Optimal. Leaf size=23 \[ -\frac{x^4}{4 c \left (b x^2+c x^4\right )^2} \]
[Out]
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Rubi [A] time = 0.0135321, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{x^4}{4 c \left (b x^2+c x^4\right )^2} \]
Antiderivative was successfully verified.
[In] Int[x^7/(b*x^2 + c*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 4.07219, size = 14, normalized size = 0.61 \[ - \frac{1}{4 c \left (b + c x^{2}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(c*x**4+b*x**2)**3,x)
[Out]
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Mathematica [A] time = 0.00520676, size = 16, normalized size = 0.7 \[ -\frac{1}{4 c \left (b+c x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(b*x^2 + c*x^4)^3,x]
[Out]
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Maple [A] time = 0.001, size = 15, normalized size = 0.7 \[ -{\frac{1}{4\,c \left ( c{x}^{2}+b \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(c*x^4+b*x^2)^3,x)
[Out]
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Maxima [A] time = 0.689434, size = 35, normalized size = 1.52 \[ -\frac{1}{4 \,{\left (c^{3} x^{4} + 2 \, b c^{2} x^{2} + b^{2} c\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + b*x^2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247427, size = 35, normalized size = 1.52 \[ -\frac{1}{4 \,{\left (c^{3} x^{4} + 2 \, b c^{2} x^{2} + b^{2} c\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + b*x^2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.53875, size = 27, normalized size = 1.17 \[ - \frac{1}{4 b^{2} c + 8 b c^{2} x^{2} + 4 c^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(c*x**4+b*x**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.271606, size = 19, normalized size = 0.83 \[ -\frac{1}{4 \,{\left (c x^{2} + b\right )}^{2} c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + b*x^2)^3,x, algorithm="giac")
[Out]