Optimal. Leaf size=11 \[ -2 \sqrt{1-x} \]
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Rubi [A] time = 0.0192077, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {6129, 32} \[ -2 \sqrt{1-x} \]
Antiderivative was successfully verified.
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Rule 6129
Rule 32
Rubi steps
\begin{align*} \int \frac{e^{\tanh ^{-1}(x)}}{\sqrt{1+x}} \, dx &=\int \frac{1}{\sqrt{1-x}} \, dx\\ &=-2 \sqrt{1-x}\\ \end{align*}
Mathematica [A] time = 0.003727, size = 11, normalized size = 1. \[ -2 \sqrt{1-x} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.029, size = 20, normalized size = 1.8 \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 = 0.969603, 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 = 1.84967, 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 = 1.15086, 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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