3.231 \(\int \frac{\left (a+b x^3\right )^2}{x^9} \, dx\)

Optimal. Leaf size=30 \[ -\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2} \]

[Out]

-a^2/(8*x^8) - (2*a*b)/(5*x^5) - b^2/(2*x^2)

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Rubi [A]  time = 0.0292484, antiderivative size = 30, 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 \[ -\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^2/x^9,x]

[Out]

-a^2/(8*x^8) - (2*a*b)/(5*x^5) - b^2/(2*x^2)

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Rubi in Sympy [A]  time = 5.28071, size = 27, normalized size = 0.9 \[ - \frac{a^{2}}{8 x^{8}} - \frac{2 a b}{5 x^{5}} - \frac{b^{2}}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**2/x**9,x)

[Out]

-a**2/(8*x**8) - 2*a*b/(5*x**5) - b**2/(2*x**2)

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Mathematica [A]  time = 0.00148088, size = 30, normalized size = 1. \[ -\frac{a^2}{8 x^8}-\frac{2 a b}{5 x^5}-\frac{b^2}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^2/x^9,x]

[Out]

-a^2/(8*x^8) - (2*a*b)/(5*x^5) - b^2/(2*x^2)

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Maple [A]  time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{8\,{x}^{8}}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{b}^{2}}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^2/x^9,x)

[Out]

-1/8*a^2/x^8-2/5*a*b/x^5-1/2*b^2/x^2

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Maxima [A]  time = 1.44218, size = 35, normalized size = 1.17 \[ -\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2/x^9,x, algorithm="maxima")

[Out]

-1/40*(20*b^2*x^6 + 16*a*b*x^3 + 5*a^2)/x^8

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Fricas [A]  time = 0.261563, size = 35, normalized size = 1.17 \[ -\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2/x^9,x, algorithm="fricas")

[Out]

-1/40*(20*b^2*x^6 + 16*a*b*x^3 + 5*a^2)/x^8

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Sympy [A]  time = 1.39588, size = 27, normalized size = 0.9 \[ - \frac{5 a^{2} + 16 a b x^{3} + 20 b^{2} x^{6}}{40 x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**2/x**9,x)

[Out]

-(5*a**2 + 16*a*b*x**3 + 20*b**2*x**6)/(40*x**8)

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GIAC/XCAS [A]  time = 0.2248, size = 35, normalized size = 1.17 \[ -\frac{20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2/x^9,x, algorithm="giac")

[Out]

-1/40*(20*b^2*x^6 + 16*a*b*x^3 + 5*a^2)/x^8