Question

Integrate the function w.r.t.x. : $\frac{\cos x}{1-\sin x}$

Answer 1

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Answer 2

Answer:

$\int\:\frac{cos\:x}{1-sin\:x}dx=-log\:|1-sin\:x|+C$

Step-by-step explanation:

we can integrate the given function by

1) Substitution method

let

$1-sin\:x=t\\\\0-cos\:x\:dx=dt\\\\so\\\\cos\:x\:dx=-dt$

Now substitute the value

$\int\:\frac{cos\:x}{1-sin\:x}dx\\ \\ =\int\:\frac{-1}{t}\:dt\\\\=\:-log\:|t|+C$

Now substitute tha value of t again

$=-log\:|1-sin\:x|+C\\\\so\\\\\int\:\frac{cos\:x}{1-sin\:x}dx=-log\:|1-sin\:x|+C$