Question

Solve the integration Plzz.

Answer 1

Integration of  f(x) dx  ,  where   f(x) = Cos4x / [Cot x - Tan x] 

f(x) dx = (2 cos² 2x - 1) / [ (cos² x - sin² x) /(sinx cosx) ] dx
           = 1/2 * (2 cos² 2x - 1) * sin 2x / cos 2x  dx
 
Let cos 2x = t.    dt = - 2 sin 2x dx

f(x) dx = -1/4 (2 t² - 1)/t * dt 
           = -1/4 * (2 t - 1/t) dt
           =  -1/2 t dt + 1/4 * 1/t  dt
 
Integral :   -1/4  t² + 1/4 Ln t + K
                 -1/4 Cos² 2t + 1/4 Ln |Cos 2x | + K

Answer 2

Answer:

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