Optimal. Leaf size=9 \[ \sqrt{x^2+4} \]
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Rubi [A] time = 0.0016157, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \sqrt{x^2+4} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{4+x^2}} \, dx &=\sqrt{4+x^2}\\ \end{align*}
Mathematica [A] time = 0.0009114, size = 9, normalized size = 1. \[ \sqrt{x^2+4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 8, normalized size = 0.9 \begin{align*} \sqrt{{x}^{2}+4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924973, size = 9, normalized size = 1. \begin{align*} \sqrt{x^{2} + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.79617, size = 20, normalized size = 2.22 \begin{align*} \sqrt{x^{2} + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.125309, size = 7, normalized size = 0.78 \begin{align*} \sqrt{x^{2} + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05176, size = 9, normalized size = 1. \begin{align*} \sqrt{x^{2} + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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