Optimal. Leaf size=56 \[ -\frac{a^4}{14 x^{14}}-\frac{a^3 b}{3 x^{12}}-\frac{3 a^2 b^2}{5 x^{10}}-\frac{a b^3}{2 x^8}-\frac{b^4}{6 x^6} \]
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Rubi [A] time = 0.0877397, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{a^4}{14 x^{14}}-\frac{a^3 b}{3 x^{12}}-\frac{3 a^2 b^2}{5 x^{10}}-\frac{a b^3}{2 x^8}-\frac{b^4}{6 x^6} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^15,x]
[Out]
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Rubi in Sympy [A] time = 20.8273, size = 51, normalized size = 0.91 \[ - \frac{a^{4}}{14 x^{14}} - \frac{a^{3} b}{3 x^{12}} - \frac{3 a^{2} b^{2}}{5 x^{10}} - \frac{a b^{3}}{2 x^{8}} - \frac{b^{4}}{6 x^{6}} \]
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**15,x)
[Out]
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Mathematica [A] time = 0.00711226, size = 56, normalized size = 1. \[ -\frac{a^4}{14 x^{14}}-\frac{a^3 b}{3 x^{12}}-\frac{3 a^2 b^2}{5 x^{10}}-\frac{a b^3}{2 x^8}-\frac{b^4}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^15,x]
[Out]
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Maple [A] time = 0.008, size = 47, normalized size = 0.8 \[ -{\frac{{a}^{4}}{14\,{x}^{14}}}-{\frac{{a}^{3}b}{3\,{x}^{12}}}-{\frac{3\,{a}^{2}{b}^{2}}{5\,{x}^{10}}}-{\frac{a{b}^{3}}{2\,{x}^{8}}}-{\frac{{b}^{4}}{6\,{x}^{6}}} \]
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^15,x)
[Out]
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Maxima [A] time = 0.694763, size = 65, normalized size = 1.16 \[ -\frac{35 \, b^{4} x^{8} + 105 \, a b^{3} x^{6} + 126 \, a^{2} b^{2} x^{4} + 70 \, a^{3} b x^{2} + 15 \, a^{4}}{210 \, x^{14}} \]
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^15,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.257721, size = 65, normalized size = 1.16 \[ -\frac{35 \, b^{4} x^{8} + 105 \, a b^{3} x^{6} + 126 \, a^{2} b^{2} x^{4} + 70 \, a^{3} b x^{2} + 15 \, a^{4}}{210 \, x^{14}} \]
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^15,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.07676, size = 51, normalized size = 0.91 \[ - \frac{15 a^{4} + 70 a^{3} b x^{2} + 126 a^{2} b^{2} x^{4} + 105 a b^{3} x^{6} + 35 b^{4} x^{8}}{210 x^{14}} \]
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**15,x)
[Out]
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GIAC/XCAS [A] time = 0.268165, size = 65, normalized size = 1.16 \[ -\frac{35 \, b^{4} x^{8} + 105 \, a b^{3} x^{6} + 126 \, a^{2} b^{2} x^{4} + 70 \, a^{3} b x^{2} + 15 \, a^{4}}{210 \, x^{14}} \]
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^15,x, algorithm="giac")
[Out]