \, b x^{\frac{11}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a*x^4 + 3/11*b*x^(11/3)

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Sympy [A]  time = 3.5993, size = 15, normalized size = 0.79 \[ \frac{a x^{4}}{4} + \frac{3 b x^{\frac{11}{3}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x**4/4 + 3*b*x**(11/3)/11

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GIAC/XCAS [A]  time = 0.218359, size = 18, normalized size = 0.95 \[ \frac{1}{4} \, a x^{4} + \frac{3}{11} \, b x^{\frac{11}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a*x^4 + 3/11*b*x^(11/3)