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evaluate ∫ 1 / 1 – sin x dx

evaluate
∫ 1 / 1 – sin x 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-sinx}dx
I = \int \frac{(1+sinx)}{(1-sinx)(1+sinx)}dx
I = \int \frac{(1+sinx)}{(1-sin^2x)}dx
I = \int \frac{(1+sinx)}{cos^2x}dx
I = \int (sec^2x+secxtanx)dx
I = \int sec^2xdx+\int secxtanxdx
I = tanx+\int secxtanxdx
I = tanx+secx+c

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