Optimal. Leaf size=50 \[ -\frac{a^4}{5 x^5}-\frac{4 a^3 b}{3 x^3}-\frac{6 a^2 b^2}{x}+4 a b^3 x+\frac{b^4 x^3}{3} \]
[Out]
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Rubi [A] time = 0.066992, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{a^4}{5 x^5}-\frac{4 a^3 b}{3 x^3}-\frac{6 a^2 b^2}{x}+4 a b^3 x+\frac{b^4 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^6,x]
[Out]
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Rubi in Sympy [A] time = 17.142, size = 46, normalized size = 0.92 \[ - \frac{a^{4}}{5 x^{5}} - \frac{4 a^{3} b}{3 x^{3}} - \frac{6 a^{2} b^{2}}{x} + 4 a b^{3} x + \frac{b^{4} x^{3}}{3} \]
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**6,x)
[Out]
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Mathematica [A] time = 0.0136454, size = 50, normalized size = 1. \[ -\frac{a^4}{5 x^5}-\frac{4 a^3 b}{3 x^3}-\frac{6 a^2 b^2}{x}+4 a b^3 x+\frac{b^4 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^2/x^6,x]
[Out]
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Maple [A] time = 0.008, size = 45, normalized size = 0.9 \[ -{\frac{{a}^{4}}{5\,{x}^{5}}}-{\frac{4\,{a}^{3}b}{3\,{x}^{3}}}-6\,{\frac{{a}^{2}{b}^{2}}{x}}+4\,a{b}^{3}x+{\frac{{b}^{4}{x}^{3}}{3}} \]
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^6,x)
[Out]
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Maxima [A] time = 0.696255, size = 63, normalized size = 1.26 \[ \frac{1}{3} \, b^{4} x^{3} + 4 \, a b^{3} x - \frac{90 \, a^{2} b^{2} x^{4} + 20 \, a^{3} b x^{2} + 3 \, a^{4}}{15 \, x^{5}} \]
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^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247926, size = 65, normalized size = 1.3 \[ \frac{5 \, b^{4} x^{8} + 60 \, a b^{3} x^{6} - 90 \, a^{2} b^{2} x^{4} - 20 \, a^{3} b x^{2} - 3 \, a^{4}}{15 \, x^{5}} \]
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^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.35551, size = 48, normalized size = 0.96 \[ 4 a b^{3} x + \frac{b^{4} x^{3}}{3} - \frac{3 a^{4} + 20 a^{3} b x^{2} + 90 a^{2} b^{2} x^{4}}{15 x^{5}} \]
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**6,x)
[Out]
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GIAC/XCAS [A] time = 0.268019, size = 63, normalized size = 1.26 \[ \frac{1}{3} \, b^{4} x^{3} + 4 \, a b^{3} x - \frac{90 \, a^{2} b^{2} x^{4} + 20 \, a^{3} b x^{2} + 3 \, a^{4}}{15 \, x^{5}} \]
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^6,x, algorithm="giac")
[Out]