Now separating variable x on one side and variable y on other side, we have

Using identities:

and on RHS side assuming e^y = t, so e^ydy = dt by differentiating both sides.

Now integrating both sides

– log |sin(x)| = log(t+1) + c

Replacing t by e^y

– log |sin(x)| = log(e^y+1) + c

[sin(x)] (e^y+1) = c