Optimal. Leaf size=30 \[ -\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4} \]
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Rubi [A] time = 0.014229, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^2}{x^9} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x^5} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (\frac{a^2}{x^5}+\frac{2 a b}{x^4}+\frac{b^2}{x^3}\right ) \, dx,x,x^2\right )\\ &=-\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.0007617, size = 30, normalized size = 1. \[ -\frac{a^2}{8 x^8}-\frac{a b}{3 x^6}-\frac{b^2}{4 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{8\,{x}^{8}}}-{\frac{ab}{3\,{x}^{6}}}-{\frac{{b}^{2}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.04931, size = 35, normalized size = 1.17 \begin{align*} -\frac{6 \, b^{2} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.37859, size = 58, normalized size = 1.93 \begin{align*} -\frac{6 \, b^{2} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.39098, size = 27, normalized size = 0.9 \begin{align*} - \frac{3 a^{2} + 8 a b x^{2} + 6 b^{2} x^{4}}{24 x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.63579, size = 35, normalized size = 1.17 \begin{align*} -\frac{6 \, b^{2} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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