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evaluate the following integral ∫ 1 / sqrt(1 – cos 2x) dx

evaluate the following integral
∫ 1 / sqrt(1 – cos 2x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1}{\sqrt{1-cos2x}}dx
I = \int \frac{1}{\sqrt{2sin^{2}x}}dx
I = \int \frac{1}{\sqrt{2}sinx}dx
I = \int \frac{cosecx}{\sqrt{2}}dx
I = \int \frac{cosecx(cosecx+cotx)}{\sqrt{2}(cosecx+cotx)}dx
cosecx+cotx = t
(-cosecxcotx-cot^{2}x)dx = dt
I = \int \frac{-1}{\sqrt{2}t}dt
I = \frac{-log(t)}{\sqrt{2}}
I = \frac{-log(cosecx+cotx)}{\sqrt{2}}

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