how to integrate the following:

Integration [(1+cos x ) /sin x . cos x ] w. r. t. dx.

Question

how to integrate the following:

Integration  [(1+cos x ) /sin x . cos x ] w. r. t.  dx.

anonymous · Answer

anyone please??/

anonymous · Answer

are w. r. t  constants?
if so. 1+cos x/(sin x . cos x) = 1/(sin x . cos x)  + 1/(sin x) = 2/sin 2x + 1/(sin x) = 2 . Cosec 2x + Cosec x.  in this form you can find the integral in an integration table. I hope it helps.

anonymous · Answer

yep.. thank you sir @juancarlosquintero_EC

anonymous · Answer

Take 1+cosx = cos^2(x/2)+sin^2(x/2)+cos^2(x/2)-sin^2(x/2)
                    = 2*cos^2(x/2)
Similarly, break the terms in denominator and then cancel the common terms.

Finally write dx=2*d(x/2)

And integrate the expression wrt d(x/2).

:)