Optimal. Leaf size=10 \[ \frac {1}{3} \sin ^{-1}\left (\frac {3 x}{2}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {216} \begin {gather*} \frac {1}{3} \sin ^{-1}\left (\frac {3 x}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 216
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {4-9 x^2}} \, dx &=\frac {1}{3} \sin ^{-1}\left (\frac {3 x}{2}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {1}{3} \sin ^{-1}\left (\frac {3 x}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [C] time = 0.03, size = 24, normalized size = 2.40 \begin {gather*} \frac {1}{3} i \log \left (\sqrt {4-9 x^2}-3 i x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 19, normalized size = 1.90 \begin {gather*} -\frac {2}{3} \, \arctan \left (\frac {\sqrt {-9 \, x^{2} + 4} - 2}{3 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 6, normalized size = 0.60 \begin {gather*} \frac {1}{3} \, \arcsin \left (\frac {3}{2} \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 0.70 \begin {gather*} \frac {\arcsin \left (\frac {3 x}{2}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.96, size = 6, normalized size = 0.60 \begin {gather*} \frac {1}{3} \, \arcsin \left (\frac {3}{2} \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 6, normalized size = 0.60 \begin {gather*} \frac {\mathrm {asin}\left (\frac {3\,x}{2}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 7, normalized size = 0.70 \begin {gather*} \frac {\operatorname {asin}{\left (\frac {3 x}{2} \right )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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