∫f(x)lnxdx=arctanx+c 等式左右对x求导,则 f(x)lnx=1/(x^2+1) 1/f(x)=lnx(x^2+1) ∫dx/f(x)=∫lnx(x^2+1)dx=lnx[(x^3/3)+x)]-∫[1+1/(3x^2)]dx=lnx[(x^3/3)+x)]-(x^3/9)-x 代入上下限,得 ∫dx/f(x)=(14/3)ln2-16/9
