符号错了，sinx =d (－cosx)那里你好好检查一下
∫(0->π/4) sinx/(1+sinx) dx
=∫(0->π/4) sinx.(1-sinx)/(cosx)^2 dx
=∫(0->π/4) [sinx - (sinx)^2]/(cosx)^2 dx
=∫(0->π/4) [sinx - 1+(cosx)^2]/(cosx)^2 dx
=∫(0->π/4) sinx/(cosx)^2 dx - ∫(0->π/4) (secx)^2 dx +∫(0->π/4) dx
=-∫(0->π/4) dcosx/(cosx)^2 - [tanx]|(0->π/4) + [x]|(0->π/4)
=[1/cosx]|(0->π/4) - ( 1-0) +(π/4-0)
=(√2 -1) -1 +π/4
=√2 -2 +π/4
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