Optimal. Leaf size=54 \[ -\frac{a^2}{10 x^{10}}-\frac{2 a c+b^2}{6 x^6}-\frac{a b}{4 x^8}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2} \]
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Rubi [A] time = 0.0374664, 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, Rules used = {1114, 698} \[ -\frac{a^2}{10 x^{10}}-\frac{2 a c+b^2}{6 x^6}-\frac{a b}{4 x^8}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 1114
Rule 698
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2+c x^4\right )^2}{x^{11}} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{\left (a+b x+c x^2\right )^2}{x^6} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (\frac{a^2}{x^6}+\frac{2 a b}{x^5}+\frac{b^2+2 a c}{x^4}+\frac{2 b c}{x^3}+\frac{c^2}{x^2}\right ) \, dx,x,x^2\right )\\ &=-\frac{a^2}{10 x^{10}}-\frac{a b}{4 x^8}-\frac{b^2+2 a c}{6 x^6}-\frac{b c}{2 x^4}-\frac{c^2}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.015071, 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.
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Maple [A] time = 0.048, size = 45, normalized size = 0.8 \begin{align*} -{\frac{bc}{2\,{x}^{4}}}-{\frac{{c}^{2}}{2\,{x}^{2}}}-{\frac{ab}{4\,{x}^{8}}}-{\frac{2\,ac+{b}^{2}}{6\,{x}^{6}}}-{\frac{{a}^{2}}{10\,{x}^{10}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.957288, size = 62, normalized size = 1.15 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4316, size = 111, normalized size = 2.06 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.1357, size = 49, normalized size = 0.91 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15229, size = 65, normalized size = 1.2 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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