Integrate ∫11+cotxdx
Solve the given integral
Given integral,
∫11+cotxdx
We know that ,
cotx=cosxsinx
Now,
=∫11+cosxsinxdx=∫sinxsinx+cosxdx=12∫2sinxsinx+cosxdx=12∫sinx+cosx-cosx-sinxsinx+cosxdx=12∫1dx-∫cosx-sinxsinx+cosxdx=12x-∫1udu
Where , u=sinx+cosxanddu=(cosx-sinx)dx
=x2-12ln|u|+C=x2-12ln|sinx+cosx|+C
Hence , Integral ∫11+cotxdx is x2-12ln|sinx+cosx|+C.