Optimal. Leaf size=82 \[ -\frac{a^6}{17 x^{17}}-\frac{2 a^5 b}{5 x^{15}}-\frac{15 a^4 b^2}{13 x^{13}}-\frac{20 a^3 b^3}{11 x^{11}}-\frac{5 a^2 b^4}{3 x^9}-\frac{6 a b^5}{7 x^7}-\frac{b^6}{5 x^5} \]
[Out]
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Rubi [A] time = 0.0968595, antiderivative size = 82, 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 \[ -\frac{a^6}{17 x^{17}}-\frac{2 a^5 b}{5 x^{15}}-\frac{15 a^4 b^2}{13 x^{13}}-\frac{20 a^3 b^3}{11 x^{11}}-\frac{5 a^2 b^4}{3 x^9}-\frac{6 a b^5}{7 x^7}-\frac{b^6}{5 x^5} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^18,x]
[Out]
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Rubi in Sympy [A] time = 23.2612, size = 82, normalized size = 1. \[ - \frac{a^{6}}{17 x^{17}} - \frac{2 a^{5} b}{5 x^{15}} - \frac{15 a^{4} b^{2}}{13 x^{13}} - \frac{20 a^{3} b^{3}}{11 x^{11}} - \frac{5 a^{2} b^{4}}{3 x^{9}} - \frac{6 a b^{5}}{7 x^{7}} - \frac{b^{6}}{5 x^{5}} \]
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**18,x)
[Out]
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Mathematica [A] time = 0.0113776, size = 82, normalized size = 1. \[ -\frac{a^6}{17 x^{17}}-\frac{2 a^5 b}{5 x^{15}}-\frac{15 a^4 b^2}{13 x^{13}}-\frac{20 a^3 b^3}{11 x^{11}}-\frac{5 a^2 b^4}{3 x^9}-\frac{6 a b^5}{7 x^7}-\frac{b^6}{5 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^18,x]
[Out]
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Maple [A] time = 0.008, size = 69, normalized size = 0.8 \[ -{\frac{{a}^{6}}{17\,{x}^{17}}}-{\frac{2\,{a}^{5}b}{5\,{x}^{15}}}-{\frac{15\,{a}^{4}{b}^{2}}{13\,{x}^{13}}}-{\frac{20\,{a}^{3}{b}^{3}}{11\,{x}^{11}}}-{\frac{5\,{a}^{2}{b}^{4}}{3\,{x}^{9}}}-{\frac{6\,a{b}^{5}}{7\,{x}^{7}}}-{\frac{{b}^{6}}{5\,{x}^{5}}} \]
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^18,x)
[Out]
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Maxima [A] time = 0.687985, size = 95, normalized size = 1.16 \[ -\frac{51051 \, b^{6} x^{12} + 218790 \, a b^{5} x^{10} + 425425 \, a^{2} b^{4} x^{8} + 464100 \, a^{3} b^{3} x^{6} + 294525 \, a^{4} b^{2} x^{4} + 102102 \, a^{5} b x^{2} + 15015 \, a^{6}}{255255 \, x^{17}} \]
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^18,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248219, size = 95, normalized size = 1.16 \[ -\frac{51051 \, b^{6} x^{12} + 218790 \, a b^{5} x^{10} + 425425 \, a^{2} b^{4} x^{8} + 464100 \, a^{3} b^{3} x^{6} + 294525 \, a^{4} b^{2} x^{4} + 102102 \, a^{5} b x^{2} + 15015 \, a^{6}}{255255 \, x^{17}} \]
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^18,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.81031, size = 75, normalized size = 0.91 \[ - \frac{15015 a^{6} + 102102 a^{5} b x^{2} + 294525 a^{4} b^{2} x^{4} + 464100 a^{3} b^{3} x^{6} + 425425 a^{2} b^{4} x^{8} + 218790 a b^{5} x^{10} + 51051 b^{6} x^{12}}{255255 x^{17}} \]
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**18,x)
[Out]
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GIAC/XCAS [A] time = 0.268499, size = 95, normalized size = 1.16 \[ -\frac{51051 \, b^{6} x^{12} + 218790 \, a b^{5} x^{10} + 425425 \, a^{2} b^{4} x^{8} + 464100 \, a^{3} b^{3} x^{6} + 294525 \, a^{4} b^{2} x^{4} + 102102 \, a^{5} b x^{2} + 15015 \, a^{6}}{255255 \, x^{17}} \]
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^18,x, algorithm="giac")
[Out]