integration by substitution

By putting t = π/2-2x, show that ∫ dx/1+sin(2x) = 1/2 [tan(x-π/4)]+C where C is a constant.


dt = -2 dx
dx = dt/-2

t = π/2-2x
x = (t-π/2)/-2

所以 ∫ dx/1+sin(2x) = -1/2 ∫ dt/1+cos t

跟著我唔識做落去......