Question

integration of square root of (1+sin2x)

Answer 1

we know
$(sinx + cosx) {}^{2} = {sin}^{2} x + {cos}^{2} x + 2sinxcosx \\ = 1 + sin2x$
therefore
$\sqrt{ {(sinx + cosx)}^{2} } \\ = sinx + cosx$
it's integration
$= - cosx + sinx$
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