Question

What is the integral of `int cosx/sqrt(1-2sinx)`?

Answer 1

`-sqrt(1-2sin(x))+c`

Explanation:

Start by substituting `u=1-2sin(x)` and `du=-2cos(x)dx`
`int cosx/sqrt(1-2sinx)dx=int(-1/2)/sqrt(u)du=-1/2int1/sqrt(u)du`
`int1/sqrt(u)du=intu^(-1/2)du=2u^(1/2)+c`

All in all:
`-1/2*2u^(1/2)+c=-sqrt(u)+c`

Substitute back

`-sqrt(u)+c=-sqrt(1-2sin(x))+c`