求解一道大一的高数题.

转证：(1+x)*[ln(1+x)] >= arctanx,f(x) = (1+x)*[ln(1+x)] - arctanx,f(0) = 0,f'(x) = ln(1+x) +1 - 1/(1+x*x) = ln(1+x) +(x*x)/(1+x*x) >0,so f(x)严格单调递增,f(x)>=f(0),so (1+x)*[ln(1+x)] - arctanx>=0,so (1+x)*[ln(1+x)] >=arctanx,so ln(1+x) >=arctanx/(1+x)