Question

Integrate the following functions with respect to x :

`(cos 2x)/(sin^2x cos^2x)`

Answer 1

`int (cos 2x)/(sin^2x cos^2x)  "d"x = int (cos^2x - sin^2alpha)/(sin^2x  cos^2x)  "d"x`

= `int ((cos^2x)/(sin^2x  cos^2x) - (sin^2x)/(sin^2x cos^2x)) "d"x`

= `int (1/(sin^2x) - 1/(cos^2x)) "d"x`

= `int ("cosec"^2x - sec^2x)  "d"x`

= `int "cosec"^2x  "d"x - int sec^2x  "d"x`

= `- cot x - tan x + "c"`

= `- [cosx/sinx + sinx/cosx] + "c"`

= `-[(cos^2x + sin^2x)/(sinx  cosx)] + "c"`

= `- 2/(sin 2x) + "c"`

= –  2 cosec 2x + c