Question

How do you find the antiderivative of `sinx/(1+cosx)`?

Answer 1

`- ln (1 + cos x)`

Explanation:

spotting the pattern is the easiest way

we know from the chain rule that `d/dx ln(f(x)) = 1/(f(x) )* f'(x)`

here we have `(-f'(x)) / f(x)` because `(1 + cos x)' = - sin x`

so the answer is simply `- ln (1 + cos x)`