Optimal. Leaf size=25 \[ -\frac {\sqrt {9-x^2}}{x}-\sin ^{-1}\left (\frac {x}{3}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {277, 216} \[ -\frac {\sqrt {9-x^2}}{x}-\sin ^{-1}\left (\frac {x}{3}\right ) \]
Antiderivative was successfully verified.
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Rule 216
Rule 277
Rubi steps
\begin {align*} \int \frac {\sqrt {9-x^2}}{x^2} \, dx &=-\frac {\sqrt {9-x^2}}{x}-\int \frac {1}{\sqrt {9-x^2}} \, dx\\ &=-\frac {\sqrt {9-x^2}}{x}-\sin ^{-1}\left (\frac {x}{3}\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.00 \[ -\frac {\sqrt {9-x^2}}{x}-\sin ^{-1}\left (\frac {x}{3}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 35, normalized size = 1.40 \[ \frac {2 \, x \arctan \left (\frac {\sqrt {-x^{2} + 9} - 3}{x}\right ) - \sqrt {-x^{2} + 9}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 39, normalized size = 1.56 \[ \frac {x}{2 \, {\left (\sqrt {-x^{2} + 9} - 3\right )}} - \frac {\sqrt {-x^{2} + 9} - 3}{2 \, x} - \arcsin \left (\frac {1}{3} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 34, normalized size = 1.36 \[ -\frac {\sqrt {-x^{2}+9}\, x}{9}-\arcsin \left (\frac {x}{3}\right )-\frac {\left (-x^{2}+9\right )^{\frac {3}{2}}}{9 x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 21, normalized size = 0.84 \[ -\frac {\sqrt {-x^{2} + 9}}{x} - \arcsin \left (\frac {1}{3} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 21, normalized size = 0.84 \[ -\mathrm {asin}\left (\frac {x}{3}\right )-\frac {\sqrt {9-x^2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 15, normalized size = 0.60 \[ - \operatorname {asin}{\left (\frac {x}{3} \right )} - \frac {\sqrt {9 - x^{2}}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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