Optimal. Leaf size=74 \[ -\frac{a^6}{9 x^9}-\frac{6 a^5 b}{7 x^7}-\frac{3 a^4 b^2}{x^5}-\frac{20 a^3 b^3}{3 x^3}-\frac{15 a^2 b^4}{x}+6 a b^5 x+\frac{b^6 x^3}{3} \]
[Out]
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Rubi [A] time = 0.0937105, antiderivative size = 74, 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 \[ -\frac{a^6}{9 x^9}-\frac{6 a^5 b}{7 x^7}-\frac{3 a^4 b^2}{x^5}-\frac{20 a^3 b^3}{3 x^3}-\frac{15 a^2 b^4}{x}+6 a b^5 x+\frac{b^6 x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^10,x]
[Out]
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Rubi in Sympy [A] time = 22.4119, size = 71, normalized size = 0.96 \[ - \frac{a^{6}}{9 x^{9}} - \frac{6 a^{5} b}{7 x^{7}} - \frac{3 a^{4} b^{2}}{x^{5}} - \frac{20 a^{3} b^{3}}{3 x^{3}} - \frac{15 a^{2} b^{4}}{x} + 6 a b^{5} x + \frac{b^{6} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**10,x)
[Out]
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Mathematica [A] time = 0.0154171, size = 74, normalized size = 1. \[ -\frac{a^6}{9 x^9}-\frac{6 a^5 b}{7 x^7}-\frac{3 a^4 b^2}{x^5}-\frac{20 a^3 b^3}{3 x^3}-\frac{15 a^2 b^4}{x}+6 a b^5 x+\frac{b^6 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^10,x]
[Out]
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Maple [A] time = 0.009, size = 67, normalized size = 0.9 \[ -{\frac{{a}^{6}}{9\,{x}^{9}}}-{\frac{6\,{a}^{5}b}{7\,{x}^{7}}}-3\,{\frac{{a}^{4}{b}^{2}}{{x}^{5}}}-{\frac{20\,{a}^{3}{b}^{3}}{3\,{x}^{3}}}-15\,{\frac{{a}^{2}{b}^{4}}{x}}+6\,a{b}^{5}x+{\frac{{b}^{6}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b^2*x^4+2*a*b*x^2+a^2)^3/x^10,x)
[Out]
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Maxima [A] time = 0.69522, size = 93, normalized size = 1.26 \[ \frac{1}{3} \, b^{6} x^{3} + 6 \, a b^{5} x - \frac{945 \, a^{2} b^{4} x^{8} + 420 \, a^{3} b^{3} x^{6} + 189 \, a^{4} b^{2} x^{4} + 54 \, a^{5} b x^{2} + 7 \, a^{6}}{63 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3/x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246904, size = 95, normalized size = 1.28 \[ \frac{21 \, b^{6} x^{12} + 378 \, a b^{5} x^{10} - 945 \, a^{2} b^{4} x^{8} - 420 \, a^{3} b^{3} x^{6} - 189 \, a^{4} b^{2} x^{4} - 54 \, a^{5} b x^{2} - 7 \, a^{6}}{63 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3/x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.96051, size = 71, normalized size = 0.96 \[ 6 a b^{5} x + \frac{b^{6} x^{3}}{3} - \frac{7 a^{6} + 54 a^{5} b x^{2} + 189 a^{4} b^{2} x^{4} + 420 a^{3} b^{3} x^{6} + 945 a^{2} b^{4} x^{8}}{63 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.269932, size = 93, normalized size = 1.26 \[ \frac{1}{3} \, b^{6} x^{3} + 6 \, a b^{5} x - \frac{945 \, a^{2} b^{4} x^{8} + 420 \, a^{3} b^{3} x^{6} + 189 \, a^{4} b^{2} x^{4} + 54 \, a^{5} b x^{2} + 7 \, a^{6}}{63 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3/x^10,x, algorithm="giac")
[Out]