Optimal. Leaf size=48 \[ -\frac{a^2}{8 x^8}-\frac{2 a c+b^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b c}{x^2}+c^2 \log (x) \]
[Out]
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Rubi [A] time = 0.0866348, antiderivative size = 48, 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 \[ -\frac{a^2}{8 x^8}-\frac{2 a c+b^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b c}{x^2}+c^2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2/x^9,x]
[Out]
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Rubi in Sympy [A] time = 14.98, size = 46, normalized size = 0.96 \[ - \frac{a^{2}}{8 x^{8}} - \frac{a b}{3 x^{6}} - \frac{b c}{x^{2}} + \frac{c^{2} \log{\left (x^{2} \right )}}{2} - \frac{\frac{a c}{2} + \frac{b^{2}}{4}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2/x**9,x)
[Out]
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Mathematica [A] time = 0.046921, size = 50, normalized size = 1.04 \[ -\frac{a^2}{8 x^8}+\frac{-2 a c-b^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b c}{x^2}+c^2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2/x^9,x]
[Out]
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Maple [A] time = 0.009, size = 45, normalized size = 0.9 \[ -{\frac{{a}^{2}}{8\,{x}^{8}}}-{\frac{ab}{3\,{x}^{6}}}+{c}^{2}\ln \left ( x \right ) -{\frac{bc}{{x}^{2}}}-{\frac{ac}{2\,{x}^{4}}}-{\frac{{b}^{2}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2/x^9,x)
[Out]
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Maxima [A] time = 0.684689, size = 65, normalized size = 1.35 \[ \frac{1}{2} \, c^{2} \log \left (x^{2}\right ) - \frac{24 \, b c x^{6} + 6 \,{\left (b^{2} + 2 \, a c\right )} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.254708, size = 65, normalized size = 1.35 \[ \frac{24 \, c^{2} x^{8} \log \left (x\right ) - 24 \, b c x^{6} - 6 \,{\left (b^{2} + 2 \, a c\right )} x^{4} - 8 \, a b x^{2} - 3 \, a^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.65832, size = 46, normalized size = 0.96 \[ c^{2} \log{\left (x \right )} - \frac{3 a^{2} + 8 a b x^{2} + 24 b c x^{6} + x^{4} \left (12 a c + 6 b^{2}\right )}{24 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.262694, size = 78, normalized size = 1.62 \[ \frac{1}{2} \, c^{2}{\rm ln}\left (x^{2}\right ) - \frac{25 \, c^{2} x^{8} + 24 \, b c x^{6} + 6 \, b^{2} x^{4} + 12 \, a c x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^9,x, algorithm="giac")
[Out]