Optimal. Leaf size=9 \[ 2 \sqrt{x+1} \]
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Rubi [A] time = 0.0011453, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095, Rules used = {26, 32} \[ 2 \sqrt{x+1} \]
Antiderivative was successfully verified.
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Rule 26
Rule 32
Rubi steps
\begin{align*} \int \frac{\sqrt{1-x}}{\sqrt{1-x^2}} \, dx &=\int \frac{1}{\sqrt{1+x}} \, dx\\ &=2 \sqrt{1+x}\\ \end{align*}
Mathematica [B] time = 0.0226464, size = 25, normalized size = 2.78 \[ \frac{2 \sqrt{1-x} (x+1)}{\sqrt{1-x^2}} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 22, normalized size = 2.4 \begin{align*} 2\,{\frac{ \left ( 1+x \right ) \sqrt{1-x}}{\sqrt{-{x}^{2}+1}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.47036, size = 9, normalized size = 1. \begin{align*} 2 \, \sqrt{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [C] time = 1.43803, size = 54, normalized size = 6. \begin{align*} -\frac{2 \, \sqrt{-x^{2} + 1} \sqrt{-x + 1}}{x - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{1 - x}}{\sqrt{- \left (x - 1\right ) \left (x + 1\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12649, size = 18, normalized size = 2. \begin{align*} -2 \, \sqrt{2} + 2 \, \sqrt{x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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