Optimal. Leaf size=15 \[ \frac{1}{4} \sqrt{4 x^2-9} \]
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Rubi [A] time = 0.0020956, antiderivative size = 15, 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 = {261} \[ \frac{1}{4} \sqrt{4 x^2-9} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{-9+4 x^2}} \, dx &=\frac{1}{4} \sqrt{-9+4 x^2}\\ \end{align*}
Mathematica [A] time = 0.0012402, size = 15, normalized size = 1. \[ \frac{1}{4} \sqrt{4 x^2-9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 22, normalized size = 1.5 \begin{align*}{\frac{ \left ( -3+2\,x \right ) \left ( 3+2\,x \right ) }{4}{\frac{1}{\sqrt{4\,{x}^{2}-9}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.956, size = 15, normalized size = 1. \begin{align*} \frac{1}{4} \, \sqrt{4 \, x^{2} - 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.18828, size = 28, normalized size = 1.87 \begin{align*} \frac{1}{4} \, \sqrt{4 \, x^{2} - 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.135896, size = 10, normalized size = 0.67 \begin{align*} \frac{\sqrt{4 x^{2} - 9}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.67957, size = 15, normalized size = 1. \begin{align*} \frac{1}{4} \, \sqrt{4 \, x^{2} - 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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