3.438 \(\int \frac{\left (a^2+2 a b x^2+b^2 x^4\right )^2}{x^{11}} \, dx\)

Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^5}{10 a x^{10}} \]

[Out]

-(a + b*x^2)^5/(10*a*x^10)

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Rubi [A]  time = 0.0244275, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{\left (a+b x^2\right )^5}{10 a x^{10}} \]

Antiderivative was successfully verified.

[In]  Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^11,x]

[Out]

-(a + b*x^2)^5/(10*a*x^10)

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Rubi in Sympy [A]  time = 8.25463, size = 15, normalized size = 0.79 \[ - \frac{\left (a + b x^{2}\right )^{5}}{10 a x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**11,x)

[Out]

-(a + b*x**2)**5/(10*a*x**10)

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Mathematica [B]  time = 0.00727545, size = 52, normalized size = 2.74 \[ -\frac{a^4}{10 x^{10}}-\frac{a^3 b}{2 x^8}-\frac{a^2 b^2}{x^6}-\frac{a b^3}{x^4}-\frac{b^4}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^11,x]

[Out]

-a^4/(10*x^10) - (a^3*b)/(2*x^8) - (a^2*b^2)/x^6 - (a*b^3)/x^4 - b^4/(2*x^2)

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Maple [B]  time = 0.008, size = 47, normalized size = 2.5 \[ -{\frac{{a}^{3}b}{2\,{x}^{8}}}-{\frac{{a}^{2}{b}^{2}}{{x}^{6}}}-{\frac{{b}^{4}}{2\,{x}^{2}}}-{\frac{{a}^{4}}{10\,{x}^{10}}}-{\frac{a{b}^{3}}{{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b^2*x^4+2*a*b*x^2+a^2)^2/x^11,x)

[Out]

-1/2*a^3*b/x^8-a^2*b^2/x^6-1/2*b^4/x^2-1/10*a^4/x^10-a*b^3/x^4

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Maxima [A]  time = 0.699252, size = 62, normalized size = 3.26 \[ -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^11,x, algorithm="maxima")

[Out]

-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/x^10

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Fricas [A]  time = 0.251983, size = 62, normalized size = 3.26 \[ -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^11,x, algorithm="fricas")

[Out]

-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/x^10

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Sympy [A]  time = 1.8601, size = 49, normalized size = 2.58 \[ - \frac{a^{4} + 5 a^{3} b x^{2} + 10 a^{2} b^{2} x^{4} + 10 a b^{3} x^{6} + 5 b^{4} x^{8}}{10 x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b**2*x**4+2*a*b*x**2+a**2)**2/x**11,x)

[Out]

-(a**4 + 5*a**3*b*x**2 + 10*a**2*b**2*x**4 + 10*a*b**3*x**6 + 5*b**4*x**8)/(10*x
**10)

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GIAC/XCAS [A]  time = 0.267656, size = 62, normalized size = 3.26 \[ -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \, x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^2/x^11,x, algorithm="giac")

[Out]

-1/10*(5*b^4*x^8 + 10*a*b^3*x^6 + 10*a^2*b^2*x^4 + 5*a^3*b*x^2 + a^4)/x^10