Question

高数题，划线部分怎么计算出来的

Answer 1

如神核图世瞎敏搜枝所示

Answer 2

let
u=π/2-x
du=-dx
x=0, u=π/2
x=π/2, u=0
I
=∫(0->π/2) dx/[1+(tanx)^a]
=∫(π/2 ->0 ) -du/[1+(cotu)^a]
=∫(0->π/2) du/[1+(cotu)^a]
=∫(0->π/2) dx/[1+(cotx)^a]
2I
=∫(0->π/2) dx/慎含[1+(tanx)^a] +∫(0->π/2) dx/[1+(cotx)^a]
=∫(0->π/2) [1+(cotx)^a +1+(tanx)^a ]/宽首笑{ [1+(tanx)^a].[1+(cotx)^a] } dx
=∫(0->π/2) [2+(cotx)^a +(tanx)^a ]/[2+(tanx)^a+(cotx)^a] dx
=∫(0->π/2) dx
=π/2
I =π/4
=>∫芹腊(0->π/2) dx/[1+(tanx)^a] =π/4