∫ ((sin x−cos x)/( (√(sin 2x)))) dx ?


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Question Number 116501 by bemath last updated on 04/Oct/20

$\int \frac{\sin x - \cos x}{\sqrt{\sin 2 x}} dx ?$
	Answered by TANMAY PANACEA last updated on 04/Oct/20

	$\frac{d}{d x} (s i n x + c o s x) = c o s x - s i n x$ $\int \frac{- d (s i n x + c o s x)}{\sqrt{1 - 1 + s i n 2 x}}$ $\int \frac{- d (s i n x + c o s x)}{\sqrt{{(s i n x + c o s x)}^{2} - 1}}$ $\int \frac{d t}{\sqrt{t^{2} - 1}} f o r m u l a$
	Commented by bemath last updated on 04/Oct/20

	$= - \ln ∣ t + \sqrt{t^{2} - 1} ∣ + c$ $= - \ln ∣ \sin x + \cos x + \sqrt{\sin 2 x} ∣ + c ?$
	Commented by MJS_new last updated on 04/Oct/20

	$yes$
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