Optimal. Leaf size=9 \[ 2 \sqrt {x+1} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {26, 32} \[ 2 \sqrt {x+1} \]
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*}
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Mathematica [B] time = 0.02, size = 25, normalized size = 2.78 \[ \frac {2 \sqrt {1-x} (x+1)}{\sqrt {1-x^2}} \]
Antiderivative was successfully verified.
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fricas [C] time = 0.41, size = 23, normalized size = 2.56 \[ -\frac {2 \, \sqrt {-x^{2} + 1} \sqrt {-x + 1}}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 13, normalized size = 1.44 \[ -2 \, \sqrt {2} + 2 \, \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 22, normalized size = 2.44 \[ \frac {2 \left (x +1\right ) \sqrt {-x +1}}{\sqrt {-x^{2}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 7, normalized size = 0.78 \[ 2 \, \sqrt {x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.64, size = 18, normalized size = 2.00 \[ \frac {2\,\sqrt {1-x^2}}{\sqrt {1-x}} \]
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 \[ \int \frac {\sqrt {1 - x}}{\sqrt {- \left (x - 1\right ) \left (x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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