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