Optimal. Leaf size=18 \[ -\frac{\sqrt{4 x^2+9}}{9 x} \]
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Rubi [A] time = 0.003062, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{\sqrt{4 x^2+9}}{9 x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{9+4 x^2}} \, dx &=-\frac{\sqrt{9+4 x^2}}{9 x}\\ \end{align*}
Mathematica [A] time = 0.0023532, size = 18, normalized size = 1. \[ -\frac{\sqrt{4 x^2+9}}{9 x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.8 \begin{align*} -{\frac{1}{9\,x}\sqrt{4\,{x}^{2}+9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.12417, size = 19, normalized size = 1.06 \begin{align*} -\frac{\sqrt{4 \, x^{2} + 9}}{9 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.21919, size = 43, normalized size = 2.39 \begin{align*} -\frac{2 \, x + \sqrt{4 \, x^{2} + 9}}{9 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.706813, size = 15, normalized size = 0.83 \begin{align*} - \frac{2 \sqrt{1 + \frac{9}{4 x^{2}}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.26969, size = 31, normalized size = 1.72 \begin{align*} \frac{4}{{\left (2 \, x - \sqrt{4 \, x^{2} + 9}\right )}^{2} - 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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