Question

Integration of cosx/cos(x+alpha) dx

Answer 1

Step-by-step explanation:

alpha is constant term so,cos alpha and sin alpha are constant

integration tanx = log|secx| +c

or,. - log|cosx| +c

u can use any of them,there will be no problem

Answer 2

Answer:

Please find the answer below:

Step-by-step explanation:

∫cos x/ [ cos( x+α ) ] * dx

We know that cos + α = z

and dx = dz

∫ cos(z-α)dz / cos z

∫( cos z * cos α + sin z * sin α )dz/cos z

∫( cos z . cos α ). dz /cos z ) + ∫( sin z. sin α . dz/cos z)

cos α∫dz + sin α∫ tan z.dz

z cos α + sin α log | sec z | + C (integration constant)

(x+α)cos α + sinα log | sec (x+α) | + C

This is the answer .