第1个回答 2019-10-20
sint +cost = 根号2 sin(t+pi/4)，然后用s=t+pi/4做变量替换，在对csc s进行积分即可本回答被网友采纳
第2个回答 2019-12-31
∫(0->π/2) dx/(sinx+cosx)
=(1/√2)∫(0->π/2) dx/sin(x+π/4)
=(1/√2)[ ln|csc(x+π/4) -cot(x+π/4)| ]|(0->π/2)
=(1/√2)[ ln(√2 +1) - ln(√2-1) ]
=(1/√2)∫(0->π/2) dx/sin(x+π/4)
=(1/√2)[ ln|csc(x+π/4) -cot(x+π/4)| ]|(0->π/2)
=(1/√2)[ ln(√2 +1) - ln(√2-1) ]
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