Question

Evaluate the integral of : cosecx*cotX all devide by 2-cosecX dx?

Answer 1

`I=ln(abs(2-csc(x)))+C`

Explanation:

We want to integrate

`I=int(csc(x)cot(x))/(2-csc(x))dx`

Make a substitution `color(red)(u=2-csc(x)=>du=cot(x)csc(x)dx`

`I=int1/udu`

`color(white)(I)=ln(abs(u))+C`

Substitute back `color(red)(u=2-csc(x)`

`I=ln(abs(2-csc(x)))+C`