Optimal. Leaf size=11 \[ -2 \sqrt {1-x} \]
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Rubi [A] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, 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 32
Rule 6129
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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ -2 \sqrt {1-x} \]
Antiderivative was successfully verified.
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fricas [C] time = 0.41, size = 16, normalized size = 1.45 \[ -\frac {2 \, \sqrt {-x^{2} + 1}}{\sqrt {x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 15, normalized size = 1.36 \[ 2 \, \sqrt {2} - 2 \, \sqrt {-x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 20, normalized size = 1.82 \[ \frac {2 \left (-1+x \right ) \sqrt {1+x}}{\sqrt {-x^{2}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.37, size = 12, normalized size = 1.09 \[ \frac {2 \, {\left (x - 1\right )}}{\sqrt {-x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 16, normalized size = 1.45 \[ -\frac {2\,\sqrt {1-x^2}}{\sqrt {x+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {x + 1}}{\sqrt {- \left (x - 1\right ) \left (x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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