Optimal. Leaf size=2 \[ \sin ^{-1}(x) \]
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Rubi [A] time = 0.0010183, antiderivative size = 2, 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 = {216} \[ \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{1-x^2}} \, dx &=\sin ^{-1}(x)\\ \end{align*}
Mathematica [A] time = 0.0036128, size = 2, normalized size = 1. \[ \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 3, normalized size = 1.5 \begin{align*} \arcsin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.85818, size = 3, normalized size = 1.5 \begin{align*} \arcsin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.40812, size = 47, normalized size = 23.5 \begin{align*} -2 \, \arctan \left (\frac{\sqrt{-x^{2} + 1} - 1}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.124319, size = 2, normalized size = 1. \begin{align*} \operatorname{asin}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12543, size = 3, normalized size = 1.5 \begin{align*} \arcsin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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