Question

$y=\int \frac{\cos x}{1+\sin x}dx$.

Answer 1

We have,

$y=\int \frac{\cos x}{1+\sin x}dx$

Let

$t=1+\sin x$

$dt=\cos xdx$

Therefore,

$y=\int \frac{dt}{t}$

$y=\ln t+C$

On putting the value of $t$, we get

$y=\ln (1+\sin x)+C$

Hence, this is the answer.