求∫sinx/(sinx-cosx)dx．

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问题求∫sinx/(sinx-cosx)dx．

选项

答案∫sinx/(sinx-cosx)dx=1/2∫sin[(x-π/4)+π/4]/sin(x-π/4)dx=1/2∫[sin(x-π/4)+cos(x-π/4)]/sin(x-π/4)dx=x/2+1/2ln｜sin(x-π/4)｜+C．

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考研数学二

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