3.1547 \(\int \left (a+\frac{b}{x}\right ) x^3 \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^4}{4}+\frac{b x^3}{3} \]

[Out]

(b*x^3)/3 + (a*x^4)/4

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Rubi [A]  time = 0.0206139, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^4}{4}+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)*x^3,x]

[Out]

(b*x^3)/3 + (a*x^4)/4

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Rubi in Sympy [A]  time = 2.88598, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)*x**3,x)

[Out]

a*x**4/4 + b*x**3/3

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Mathematica [A]  time = 0.00189654, size = 17, normalized size = 1. \[ \frac{a x^4}{4}+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)*x^3,x]

[Out]

(b*x^3)/3 + (a*x^4)/4

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Maple [A]  time = 0.002, size = 14, normalized size = 0.8 \[{\frac{b{x}^{3}}{3}}+{\frac{a{x}^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)*x^3,x)

[Out]

1/3*b*x^3+1/4*a*x^4

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Maxima [A]  time = 1.42491, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, a x^{4} + \frac{1}{3} \, b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a*x^4 + 1/3*b*x^3

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Fricas [A]  time = 0.21432, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, a x^{4} + \frac{1}{3} \, b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a*x^4 + 1/3*b*x^3

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Sympy [A]  time = 0.066039, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)*x**3,x)

[Out]

a*x**4/4 + b*x**3/3

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GIAC/XCAS [A]  time = 0.22269, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, a x^{4} + \frac{1}{3} \, b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a*x^4 + 1/3*b*x^3