求下列不定积分:∫[(x2+1)/(x2-1)]dx.
∫[(x2+1)/(x2-1)]dx=∫[(x2-1+2)/(x2-1)]dx=∫[1+2/(x2-1)]dx=x+∫[(x+1)-(x-1)/(x-1)(x+1)]dx.=x+∫[(1/(x-1)-1/(x+1)]dx=x+ln|x-1/x+1|+c
求下列不定积分:∫[(x2+1)/(x2-1)]dx.
∫[(x2+1)/(x2-1)]dx=∫[(x2-1+2)/(x2-1)]dx=∫[1+2/(x2-1)]dx=x+∫[(x+1)-(x-1)/(x-1)(x+1)]dx.=x+∫[(1/(x-1)-1/(x+1)]dx=x+ln|x-1/x+1|+c