吧友求助一下，有点奇怪

u=π-x
du=-dx
x=π/2, u=π
x=π, u=0
∫(0->π) (cosx)^n dx
=∫(0->π/2) (cosx)^n dx + ∫(π/2->π) (cosx)^n dx
=∫(0->π/2) (cosx)^n dx + ∫(π/2->0) (-cosu)^n (-du)
=∫(0->π/2) (cosx)^n dx + ∫(0->π/2) (-cosx)^n dx
case 1: n 为奇数
∫(0->π) (cosx)^n dx
=∫(0->π/2) (cosx)^n dx + ∫(0->π/2) (-cosx)^n dx
=∫(0->π/2) (cosx)^n dx - ∫(0->π/2) (cosx)^n dx
=0
case 2: n 为偶数
∫(0->π) (cosx)^n dx
=∫(0->π/2) (cosx)^n dx + ∫(0->π/2) (-cosx)^n dx
=∫(0->π/2) (cosx)^n dx + ∫(0->π/2) (cosx)^n dx
=2∫(0->π/2) (cosx)^n dx