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integrate the following integral ∫ 1 + cos x / 1 – cos x dx

 
integrate the following integral
∫ 1 + 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{1+cosx}{1-cosx}dx
I = \int \frac{2cos^{2}\frac{x}{2}}{2sin^{2}\frac{x}{2}}dx
I = \int cot^{2}\frac{x}{2}dx
I = \int (cosec^{2}\frac{x}{2}-1)dx
I = \int cosec^{2}\frac{x}{2}dx-\int dx
I = -2cot\frac{x}{2}-\int dx
I = -2cot\frac{x}{2}-x+c

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