Optimal. Leaf size=2 \[ \sin ^{-1}(x) \]
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Rubi [A] time = 0.02, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.300, Rules used = {6129, 41, 216} \[ \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Rule 41
Rule 216
Rule 6129
Rubi steps
\begin {align*} \int \frac {e^{\tanh ^{-1}(x)}}{1+x} \, dx &=\int \frac {1}{\sqrt {1-x} \sqrt {1+x}} \, dx\\ &=\int \frac {1}{\sqrt {1-x^2}} \, dx\\ &=\sin ^{-1}(x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 2, normalized size = 1.00 \[ \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 18, normalized size = 9.00 \[ -2 \, \arctan \left (\frac {\sqrt {-x^{2} + 1} - 1}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 2, normalized size = 1.00 \[ \arcsin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 3, normalized size = 1.50 \[ \arcsin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 2, normalized size = 1.00 \[ \arcsin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 2, normalized size = 1.00 \[ \mathrm {asin}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 2, normalized size = 1.00 \[ \operatorname {asin}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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