Optimal. Leaf size=54 \[ -\frac{a^2}{10 x^{10}}-\frac{2 a c+b^2}{6 x^6}-\frac{a b}{4 x^8}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2} \]
[Out]
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Rubi [A] time = 0.088051, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{a^2}{10 x^{10}}-\frac{2 a c+b^2}{6 x^6}-\frac{a b}{4 x^8}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2/x^11,x]
[Out]
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Rubi in Sympy [A] time = 15.3318, size = 48, normalized size = 0.89 \[ - \frac{a^{2}}{10 x^{10}} - \frac{a b}{4 x^{8}} - \frac{b c}{2 x^{4}} - \frac{c^{2}}{2 x^{2}} - \frac{\frac{a c}{3} + \frac{b^{2}}{6}}{x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2/x**11,x)
[Out]
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Mathematica [A] time = 0.0290196, size = 53, normalized size = 0.98 \[ -\frac{6 a^2+5 a \left (3 b x^2+4 c x^4\right )+10 x^4 \left (b^2+3 b c x^2+3 c^2 x^4\right )}{60 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2/x^11,x]
[Out]
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Maple [A] time = 0.007, size = 45, normalized size = 0.8 \[ -{\frac{ab}{4\,{x}^{8}}}-{\frac{2\,ac+{b}^{2}}{6\,{x}^{6}}}-{\frac{{c}^{2}}{2\,{x}^{2}}}-{\frac{{a}^{2}}{10\,{x}^{10}}}-{\frac{bc}{2\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2/x^11,x)
[Out]
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Maxima [A] time = 0.685209, size = 62, normalized size = 1.15 \[ -\frac{30 \, c^{2} x^{8} + 30 \, b c x^{6} + 10 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 15 \, a b x^{2} + 6 \, a^{2}}{60 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246775, size = 62, normalized size = 1.15 \[ -\frac{30 \, c^{2} x^{8} + 30 \, b c x^{6} + 10 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 15 \, a b x^{2} + 6 \, a^{2}}{60 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.52052, size = 49, normalized size = 0.91 \[ - \frac{6 a^{2} + 15 a b x^{2} + 30 b c x^{6} + 30 c^{2} x^{8} + x^{4} \left (20 a c + 10 b^{2}\right )}{60 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.262013, size = 65, normalized size = 1.2 \[ -\frac{30 \, c^{2} x^{8} + 30 \, b c x^{6} + 10 \, b^{2} x^{4} + 20 \, a c x^{4} + 15 \, a b x^{2} + 6 \, a^{2}}{60 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^11,x, algorithm="giac")
[Out]