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integrate the following integral ∫ 1 / 1 – sin x/2 dx

 
integrate the following integral
∫ 1 / 1 – sin x/2 dx

Grade:12

1 Answers

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

I = \int \frac{1}{1-sin\frac{x}{2}}dx
I = \int \frac{(1+sin\frac{x}{2})}{(1-sin\frac{x}{2})(1+sin\frac{x}{2})}dx
I = \int \frac{(1+sin\frac{x}{2})}{(1-sin^{2}\frac{x}{2})}dx
I = \int \frac{(1+sin\frac{x}{2})}{cos^{2}\frac{x}{2} }dx
I = \int (sec^{2}\frac{x}{2}+sec\frac{x}{2}tan\frac{x}{2})dx
I = \int sec^{2}\frac{x}{2}dx+\int sec\frac{x}{2}tan\frac{x}{2}dx
I = 2tan\frac{x}{2}+\int sec\frac{x}{2}tan\frac{x}{2}dx
I = 2tan\frac{x}{2}+2sec\frac{x}{2}+c

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