令x=tant/2,则dx=sec^2t/2dt,t=arctan2x∫x+2／√2x+1•dx=∫(tan/2+2)／sect*sec^2t/2dt=1/2∫sect(tant/2+2)dt=1/4∫secttantdt+∫sectdt=1/4sect+lnsect+tant+c=1/4sec(arctan2x)+ln |sec(arctan2x)+2x|+c...