>>882

∫cosx log(cosx) dx = ∫(sinx)' log(cosx) dx
= sinx log(cosx) - ∫sinx (-sinx/cosx) dx
= sinx log(cosx) - sinx + ∫(1/cosx)dx
= sinx log(cosx) - sinx + ∫{(1+t^2)/(1-t^2)}{2dt/(1+t^2)} ; tan(x/2)=t　と置くと、cosx=(1-t^2)/(1+t^2),dx=2dt/(1+t^2)
= sinx log(cosx) - sinx + ∫2dt/(1-t^2)
= sinx log(cosx) - sinx + log|(t+1)/(t-1)|
= sinx log(cosx) - sinx + log|(tan(x/2)+1)/(tan(x/2)-1)|

与式 = (√2/2)(log(√2/2)-1) + log|{tan(π/8)+1}/{tan(π/8)-1}| = -0.07079773...