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 = 0.04, antiderivative size = 54, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\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} \end {gather*}
Antiderivative was successfully verified.
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Rule 698
Rule 1114
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*}
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Mathematica [A] time = 0.02, size = 53, normalized size = 0.98 \begin {gather*} -\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}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^2+c x^4\right )^2}{x^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.77, size = 46, normalized size = 0.85 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 48, normalized size = 0.89 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 0.83 \begin {gather*} -\frac {c^{2}}{2 x^{2}}-\frac {b c}{2 x^{4}}-\frac {a b}{4 x^{8}}-\frac {2 a c +b^{2}}{6 x^{6}}-\frac {a^{2}}{10 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 46, normalized size = 0.85 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.12, size = 47, normalized size = 0.87 \begin {gather*} -\frac {\frac {a^2}{10}+x^4\,\left (\frac {b^2}{6}+\frac {a\,c}{3}\right )+\frac {c^2\,x^8}{2}+\frac {a\,b\,x^2}{4}+\frac {b\,c\,x^6}{2}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.08, size = 49, normalized size = 0.91 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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