∫(0,π)[sinx/(1+cos²x)]dx
=-∫(0,π)d(cosx)/(1+cos²x)
=-arctancosx|(0,π)
=-arctancosπ-(-arctancos0)
=-arctan(-1)-(-arctan1)
=-arctan(-1)+arctan1
=-(-π/4)+π/4
=π/2
∫(0,π)[sinx/(1+cos²x)]dx
=-∫(0,π)d(cosx)/(1+cos²x)
=-arctancosx|(0,π)
=-arctancosπ-(-arctancos0)
=-arctan(-1)-(-arctan1)
=-arctan(-1)+arctan1
=-(-π/4)+π/4
=π/2