Optimal. Leaf size=19 \[ \frac{x^4}{4 b \left (b+c x^2\right )^2} \]
[Out]
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Rubi [A] time = 0.0248147, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{x^4}{4 b \left (b+c x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Int[x^9/(b*x^2 + c*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 5.23147, size = 14, normalized size = 0.74 \[ \frac{x^{4}}{4 b \left (b + c x^{2}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(c*x**4+b*x**2)**3,x)
[Out]
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Mathematica [A] time = 0.0122253, size = 24, normalized size = 1.26 \[ -\frac{b+2 c x^2}{4 c^2 \left (b+c x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(b*x^2 + c*x^4)^3,x]
[Out]
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Maple [A] time = 0.011, size = 31, normalized size = 1.6 \[ -{\frac{1}{ \left ( 2\,c{x}^{2}+2\,b \right ){c}^{2}}}+{\frac{b}{4\,{c}^{2} \left ( c{x}^{2}+b \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(c*x^4+b*x^2)^3,x)
[Out]
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Maxima [A] time = 0.708922, size = 49, normalized size = 2.58 \[ -\frac{2 \, c x^{2} + b}{4 \,{\left (c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(c*x^4 + b*x^2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250397, size = 49, normalized size = 2.58 \[ -\frac{2 \, c x^{2} + b}{4 \,{\left (c^{4} x^{4} + 2 \, b c^{3} x^{2} + b^{2} c^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(c*x^4 + b*x^2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.6502, size = 36, normalized size = 1.89 \[ - \frac{b + 2 c x^{2}}{4 b^{2} c^{2} + 8 b c^{3} x^{2} + 4 c^{4} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(c*x**4+b*x**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.269287, size = 30, normalized size = 1.58 \[ -\frac{2 \, c x^{2} + b}{4 \,{\left (c x^{2} + b\right )}^{2} c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(c*x^4 + b*x^2)^3,x, algorithm="giac")
[Out]