Question

$\int \frac{\cos x}{\cos (x-a)}dx$

Answer 1

$\int \frac{\cos x}{\cos (x-a)}dx$

Put $x-a=t$

$dx=at$

$\int \frac{\cos (a+t)}{\cos t}at=\int \frac{\cos a\cos t-\sin a\sin t}{\cos t}at$

$\int \cos at-\sin a\int \tan t.at$

$cosa.t-\sin a\ln \left|\sec t\right|+c$ $wheret=x-a$