Optimal. Leaf size=11 \[ \frac {2}{3} (x+1)^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 11, 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} \[ \frac {2}{3} (x+1)^{3/2} \]
Antiderivative was successfully verified.
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Rule 26
Rule 32
Rubi steps
\begin {align*} \int \frac {\sqrt {1-x^2}}{\sqrt {1-x}} \, dx &=\int \sqrt {1+x} \, dx\\ &=\frac {2}{3} (1+x)^{3/2}\\ \end {align*}
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Mathematica [B] time = 0.02, size = 27, normalized size = 2.45 \[ \frac {2 (x+1) \sqrt {1-x^2}}{3 \sqrt {1-x}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 26, normalized size = 2.36 \[ -\frac {2 \, \sqrt {-x^{2} + 1} {\left (x + 1\right )} \sqrt {-x + 1}}{3 \, {\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 13, normalized size = 1.18 \[ \frac {2}{3} \, {\left (x + 1\right )}^{\frac {3}{2}} - \frac {4}{3} \, \sqrt {2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 22, normalized size = 2.00 \[ \frac {2 \left (x +1\right ) \sqrt {-x^{2}+1}}{3 \sqrt {-x +1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.92, size = 7, normalized size = 0.64 \[ \frac {2}{3} \, {\left (x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.49, size = 22, normalized size = 2.00 \[ \frac {\left (\frac {2\,x}{3}+\frac {2}{3}\right )\,\sqrt {1-x^2}}{\sqrt {1-x}} \]
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 \[ \int \frac {\sqrt {- \left (x - 1\right ) \left (x + 1\right )}}{\sqrt {1 - x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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