Question

用万能公式解cost/(sint+cost)的不定积分

Answer 1

干嘛非用万能公式不可
cost=1/2[(sint+cost)+(cost-sint)]
∫cost/(sint+cost)dt
=1/2∫[1+(cost-sint)/(sint+cost)]dt
=1/2[t+ln|sint+cost|]+C

Answer 2

let
cost = k1.(sint+cost)+ k2.(cost -sint)
=>
k1-k2=0 (1)
k1+k2 =1 (2)
得出 k1=k2=1/2
∫ cost/(sint+cost) dt

=(1/2)∫ [ 1+ (cost+sint)/(sint+cost)] dt
=(1/2)[ t+ ln|sint+cost|] + C