Optimal. Leaf size=19 \[ \frac{x^{10}}{10 a \left (a+b x^2\right )^5} \]
[Out]
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Rubi [A] time = 0.0254028, 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 \[ \frac{x^{10}}{10 a \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
[In] Int[x^9/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 8.09373, size = 14, normalized size = 0.74 \[ \frac{x^{10}}{10 a \left (a + b x^{2}\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(b**2*x**4+2*a*b*x**2+a**2)**3,x)
[Out]
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Mathematica [B] time = 0.0277281, size = 57, normalized size = 3. \[ -\frac{a^4+5 a^3 b x^2+10 a^2 b^2 x^4+10 a b^3 x^6+5 b^4 x^8}{10 b^5 \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
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Maple [B] time = 0.012, size = 81, normalized size = 4.3 \[ -{\frac{{a}^{2}}{{b}^{5} \left ( b{x}^{2}+a \right ) ^{3}}}+{\frac{{a}^{3}}{2\,{b}^{5} \left ( b{x}^{2}+a \right ) ^{4}}}-{\frac{{a}^{4}}{10\,{b}^{5} \left ( b{x}^{2}+a \right ) ^{5}}}+{\frac{a}{{b}^{5} \left ( b{x}^{2}+a \right ) ^{2}}}-{\frac{1}{ \left ( 2\,b{x}^{2}+2\,a \right ){b}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(b^2*x^4+2*a*b*x^2+a^2)^3,x)
[Out]
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Maxima [A] time = 0.703241, size = 138, normalized size = 7.26 \[ -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \,{\left (b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="maxima")
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Fricas [A] time = 0.260259, size = 138, normalized size = 7.26 \[ -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \,{\left (b^{10} x^{10} + 5 \, a b^{9} x^{8} + 10 \, a^{2} b^{8} x^{6} + 10 \, a^{3} b^{7} x^{4} + 5 \, a^{4} b^{6} x^{2} + a^{5} b^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="fricas")
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Sympy [A] time = 4.33424, size = 107, normalized size = 5.63 \[ - \frac{a^{4} + 5 a^{3} b x^{2} + 10 a^{2} b^{2} x^{4} + 10 a b^{3} x^{6} + 5 b^{4} x^{8}}{10 a^{5} b^{5} + 50 a^{4} b^{6} x^{2} + 100 a^{3} b^{7} x^{4} + 100 a^{2} b^{8} x^{6} + 50 a b^{9} x^{8} + 10 b^{10} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(b**2*x**4+2*a*b*x**2+a**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.272949, size = 74, normalized size = 3.89 \[ -\frac{5 \, b^{4} x^{8} + 10 \, a b^{3} x^{6} + 10 \, a^{2} b^{2} x^{4} + 5 \, a^{3} b x^{2} + a^{4}}{10 \,{\left (b x^{2} + a\right )}^{5} b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="giac")
[Out]