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

1 Answer
Apr 28, 2018

#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#