Simone
∫ ln(t+1)/t dt=-∫ ln(t+1) d(1/t^2)=-(1/t^2).ln(t+1)+ ∫灶野谈 dt/[t^2.(t+1) ]=-(1/t^2).ln(t+1) -ln|t| -1/t +ln|t+1| + Clet1/脊皮[t^2.(t+1) ]≡ A/t +B/t^2 +C/(t+1)=>1≡ At(t+1) +B(t+1) +Ct^2t=0, => B=1t=-1, =>C=1coef. of t^2A+C =0A= -11/[t^2.(t+1) ]≡ -1/t +1/t^2 +1/(t+1)∫ dt/[t^2.(t+1) ]= ∫隐碰 [-1/t +1/t^2 +1/(t+1)] dt=-ln|t| -1/t +ln|t+1| + C'
