3.2387 \(\int \left (a+\frac{b}{\sqrt [3]{x}}\right ) x^4 \, dx\)

Optimal. Leaf size=19 \[ \frac{a x^5}{5}+\frac{3}{14} b x^{14/3} \]

[Out]

(3*b*x^(14/3))/14 + (a*x^5)/5

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Rubi [A]  time = 0.0169405, 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 \[ \frac{a x^5}{5}+\frac{3}{14} b x^{14/3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(1/3))*x^4,x]

[Out]

(3*b*x^(14/3))/14 + (a*x^5)/5

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Rubi in Sympy [A]  time = 2.80179, size = 15, normalized size = 0.79 \[ \frac{a x^{5}}{5} + \frac{3 b x^{\frac{14}{3}}}{14} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**(1/3))*x**4,x)

[Out]

a*x**5/5 + 3*b*x**(14/3)/14

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Mathematica [A]  time = 0.00806421, size = 19, normalized size = 1. \[ \frac{a x^5}{5}+\frac{3}{14} b x^{14/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^(1/3))*x^4,x]

[Out]

(3*b*x^(14/3))/14 + (a*x^5)/5

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Maple [A]  time = 0.002, size = 14, normalized size = 0.7 \[{\frac{3\,b}{14}{x}^{{\frac{14}{3}}}}+{\frac{a{x}^{5}}{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(1/3))*x^4,x)

[Out]

3/14*b*x^(14/3)+1/5*a*x^5

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Maxima [A]  time = 1.4179, size = 20, normalized size = 1.05 \[ \frac{1}{70} \,{\left (14 \, a + \frac{15 \, b}{x^{\frac{1}{3}}}\right )} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))*x^4,x, algorithm="maxima")

[Out]

1/70*(14*a + 15*b/x^(1/3))*x^5

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Fricas [A]  time = 0.226547, size = 18, normalized size = 0.95 \[ \frac{1}{5} \, a x^{5} + \frac{3}{14} \, b x^{\frac{14}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))*x^4,x, algorithm="fricas")

[Out]

1/5*a*x^5 + 3/14*b*x^(14/3)

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Sympy [A]  time = 7.54741, size = 15, normalized size = 0.79 \[ \frac{a x^{5}}{5} + \frac{3 b x^{\frac{14}{3}}}{14} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**(1/3))*x**4,x)

[Out]

a*x**5/5 + 3*b*x**(14/3)/14

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GIAC/XCAS [A]  time = 0.218596, size = 18, normalized size = 0.95 \[ \frac{1}{5} \, a x^{5} + \frac{3}{14} \, b x^{\frac{14}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))*x^4,x, algorithm="giac")

[Out]

1/5*a*x^5 + 3/14*b*x^(14/3)