Question

Intergrate sinx/√(1-cosx) ?

Answer 1

We know that,
`color(blue)(int(f'(x))/sqrt(f(x))dx=2sqrt(f(x))+c`
`:.intsinx/sqrt(1-cosx)dx=2sqrt(1-cosx)+c`
Why ? Bcoz,
`color(blue)(f(x)=1-cosx=>f'(x)=sinx`

Explanation:

`I=intsinx/sqrt(1-cosx)dx`

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

`=int(1-cosx)^(-1/2)d/(dx)(1-cosx)dx`

`=(1-cosx)^(-1/2+1)/(-1/2+1)+c`

`=(1-cosx)^(1/2)/(1/2)+c`

`=2sqrt(1-cosx)+c`