Optimal. Leaf size=14 \[ \frac {2 \cos (x)}{\sqrt {1-\sin (x)}} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2646} \[ \frac {2 \cos (x)}{\sqrt {1-\sin (x)}} \]
Antiderivative was successfully verified.
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Rule 2646
Rubi steps
\begin {align*} \int \sqrt {1-\sin (x)} \, dx &=\frac {2 \cos (x)}{\sqrt {1-\sin (x)}}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 42, normalized size = 3.00 \[ \frac {2 \sqrt {1-\sin (x)} \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )}{\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 26, normalized size = 1.86 \[ \frac {2 \, {\left (\cos \relax (x) + \sin \relax (x) + 1\right )} \sqrt {-\sin \relax (x) + 1}}{\cos \relax (x) - \sin \relax (x) + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.20, size = 35, normalized size = 2.50 \[ -2 \, \sqrt {2} {\left (\cos \left (-\frac {1}{4} \, \pi + \frac {1}{2} \, x\right ) \mathrm {sgn}\left (\sin \left (-\frac {1}{4} \, \pi + \frac {1}{2} \, x\right )\right ) - \mathrm {sgn}\left (\sin \left (-\frac {1}{4} \, \pi + \frac {1}{2} \, x\right )\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 23, normalized size = 1.64 \[ -\frac {2 \left (\sin \relax (x )-1\right ) \left (\sin \relax (x )+1\right )}{\sqrt {-\sin \relax (x )+1}\, \cos \relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {-\sin \relax (x) + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 18, normalized size = 1.29 \[ \frac {2\,\sqrt {1-\sin \relax (x)}\,\left (\sin \relax (x)+1\right )}{\cos \relax (x)} \]
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 \[ \int \sqrt {1 - \sin {\relax (x )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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