令x-1=tdx=dt∫2 0 f(x-1)dx=∫1 -1 f(t)dt=∫0 -1 f(t)dt + ∫1 0 f(t)dt=∫0 -1 dt/(1+e^t) + ∫1 0 dt/(1+t)=[t-ln(1+e^t)]0 -1 + [ln(1+x)]1 0=1+ln(1+1/e)+ln2=1+ln(2+2/e)
