大神们，这个题怎么做，小弟跪谢了，急急急

let
cosx ≡ k1.(cosx-sinx) +k2.(-sinx-cosx)
=>
k1-k2=1 (1) and
-k1-k2=0 (2)
(1)+(2)
-2k2=1
k2=-1/2
from (1) => k1=1/2
ie
cosx ≡ (1/2)[(cosx-sinx) -(-sinx-cosx)]
∫(0->π/6) cosx/(cosx-sinx) dx
=(1/2)∫(0->π/6) [(cosx-sinx) -(-sinx-cosx)]/(cosx-sinx) dx
=(1/2)∫(0->π/6) [1-(-sinx-cosx)/(cosx-sinx)] dx
=(1/2)[x -ln|cosx-sinx|]|(0->π/6)
=(1/2)(π/6 -ln|√3/2 -1/2| )
=(1/2)(π/6 -ln(√3-1) +ln2 )