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Integration of √(cosecx-1)

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Integration of √(cosecx-1)

Posted by Akash Arora 8 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Mohit Sharma 7 years, 10 months ago

∫ √(1 + cosecx) dx
= ∫ √[(1 + cosecx)*(cosecx - 1)] / √(cosecx - 1) dx
= ∫ cotx / √(cosecx - 1) dx
= ∫ cosecx cotx dx / [cosecx √(cosecx - 1)]

Let cosecx - 1 = u^2
=> - cosecx cotx dx = 2udu
=> integral
= - 2 ∫ u du / [(u^2 + 1) * u]
= - 2 arctanu + c
= - 2arctan(√(cosecx - 1) + c.

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