Question

◆ Infinite Integration ◆
Integrate :-
$\frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x ) - \cos( \alpha ) } .dx$

Answer 1

 ∫cos2x−cos2acosx−cosadx∫cos⁡2x−cos⁡2acos⁡x−cos⁡adx

         =∫(2 cos2x − 1)−(2 cos2α − 1)/cosx − cosα .dx

         =∫(2(cos x−cosα)(cosx−cosα))/(cosx−cosα) .dx

         =2∫(cos⁡x + cos⁡α) .dx 

         =2(sinx+x cos α)+c

Hope my answer is clear.

Answer 2

Hello...

Q :- $\frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x ) - \cos( \alpha ) } .dx$

Ans : Answer is in this attachment..