Optimal. Leaf size=11 \[ -2 \sqrt{1-x} \]
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Rubi [A] time = 0.001246, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105, Rules used = {26, 32} \[ -2 \sqrt{1-x} \]
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 = 0.02142, size = 23, normalized size = 2.09 \[ \frac{2 (x-1) \sqrt{x+1}}{\sqrt{1-x^2}} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 20, normalized size = 1.8 \begin{align*} 2\,{\frac{ \left ( x-1 \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 = 1.42184, size = 16, normalized size = 1.45 \begin{align*} \frac{2 \,{\left (x - 1\right )}}{\sqrt{-x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [C] time = 1.45357, size = 42, normalized size = 3.82 \begin{align*} -\frac{2 \, \sqrt{-x^{2} + 1}}{\sqrt{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{x + 1}}{\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 = 1.08708, size = 20, normalized size = 1.82 \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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