How to find $$\int \sqrt{\frac{(1-\sin x)(2-\sin x)}{(1+\sin x)(2+\sin x)}}dx$$ ?
I could get rid of of $(1+\sin x)$ by multiplying numerator and denominator by $(1-\sin x)$.What about the $(2+\sin x)$ term? Any other method possible?
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3Have you tried tangent-half-angle substitution? – Kenny Lau Aug 02 '16 at 08:09
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1I see elliptic integrals here. Wolfram Alpha doesn't show any closed form though – Yuriy S Aug 02 '16 at 08:13
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I tried after you said.But I still can't simplify the term $(2-\sin x)/(2+\sin x) $which comes out as $(1-t+t^2)/(1+t+t^2)$.What to do? – Aug 02 '16 at 08:17
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@SanchayanDutta, as I said, look up elliptic integrals. Are you certain you need the indefinite integral? – Yuriy S Aug 02 '16 at 08:18