Optimal. Leaf size=29 \[ \frac {1}{2} \sqrt {3-x^2} x+\frac {3}{2} \sin ^{-1}\left (\frac {x}{\sqrt {3}}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 29, 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 = {195, 216} \[ \frac {1}{2} \sqrt {3-x^2} x+\frac {3}{2} \sin ^{-1}\left (\frac {x}{\sqrt {3}}\right ) \]
Antiderivative was successfully verified.
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Rule 195
Rule 216
Rubi steps
\begin {align*} \int \sqrt {3-x^2} \, dx &=\frac {1}{2} x \sqrt {3-x^2}+\frac {3}{2} \int \frac {1}{\sqrt {3-x^2}} \, dx\\ &=\frac {1}{2} x \sqrt {3-x^2}+\frac {3}{2} \sin ^{-1}\left (\frac {x}{\sqrt {3}}\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \[ \frac {1}{2} \sqrt {3-x^2} x+\frac {3}{2} \sin ^{-1}\left (\frac {x}{\sqrt {3}}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 29, normalized size = 1.00 \[ \frac {1}{2} \, \sqrt {-x^{2} + 3} x - \frac {3}{2} \, \arctan \left (\frac {\sqrt {-x^{2} + 3}}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 22, normalized size = 0.76 \[ \frac {1}{2} \, \sqrt {-x^{2} + 3} x + \frac {3}{2} \, \arcsin \left (\frac {1}{3} \, \sqrt {3} x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.79 \[ \frac {\sqrt {-x^{2}+3}\, x}{2}+\frac {3 \arcsin \left (\frac {\sqrt {3}\, x}{3}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.14, size = 22, normalized size = 0.76 \[ \frac {1}{2} \, \sqrt {-x^{2} + 3} x + \frac {3}{2} \, \arcsin \left (\frac {1}{3} \, \sqrt {3} x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 22, normalized size = 0.76 \[ \frac {3\,\mathrm {asin}\left (\frac {\sqrt {3}\,x}{3}\right )}{2}+\frac {x\,\sqrt {3-x^2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 24, normalized size = 0.83 \[ \frac {x \sqrt {3 - x^{2}}}{2} + \frac {3 \operatorname {asin}{\left (\frac {\sqrt {3} x}{3} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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