11+sinx1 sinx1 sin^2_x = 1 sinxcos^2_x =(sec^2_x secxtanx) = gt; ∫ (secx secxtanx)dx = gt; tan x sec x + C. ...

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Complementary Ratios

Evaluate ∫d...

Question

Evaluate $\int \frac{d x}{1 + s i n x}$

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Solution

$\frac{1}{1 + s i n x} \frac{1 - s i n x}{1 - s i n^{2} x} = \frac{1 - s i n x}{c o s^{2} x} = (s e c^{2} x - s e c x t a n x)$

=> $\int (s e c x - s e c x t a n x) d x$
=> $t a n x - s e c x + C .$

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