Optimal. Leaf size=16 \[ -\frac{\sqrt{1-x^2}}{x} \]
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Rubi [A] time = 0.0031218, antiderivative size = 16, 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} \[ -\frac{\sqrt{1-x^2}}{x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{1-x^2}} \, dx &=-\frac{\sqrt{1-x^2}}{x}\\ \end{align*}
Mathematica [A] time = 0.002725, size = 16, normalized size = 1. \[ -\frac{\sqrt{1-x^2}}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 20, normalized size = 1.3 \begin{align*}{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) }{x}{\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 = 1.39644, size = 19, normalized size = 1.19 \begin{align*} -\frac{\sqrt{-x^{2} + 1}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.84782, size = 26, normalized size = 1.62 \begin{align*} -\frac{\sqrt{-x^{2} + 1}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.708029, size = 27, normalized size = 1.69 \begin{align*} \begin{cases} - \frac{i \sqrt{x^{2} - 1}}{x} & \text{for}\: \left |{x^{2}}\right | > 1 \\- \frac{\sqrt{1 - x^{2}}}{x} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06196, size = 45, normalized size = 2.81 \begin{align*} \frac{x}{2 \,{\left (\sqrt{-x^{2} + 1} - 1\right )}} - \frac{\sqrt{-x^{2} + 1} - 1}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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