Optimal. Leaf size=14 \[ -2 \sqrt {9-\sin ^2(x)} \]
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Rubi [A] time = 0.04, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 261} \[ -2 \sqrt {9-\sin ^2(x)} \]
Antiderivative was successfully verified.
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Rule 12
Rule 261
Rubi steps
\begin {align*} \int \frac {\sin (2 x)}{\sqrt {9-\sin ^2(x)}} \, dx &=\operatorname {Subst}\left (\int \frac {2 x}{\sqrt {9-x^2}} \, dx,x,\sin (x)\right )\\ &=2 \operatorname {Subst}\left (\int \frac {x}{\sqrt {9-x^2}} \, dx,x,\sin (x)\right )\\ &=-2 \sqrt {9-\sin ^2(x)}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 14, normalized size = 1.00 \[ -2 \sqrt {9-\sin ^2(x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 10, normalized size = 0.71 \[ -2 \, \sqrt {\cos \relax (x)^{2} + 8} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 12, normalized size = 0.86 \[ -2 \, \sqrt {-\sin \relax (x)^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 13, normalized size = 0.93 \[ -2 \sqrt {9-\left (\sin ^{2}\relax (x )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 12, normalized size = 0.86 \[ -2 \, \sqrt {-\sin \relax (x)^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 10, normalized size = 0.71 \[ -2\,\sqrt {{\cos \relax (x)}^2+8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.43, size = 12, normalized size = 0.86 \[ - 2 \sqrt {9 - \sin ^{2}{\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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