Evaluate the following integrals: ∫ (cos x)/(cos (x + α)) dx

Question

Evaluate the following integrals:

\(\int \frac{cos\, x}{cos(x + \alpha)} dx\)

∫ (cos x)/(cos (x + α)) dx

Answer 1

\(\Rightarrow \int \frac{cos\, x}{cos(x + \alpha)} dx\)

∫ (cos x)/(cos (x + α)) dx

Now α is a constant

⇒ x cos α - sin α log |cos (x + α)| + c

x cos α - sin α log |cos(x + α)| + c