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evaluate ∫ cos x / 1+ cos x dx

evaluate
∫  cos x / 1+ cos x 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{cosx}{1+cosx}dx
I = \int \frac{cosx(1-cosx)}{(1+cosx)(1-cosx)}dx
I = \int \frac{cosx-cos^2x}{(1-cos^2x)}dx
I = \int \frac{cosx-cos^2x}{sin^2x}dx
I = \int (cosecxcotx-cot^2x)dx
I = \int cosecxcotxdx-\int cot^2xdx
I = \int cosecxcotxdx-\int cosec^2xdx + \int dx
I = -cosecx-\int cosec^2xdx + \int dx
I = -cosecx+cotx + \int dx
I = -cosecx+cotx +x + c

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