The value of ∫−ππ cos2⁡x1+axdx,a>0 is

Let I=∫−ππ cos2⁡x1+axdxPut x=−θ to obtainI=∫π−π cos2⁡θ1+a−θ(−1)dθ=∫−ππ axcos2⁡x1+axdxAdding (1) and (2), we get 2I=∫−ππ cos2⁡xdx=2∫0π cos2⁡xdx=π⇒I=π/2