Optimal. Leaf size=17 \[ -\frac{b}{5 x^5}-\frac{c}{3 x^3} \]
[Out]
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Rubi [A] time = 0.0147413, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{b}{5 x^5}-\frac{c}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2 + c*x^4)/x^8,x]
[Out]
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Rubi in Sympy [A] time = 4.65891, size = 14, normalized size = 0.82 \[ - \frac{b}{5 x^{5}} - \frac{c}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2)/x**8,x)
[Out]
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Mathematica [A] time = 0.00361293, size = 17, normalized size = 1. \[ -\frac{b}{5 x^5}-\frac{c}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2 + c*x^4)/x^8,x]
[Out]
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Maple [A] time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{b}{5\,{x}^{5}}}-{\frac{c}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2)/x^8,x)
[Out]
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Maxima [A] time = 0.686661, size = 20, normalized size = 1.18 \[ -\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246537, size = 20, normalized size = 1.18 \[ -\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.14532, size = 15, normalized size = 0.88 \[ - \frac{3 b + 5 c x^{2}}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2)/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.268346, size = 20, normalized size = 1.18 \[ -\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)/x^8,x, algorithm="giac")
[Out]