Question

How do you integrate `int cosx/sqrt(1-2sinx)`?

Answer 1

`-sqrt(1-2sinx)+C`

Explanation:

We have:

`intcosx/sqrt(1-2sinx)dx`

Let: `u=1-2sinx`. This implies that `du=-2cosxdx`.

`intcosx/sqrt(1-2sinx)dx=-1/2int(-2cosx)/sqrt(1-2sinx)dx`

`=-1/2int(du)/sqrtu=-1/2intu^(-1/2)du=-1/2(u^(-1/2+1)/(-1/2+1))+C`

`=-u^(1/2)+C=-sqrt(1-2sinx)+C`