Optimal. Leaf size=30 \[ -\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3} \]
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Rubi [A] time = 0.0104559, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {270} \[ -\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^2}{x^8} \, dx &=\int \left (\frac{a^2}{x^8}+\frac{2 a b}{x^6}+\frac{b^2}{x^4}\right ) \, dx\\ &=-\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0007667, size = 30, normalized size = 1. \[ -\frac{a^2}{7 x^7}-\frac{2 a b}{5 x^5}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{7\,{x}^{7}}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{b}^{2}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.477, size = 35, normalized size = 1.17 \begin{align*} -\frac{35 \, b^{2} x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.39536, size = 63, normalized size = 2.1 \begin{align*} -\frac{35 \, b^{2} x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.344517, size = 27, normalized size = 0.9 \begin{align*} - \frac{15 a^{2} + 42 a b x^{2} + 35 b^{2} x^{4}}{105 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.09605, size = 35, normalized size = 1.17 \begin{align*} -\frac{35 \, b^{2} x^{4} + 42 \, a b x^{2} + 15 \, a^{2}}{105 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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