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evaluate the following integral ∫ (1 – cot x) / (1 + cot x) dx

evaluate the following integral
∫ (1 – cot x) / (1 + cot x) dx

Grade:12

1 Answers

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

I = \int \frac{1-cotx}{1+cotx}dx
I = \int \frac{1-\frac{cosx}{sinx}}{1+\frac{cosx}{sinx}}dx
I = \int \frac{sinx-cosx}{sinx+cosx}dx
sinx+cosx = t
(cosx-sinx)dx = dt
I = \int \frac{-1}{t}dt
I = -log(t) + c
I = -log(sinx+cosx) + c

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