Question

how to integrate the following:

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

Answer 1

anyone please??/

Answer 2

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.

Answer 3

yep.. thank you sir @juancarlosquintero_EC

Answer 4

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).

:)