Question

Evaluate : ∫ `cos^2`x dx

Answer 1

Let I = ∫ `cos^2`x dx

= `∫ (1 + cos2x)/2` dx          ..... [∵ 1 + cos 2θ = 2 `cos^2θ`]

= `1/2 {∫ 1 dx + ∫ cos 2x dx}`

= `1/2{x + (sin2x)/2} + c`