Optimal. Leaf size=13 \[ -\sqrt{1-x^2} \]
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Rubi [A] time = 0.0024715, antiderivative size = 13, 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} \[ -\sqrt{1-x^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{1-x^2}} \, dx &=-\sqrt{1-x^2}\\ \end{align*}
Mathematica [A] time = 0.0004805, size = 13, normalized size = 1. \[ -\sqrt{1-x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 17, normalized size = 1.3 \begin{align*}{ \left ( -1+x \right ) \left ( 1+x \right ){\frac{1}{\sqrt{-{x}^{2}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.923715, size = 15, normalized size = 1.15 \begin{align*} -\sqrt{-x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81101, size = 23, normalized size = 1.77 \begin{align*} -\sqrt{-x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127718, size = 8, normalized size = 0.62 \begin{align*} - \sqrt{1 - x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05616, size = 15, normalized size = 1.15 \begin{align*} -\sqrt{-x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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