Question

常用万能代换公式求积分公式是那些啊 求大神指点

高数 积分

Answer 1

(1)
∫ dx/(1+tanx)
=∫ cosx/(cosx+sinx) dx
=(1/2)∫ [(cosx+sinx)+ (-sinx+cosx) ]/(cosx+sinx) dx
=(1/2)[ x + ln|cosx+sinx| ] +C
(2)
∫ dx/(1+cosx)
=(1/2)∫ dx/[(1+cosx)/2]
=(1/2)∫ dx/[cos(x/2)]^2
=(1/2)∫ [sec(x/2)]^2 dx
=tan(x/2) + C
(3)
∫ dx/(sinx+cosx)
=∫ dx/[√2.sin(x+π/4)]

=(1/√2) ∫ csc(x+π/4) dx
=(1/√2) ln|csc(x+π/4) -cot(x+π/4) | + C
(4 )
∫ (2sinx+cosx)/(sinx-cosx) dx
=(1/2) ∫ [( sinx-cosx )+3( cosx +sinx) ]/(sinx-cosx) dx
=(1/2)[ x +3ln|sinx-cosx|] + C

追问

我意思是万能代换公式是啥