Optimal. Leaf size=18 \[ -\sqrt {1-x} \sqrt {x+1} \]
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Rubi [A] time = 0.03, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {6129, 74} \[ -\sqrt {1-x} \sqrt {x+1} \]
Antiderivative was successfully verified.
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Rule 74
Rule 6129
Rubi steps
\begin {align*} \int \frac {e^{\tanh ^{-1}(x)} x}{1+x} \, dx &=\int \frac {x}{\sqrt {1-x} \sqrt {1+x}} \, dx\\ &=-\sqrt {1-x} \sqrt {1+x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.72 \[ -\sqrt {1-x^2} \]
Antiderivative was successfully verified.
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fricas [C] time = 0.49, size = 11, normalized size = 0.61 \[ -\sqrt {-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [C] time = 0.29, size = 11, normalized size = 0.61 \[ -\sqrt {-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.94 \[ \frac {\left (1+x \right ) \left (-1+x \right )}{\sqrt {-x^{2}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.39, size = 11, normalized size = 0.61 \[ -\sqrt {-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 11, normalized size = 0.61 \[ -\sqrt {1-x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 8, normalized size = 0.44 \[ - \sqrt {1 - x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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