Optimal. Leaf size=52 \[ -\frac{a^2}{9 x^9}-\frac{2 a c+b^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{2 b c}{3 x^3}-\frac{c^2}{x} \]
[Out]
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Rubi [A] time = 0.0625679, antiderivative size = 52, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{a^2}{9 x^9}-\frac{2 a c+b^2}{5 x^5}-\frac{2 a b}{7 x^7}-\frac{2 b c}{3 x^3}-\frac{c^2}{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2/x^10,x]
[Out]
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Rubi in Sympy [A] time = 11.2097, size = 49, normalized size = 0.94 \[ - \frac{a^{2}}{9 x^{9}} - \frac{2 a b}{7 x^{7}} - \frac{2 b c}{3 x^{3}} - \frac{c^{2}}{x} - \frac{\frac{2 a c}{5} + \frac{b^{2}}{5}}{x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2/x**10,x)
[Out]
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Mathematica [A] time = 0.0351783, size = 50, normalized size = 0.96 \[ -\frac{35 a^2+90 a b x^2+126 a c x^4+63 b^2 x^4+210 b c x^6+315 c^2 x^8}{315 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2/x^10,x]
[Out]
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Maple [A] time = 0.008, size = 45, normalized size = 0.9 \[ -{\frac{2\,bc}{3\,{x}^{3}}}-{\frac{{a}^{2}}{9\,{x}^{9}}}-{\frac{{c}^{2}}{x}}-{\frac{2\,ac+{b}^{2}}{5\,{x}^{5}}}-{\frac{2\,ab}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2/x^10,x)
[Out]
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Maxima [A] time = 0.691133, size = 62, normalized size = 1.19 \[ -\frac{315 \, c^{2} x^{8} + 210 \, b c x^{6} + 63 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247836, size = 62, normalized size = 1.19 \[ -\frac{315 \, c^{2} x^{8} + 210 \, b c x^{6} + 63 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.93467, size = 49, normalized size = 0.94 \[ - \frac{35 a^{2} + 90 a b x^{2} + 210 b c x^{6} + 315 c^{2} x^{8} + x^{4} \left (126 a c + 63 b^{2}\right )}{315 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.261027, size = 65, normalized size = 1.25 \[ -\frac{315 \, c^{2} x^{8} + 210 \, b c x^{6} + 63 \, b^{2} x^{4} + 126 \, a c x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^10,x, algorithm="giac")
[Out]