3.1571 \(\int \left (a+\frac{b}{x}\right )^3 x^3 \, dx\)

Optimal. Leaf size=14 \[ \frac{(a x+b)^4}{4 a} \]

[Out]

(b + a*x)^4/(4*a)

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Rubi [A]  time = 0.0170673, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{(a x+b)^4}{4 a} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)^3*x^3,x]

[Out]

(b + a*x)^4/(4*a)

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Rubi in Sympy [A]  time = 2.96508, size = 8, normalized size = 0.57 \[ \frac{\left (a x + b\right )^{4}}{4 a} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(a*x + b)**4/(4*a)

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Mathematica [A]  time = 0.00254802, size = 14, normalized size = 1. \[ \frac{(a x+b)^4}{4 a} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)^3*x^3,x]

[Out]

(b + a*x)^4/(4*a)

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Maple [A]  time = 0.001, size = 13, normalized size = 0.9 \[{\frac{ \left ( ax+b \right ) ^{4}}{4\,a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)^3*x^3,x)

[Out]

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

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Maxima [A]  time = 1.44145, size = 42, normalized size = 3. \[ \frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a^3*x^4 + a^2*b*x^3 + 3/2*a*b^2*x^2 + b^3*x

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Fricas [A]  time = 0.210834, size = 42, normalized size = 3. \[ \frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a^3*x^4 + a^2*b*x^3 + 3/2*a*b^2*x^2 + b^3*x

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Sympy [A]  time = 0.105682, size = 32, normalized size = 2.29 \[ \frac{a^{3} x^{4}}{4} + a^{2} b x^{3} + \frac{3 a b^{2} x^{2}}{2} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)**3*x**3,x)

[Out]

a**3*x**4/4 + a**2*b*x**3 + 3*a*b**2*x**2/2 + b**3*x

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GIAC/XCAS [A]  time = 0.220927, size = 42, normalized size = 3. \[ \frac{1}{4} \, a^{3} x^{4} + a^{2} b x^{3} + \frac{3}{2} \, a b^{2} x^{2} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*a^3*x^4 + a^2*b*x^3 + 3/2*a*b^2*x^2 + b^3*x