Optimal. Leaf size=16 \[ -\frac{\sqrt{x^2+4}}{4 x} \]
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Rubi [A] time = 0.0027984, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ -\frac{\sqrt{x^2+4}}{4 x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{4+x^2}} \, dx &=-\frac{\sqrt{4+x^2}}{4 x}\\ \end{align*}
Mathematica [A] time = 0.0026909, size = 16, normalized size = 1. \[ -\frac{\sqrt{x^2+4}}{4 x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,x}\sqrt{{x}^{2}+4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.39813, size = 16, normalized size = 1. \begin{align*} -\frac{\sqrt{x^{2} + 4}}{4 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.04558, size = 38, normalized size = 2.38 \begin{align*} -\frac{x + \sqrt{x^{2} + 4}}{4 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.711962, size = 12, normalized size = 0.75 \begin{align*} - \frac{\sqrt{1 + \frac{4}{x^{2}}}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05554, size = 26, normalized size = 1.62 \begin{align*} \frac{2}{{\left (x - \sqrt{x^{2} + 4}\right )}^{2} - 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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