3.235 \(\int \frac{\left (a+b x^3\right )^2}{x^{13}} \, dx\)

Optimal. Leaf size=30 \[ -\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6} \]

[Out]

-a^2/(12*x^12) - (2*a*b)/(9*x^9) - b^2/(6*x^6)

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Rubi [A]  time = 0.0394555, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)^2/x^13,x]

[Out]

-a^2/(12*x^12) - (2*a*b)/(9*x^9) - b^2/(6*x^6)

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Rubi in Sympy [A]  time = 6.68423, size = 27, normalized size = 0.9 \[ - \frac{a^{2}}{12 x^{12}} - \frac{2 a b}{9 x^{9}} - \frac{b^{2}}{6 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)**2/x**13,x)

[Out]

-a**2/(12*x**12) - 2*a*b/(9*x**9) - b**2/(6*x**6)

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Mathematica [A]  time = 0.00149272, size = 30, normalized size = 1. \[ -\frac{a^2}{12 x^{12}}-\frac{2 a b}{9 x^9}-\frac{b^2}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)^2/x^13,x]

[Out]

-a^2/(12*x^12) - (2*a*b)/(9*x^9) - b^2/(6*x^6)

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Maple [A]  time = 0.008, size = 25, normalized size = 0.8 \[ -{\frac{{a}^{2}}{12\,{x}^{12}}}-{\frac{2\,ab}{9\,{x}^{9}}}-{\frac{{b}^{2}}{6\,{x}^{6}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)^2/x^13,x)

[Out]

-1/12*a^2/x^12-2/9*a*b/x^9-1/6*b^2/x^6

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Maxima [A]  time = 1.44052, size = 35, normalized size = 1.17 \[ -\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2/x^13,x, algorithm="maxima")

[Out]

-1/36*(6*b^2*x^6 + 8*a*b*x^3 + 3*a^2)/x^12

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Fricas [A]  time = 0.206616, size = 35, normalized size = 1.17 \[ -\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2/x^13,x, algorithm="fricas")

[Out]

-1/36*(6*b^2*x^6 + 8*a*b*x^3 + 3*a^2)/x^12

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Sympy [A]  time = 1.5772, size = 27, normalized size = 0.9 \[ - \frac{3 a^{2} + 8 a b x^{3} + 6 b^{2} x^{6}}{36 x^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)**2/x**13,x)

[Out]

-(3*a**2 + 8*a*b*x**3 + 6*b**2*x**6)/(36*x**12)

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GIAC/XCAS [A]  time = 0.224473, size = 35, normalized size = 1.17 \[ -\frac{6 \, b^{2} x^{6} + 8 \, a b x^{3} + 3 \, a^{2}}{36 \, x^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)^2/x^13,x, algorithm="giac")

[Out]

-1/36*(6*b^2*x^6 + 8*a*b*x^3 + 3*a^2)/x^12